problems in the world that aren't solved

Nine world issues that are still going on, but we forgot to care about

AS THE world turns its attention to Islamic State and the ongoing threat of terrorism, it seems we’ve left behind other world problems. Here’s a refresher.

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WE ARE perpetually inundated with information in this day and age.

With the combination of smart phones, social media and the 24/7 news cycle, it swirls around us constantly.

This instant gratification has debilitated our attention span and capacity for critical thinking.

Most issues or global crises seemingly get about two weeks of consideration before we lose interest. If an issue or crisis hasn’t been solved, and we don’t perceive it as impacting our daily lives, we move on to the next big thing.

Recently, we have granted much of our attention to ISIS, the spread of Ebola, Ferguson and now the protests in Hong Kong, among other issues. All of these topics certainly merit attention. However, there are many issues that were at one point the centre of our attention, but have now been pushed to the edges of our consciousnesses.

It’s true that there are still people actively addressing many of these problems, but the majority of us typically grant our attention to whatever is directly in front of us. If it’s not in our yard, or if it’s not on our newsfeed, we probably forgot about it or aren’t aware at all. Don’t be fooled into thinking that something isn’t important because it’s not trending on Facebook or Twitter.

These are just a few ongoing problems that we have largely forgot about over the past year or so, in no particular order:

ISIS and Ebola might seem like the most pressing issues in the world at the moment. Yet, for billions of people across the globe, poverty is far more threatening. Indeed, more than 1 billion people live on less than one dollar a day.

RELATED: NAURU’S DOWNFALL FROM RICH NATION TO POVERTY

Likewise, there are around 780 million people without access to clean water, and around 2.5 billion without basic sanitation. In some places, people have to walk a kilometre or more just to get water.

Tragically, a child under 5 will die every 21 seconds from a preventable water-related disease. These are diseases that were eradicated in developed countries over a century ago, but still claim millions of lives in the present-day. What’s more, there are viable solutions to this problem.

In addition to water, more than 800 million people (more than twice the population of the United States) go to bed without food every single day — 300 million are children. Every 3.6 seconds, someone in the world will die from hunger.

2. HIV/AIDS

Today, close to 33.4 million people are living with HIV/AIDs. Since 1981, when the first cases were reported, more than 25 million people have died from HIV/AIDs, and there is still no cure.

RELATED: AIDS CONFERENCE 2014 GOES ON DESPITE LOSSES

In 2012 alone, over one million people worldwide died from AIDS-related illnesses.

The vast majority of people living with HIV, close to 97 per cent, live in low and middle-income countries. Most of these people reside in sub-Saharan Africa. Hence, poverty plays a huge role in the spread of this lethal virus.

3. SLAVERY/HUMAN TRAFFICKING

At present, nearly 21 million people are working as modern day slaves as a consequence of human trafficking.

RELATED: AUSTRALIAN FINDS LETTER FROM CHINA PRISON FACTORY

Indeed, human trafficking is one of the most profitable businesses in the world. Global profits per victim per year are around $21,800, coming out to around $150 billion in total profits.

In the United States, it is estimated that around 100,000 children are trafficked for sexual exploitation every year. This is not only a problem in impoverished countries, it’s worldwide.

4. GUANTÁNAMO BAY

The Guantanamo Bay detention centre, also known as Gitmo, will forever stand as a black mark on the history of the United States. Following 9/11, the United States has detained hundreds of individuals at Gitmo without charge or criminal trial.

RELATED: GITMO PRISONER ARRESTED OVER SYRIA TERROR LINKS

Since the first detainees were sent to Gitmo in 2002, reports of secret detentions, torture, unfair trials and suicides have surfaced.

Currently, there are still 149 detainees at the detention camp, despite the fact that President Obama promised to shut it down when he came into office.

A number of the remaining detainees are on hunger strike, and are controversially being force-fed, which is arguably a form of torture. There are impending hearings surrounding this issue, which the United States has attempted to keep secret.

5. CENTRAL AFRICAN REPUBLIC

Sectarian fighting has been ravaging the Central African Republic since 2012. Yet, unlike ISIS, Syria and Iraq, it has received decidedly less attention.

RELATED: WHY ‘LIFE IS CHEAP’ IN AFRICA

Many atrocities have been committed, and the conflict is ongoing. Likewise, due to the complex causes of this war, it doesn’t look as though it will stop anytime soon.

American drone strikes have killed over 2000 people, many of whom were civilians and children.

RELATED: ISLAMABAD CONDEMNS US DRONE STRIKES

This policy has generated controversy around the world, and animosity towards to the United States. Many worry that it has the potential to perpetuate, rather than end, the War on Terror.

There is very little transparency surrounding the drone program, and we don’t have a clear picture of why targets are selected and whether or not they posed an imminent threat to America. Yet, a majority of Americans still support this policy without really questioning it.

7. CALIFORNIA DROUGHT

California has been experiencing one of the worst droughts in recent memory. Some fear that entire communities could be left without water within two months.

RELATED: 25 MILLION PEOPLE AFFECTED IN CALIFORNIA DROUGHT

The drought has had a detrimental impact on California’s agriculture, which will have consequences both within the United States and around the world. California exports rice to Asia in addition to restaurants within the United States.

Stanford University scientists believe that greenhouse gases might be the cause of this drought. Accordingly, this is yet another instance of negative impact human activities have had on the environment, and the way in which climate change affects us all.

8. IRAN’S NUCLEAR PROGRAM

The situation with ISIS has led some to believe that the United States should team up with Iran. However, there are still many around the world who are concerned about Iran’s nuclear ambitions, particularly Israel.

Indeed, Iran could pose a significant threat to both the Middle East and much of the world if it developed nuclear weapons. As the fight against ISIS rages on, this issue cannot be forgot.

9. WAR ON DRUGS

The War on Drugs has been one of the most expensive failures in history. Right now, much of the focus on this issue surrounds the debate over the legalisation of marijuana.

RELATED: ‘WAR ON DRUGS’ FUELLING HIV EPIDEMIC

However, people should also consider the way in which keeping other drugs illegal fosters violence both within the United States and around the world.

Recently, global leaders met and called for the decriminalisation of drugs, in order to make this a health issue, rather than a criminal one. When one thinks about it, this is a logical approach, and one which has worked very well for Portugal.

This article is an edited version of the original which appeared in Elite Daily .

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11 epic mysteries scientists totally can’t solve

What is the universe made out of? When did the anus evolve? Can humans live to 150 years old? And more!

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To investigate some of the biggest mysteries in science, you have to venture to some pretty far-out places: the bottom of the oceans , inside the human brain , the tops of mountains , and even the end of time .

That’s what we’ve done on Unexplainable , a science podcast that Vox launched in March to explore the most important, interesting, and awe-inspiring unanswered questions in science. We set out to ask big questions that inspire scientists to do their work — questions that fill them with wonder or a sense of purpose, or remind them that the universe is still an enormous place with untapped potential.

In exploring these stories, we’ve learned some of the surprising reasons why major scientific mysteries can go unsolved for years or even decades: Some are due to the limits of technology, others are because of human failings. Regardless, working on Unexplainable has reminded us there’s hope in a question. Why ask one if you don’t believe an answer is possible?

Here, we rounded up 11 questions that astounded us the most.

For more mysteries, subscribe to Unexplainable wherever you listen to podcasts .

What is most of the universe made out of?

It’s a simple question that’s also bafflingly unanswered: What makes up the universe? It turns out all the stars in all the galaxies in all the universe barely even begin to account for all the stuff out there. Most of the matter in the universe is actually unseeable, untouchable, and, to this day, undiscovered. It’s called dark matter, and despite searching for it for decades, scientists still have no idea what it is.

Further reading: Dark Matter, unexplained

What lives in the ocean’s “twilight zone”?

As you dive deeper into the ocean, less and less sunlight shines through, and about 200 meters beneath the surface, you reach an area called the “twilight zone.” Sunlight fades almost completely out of view, and our knowledge about these dark depths fades too.

“It’s almost easier to define it by what we don’t know than what we do know,” Andone Lavery, an acoustician at the Woods Hole Oceanographic Institution, told Vox’s Byrd Pinkerton.

Yet this region of the ocean is extremely important. It’s possible — but not certain — that there are more fish living in the twilight zone than the rest of the ocean combined, and creatures of the dark ocean play a large role in regulating the climate.

Further reading: “It’s deep. It’s dark. It’s elusive.” The ocean’s twilight zone is full of wonders.

What killed Venus?

“Hellscape” is the most appropriate word to describe the surface of Venus, the second planet from the sun. At 900 degrees Fahrenheit, it’s the hottest planet in the solar system, thanks in part to an atmosphere of almost entirely carbon dioxide. Clouds of highly corrosive sulfuric acid are draped over a volcanic landscape of razor-sharp lava flows. Most crushingly, the pressure on the surface of Venus is about 92 times the pressure you’d feel at sea level on Earth.

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Unexplainable  is a weekly science podcast about everything we don’t know. For stories about great scientific mysteries,  follow us wherever you listen to podcasts .

Yet some scientists suspect Venus was once much like Earth, with a liquid water ocean like the ones that support life on our planet. This prompts an existential question for life on Earth. “It really is a question about why are we here,” says Robin George Andrews, volcanologist and author of Super Volcanoes: What They Reveal about Earth and the Worlds Beyond .

“Venus and Earth are planetary siblings,” Andrews says. “They were made at the same time and made of the same stuff, yet Venus is apocalyptic and awful in every possible way. Earth is a paradise. So why do we have a paradise next to a paradise lost?”

There are two leading hypotheses. One is that the sun cooked Venus to death. The other is that volcanoes did.

Further reading: Venus could have been a paradise but turned into a hellscape. Earthlings, pay attention.

What will animals look like in the future?

It’s impossible to completely predict how evolution will play out in the future, but that doesn’t mean we can’t try. Reporter Mandy Nguyen asked biologists and other experts to weigh in: What could animals look like a million years from now?

The experts took the question seriously. “I do think it’s a really useful and important exercise,” Liz Alter, professor of evolutionary biology at California State University Monterey Bay, told Nguyen. In thinking about the forces that will shape the future of life on Earth, we need to think about how humans are changing environments right now.

Further reading: The animals that may exist in a million years, imagined by biologists

What causes Alzheimer’s?

There is no cure for Alzheimer’s, a neurodegenerative disease that causes dementia, and no highly effective treatments, despite decades of research. Why? For one thing, scientists don’t have a complete understanding of what causes the disease.

For years, the prevailing theory has been that Alzheimer’s is caused by pile-ups of proteins called amyloids, which effectively create plaques in the brain. But drugs that help clear amyloids from the brain don’t seem to work very well in combating the disease.

Some scientists think Alzheimer’s researchers have been too focused on this one theory, at the expense of studying other potential causes, like viral infections.

Further reading: The new Alzheimer’s drug that could break Medicare

How is a brainless yellow goo known as “slime mold” so smart?

Slime mold is an extremely simple organism that is also extraordinarily complex.

Technically, they are single-celled organisms. But many individual slime mold cells can fuse themselves together into a huge mass, capable of, well ... thinking.

Slime mold can solve mazes and seems to be able to make risk-benefit decisions. There’s even evidence that slime mold can keep track of time . They do this all without a brain or even a single brain cell. Whatever mechanism allows slime mold to solve these problems, it’s evolved in a manner different from humans. How exactly do they do this? And what can it teach us about the nature of intelligence?

Further reading: Hampshire College promoted a brainless slime mold to its faculty. And it’s working on border policy.

What’s the oldest possible age a human can reach?

Is the first human to live to 150 years old alive today? We don’t know. On average, the human lifespan has risen over the decades in most of the world, but it’s unclear if there’s a ceiling. Could a human live into their second century? The technology and medicine that could make that possible may already be in development. But if it works, there will be unsettling questions for societies to answer.

Further reading: Science reporter Ferris Jabr’s piece “ How Long Can We Live? ” for the New York Times Magazine inspired this episode.

Are long-haul symptoms unique to Covid-19?

Millions of people around the world have dealt with long-term symptoms of Covid-19 for weeks or months after their initial infection has cleared. Some scientists say these “long-haul” symptoms are not unique to Covid. Instead, they argue that many types of viral infections can leave people with long-term symptoms, which often can go under-recognized in medicine. The question is: What connects all of these long-haul symptoms?

“It has always been [and] is the case that patients who get sick experience high levels of symptoms like those described by long-Covid patients,” Megan Hosey, assistant professor at the Johns Hopkins Department of Physical Medicine and Rehabilitation, told Vox’s Julia Belluz . “We have just done a terrible job of acknowledging [and] treating them.”

Further reading: The nagging symptoms long-haulers experience reveal a frustrating blind spot in medicine.

Why don’t doctors know more about endometriosis?

In people with endometriosis, tissue similar to what grows inside the uterus grows elsewhere in the body. It’s a chronic condition that can be debilitatingly painful. Yet doctors don’t fully understand what causes it, and treatment options are limited.

Worse, many people with endometriosis find that doctors can be dismissive of their concerns. It can take years to get an accurate diagnosis, and research into the condition has been poorly funded.

Vox reporter Byrd Pinkerton highlighted how frustrating it can be to suffer from an often-ignored, chronic condition. “It’s just so, so, so soul-crushing to just live in this body day in and day out,” one patient told Pinkerton.

Further reading: People with endometriosis experience terrible pain. There’s finally a new treatment.

Why do we have anuses — or butts, for that matter?

This is a question we never even knew we wanted to answer — until we heard the Atlantic’s Katherine Wu explain that “the appearance of the anus was momentous in animal evolution.” Before the appearance of the anus, animals had to eat and excrete through the same hole. The anus allowed for a more efficient system, and allowed animal life on Earth to grow bigger and take on new shapes and forms.

But scientists don’t have a complete picture of the evolutionary history here; they don’t know which creature developed the anus first, and when. “It’s so hard to study something that must be millions and millions of years old and doesn’t fossilize,” Wu says.

And then there’s a whole other question: Why is the human butt so big, compared with other mammals?

Further reading: Katherine Wu’s “ The Body’s Most Embarrassing Organ Is an Evolutionary Marvel ,” at the Atlantic.

What the heck is ball lightning?

For millennia, people have been telling stories about mysterious spheres of light that glow, crackle, and hover eerily during thunderstorms. They’ve been spotted in homes, in rural areas, in cities, on airplanes , and even passing through windows .

They seem out of this world, but scientists believe they are very much of this world. These apparitions are called ball lightning, and they remain one of the most mysterious weather phenomena on Earth.

Ball lightning usually only lasts for a few moments, and it’s impossible to predict where and when it’ll show up. You can’t hunt ball lightning and reliably find it. Ball lightning finds you.

It’s rare, but many people have seen it. Scientists don’t know exactly where it comes from, but that hasn’t stopped them from trying to make it themselves, in their labs.

Further reading: Ball lightning is real, and very rare. This is what it’s like to experience it.

And so many more...

Those are just 11 of the mysteries we’ve explored in Unexplainable . There are so many more ! They include questions like: Can we predict when tornadoes will form? Where does all the plastic go in the ocean? Why do some people think they can talk to the dead? What’s the deal with “Havana syndrome”? How will the universe end? How tall is Mount Everest? Why does the placebo effect work? Find all the episodes here .

If you have ideas for topics for future shows, send us an email at [email protected].

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10 Hard Math Problems That Continue to Stump Even the Brightest Minds

Maybe you’ll have better luck.

For now, you can take a crack at the hardest math problems known to man, woman, and machine. ✅ More from Popular Mechanics :

• Euler’s Number Is Seriously Everywhere. Here’s What Makes It So Special
• Fourier Transforms: The Math That Made Color TV Possible
• The Game of Trees is a Mad Math Theory That Is Impossible to Prove

The Collatz Conjecture

In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is promising, the problem isn’t fully solved yet.

A refresher on the Collatz Conjecture : It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity).

✅ Down the Rabbit Hole: The Math That Helps the James Webb Space Telescope Sit Steady in Space

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But he most likely can’t adapt his methods to yield a complete solution to the problem, as Tao subsequently explained. So, we might be working on it for decades longer.

The Conjecture lives in the math discipline known as Dynamical Systems , or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed onto much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.

Goldbach’s Conjecture

One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes.” You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19. Computers have checked the Conjecture for numbers up to some magnitude. But we need proof for all natural numbers.

Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler , considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”

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Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.

Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.

The Twin Prime Conjecture

Together with Goldbach’s, the Twin Prime Conjecture is the most famous in Number Theory—or the study of natural numbers and their properties, frequently involving prime numbers. Since you've known these numbers since grade school, stating the conjectures is easy.

When two primes have a difference of 2, they’re called twin primes. So 11 and 13 are twin primes, as are 599 and 601. Now, it's a Day 1 Number Theory fact that there are infinitely many prime numbers. So, are there infinitely many twin primes? The Twin Prime Conjecture says yes.

Let’s go a bit deeper. The first in a pair of twin primes is, with one exception, always 1 less than a multiple of 6. And so the second twin prime is always 1 more than a multiple of 6. You can understand why, if you’re ready to follow a bit of heady Number Theory.

✅ Keep Learning: If We Draw Graphs Like This, We Can Change Computers Forever

All primes after 2 are odd. Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. Well, one of those three possibilities for odd numbers causes an issue. If a number is 3 more than a multiple of 6, then it has a factor of 3. Having a factor of 3 means a number isn’t prime (with the sole exception of 3 itself). And that's why every third odd number can't be prime.

How’s your head after that paragraph? Now imagine the headaches of everyone who has tried to solve this problem in the last 170 years.

The good news is that we’ve made some promising progress in the last decade. Mathematicians have managed to tackle closer and closer versions of the Twin Prime Conjecture. This was their idea: Trouble proving there are infinitely many primes with a difference of 2? How about proving there are infinitely many primes with a difference of 70,000,000? That was cleverly proven in 2013 by Yitang Zhang at the University of New Hampshire.

For the last six years, mathematicians have been improving that number in Zhang’s proof, from millions down to hundreds. Taking it down all the way to 2 will be the solution to the Twin Prime Conjecture. The closest we’ve come —given some subtle technical assumptions—is 6. Time will tell if the last step from 6 to 2 is right around the corner, or if that last part will challenge mathematicians for decades longer.

The Riemann Hypothesis

Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize Problems , with $1 million reward for its solution. It has implications deep into various branches of math, but it’s also simple enough that we can explain the basic idea right here.

There is a function, called the Riemann zeta function, written in the image above.

For each s, this function gives an infinite sum, which takes some basic calculus to approach for even the simplest values of s. For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using the imaginary number 𝑖—finding 𝜁(s) gets tricky.

So tricky, in fact, that it’s become the ultimate math question. Specifically, the Riemann Hypothesis is about when 𝜁(s)=0; the official statement is, “Every nontrivial zero of the Riemann zeta function has real part 1/2.” On the plane of complex numbers, this means the function has a certain behavior along a special vertical line. The hypothesis is that the behavior continues along that line infinitely.

✅ Stay Curious: How to Paint a Room Using Math

The Hypothesis and the zeta function come from German mathematician Bernhard Riemann, who described them in 1859. Riemann developed them while studying prime numbers and their distribution. Our understanding of prime numbers has flourished in the 160 years since, and Riemann would never have imagined the power of supercomputers. But lacking a solution to the Riemann Hypothesis is a major setback.

If the Riemann Hypothesis were solved tomorrow, it would unlock an avalanche of further progress. It would be huge news throughout the subjects of Number Theory and Analysis. Until then, the Riemann Hypothesis remains one of the largest dams to the river of math research.

The Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer Conjecture is another of the six unsolved Millennium Prize Problems, and it’s the only other one we can remotely describe in plain English. This Conjecture involves the math topic known as Elliptic Curves.

When we recently wrote about the toughest math problems that have been solved , we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir Andrew Wiles solved it using Elliptic Curves. So, you could call this a very powerful new branch of math.

✅ The Latest: Mathematicians Discovered Something Mind-Blowing About the Number 15

In a nutshell, an elliptic curve is a special kind of function. They take the unthreatening-looking form y²=x³+ax+b. It turns out functions like this have certain properties that cast insight into math topics like Algebra and Number Theory.

British mathematicians Bryan Birch and Peter Swinnerton-Dyer developed their conjecture in the 1960s. Its exact statement is very technical, and has evolved over the years. One of the main stewards of this evolution has been none other than Wiles. To see its current status and complexity, check out this famous update by Wells in 2006.

The Kissing Number Problem

A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to the idea of stacking many spheres in a given space, like fruit at the grocery store. Some questions in this study have full solutions, while some simple ones leave us stumped, like the Kissing Number Problem.

When a bunch of spheres are packed in some region, each sphere has a Kissing Number, which is the number of other spheres it’s touching; if you’re touching 6 neighboring spheres, then your kissing number is 6. Nothing tricky. A packed bunch of spheres will have an average kissing number, which helps mathematically describe the situation. But a basic question about the kissing number stands unanswered.

✅ Miracles Happen: Mathematicians Finally Make a Breakthrough on the Ramsey Number

First, a note on dimensions. Dimensions have a specific meaning in math: they’re independent coordinate axes. The x-axis and y-axis show the two dimensions of a coordinate plane. When a character in a sci-fi show says they’re going to a different dimension, that doesn’t make mathematical sense. You can’t go to the x-axis.

A 1-dimensional thing is a line, and 2-dimensional thing is a plane. For these low numbers, mathematicians have proven the maximum possible kissing number for spheres of that many dimensions. It’s 2 when you’re on a 1-D line—one sphere to your left and the other to your right. There’s proof of an exact number for 3 dimensions, although that took until the 1950s.

Beyond 3 dimensions, the Kissing Problem is mostly unsolved. Mathematicians have slowly whittled the possibilities to fairly narrow ranges for up to 24 dimensions, with a few exactly known, as you can see on this chart . For larger numbers, or a general form, the problem is wide open. There are several hurdles to a full solution, including computational limitations. So expect incremental progress on this problem for years to come.

The Unknotting Problem

The simplest version of the Unknotting Problem has been solved, so there’s already some success with this story. Solving the full version of the problem will be an even bigger triumph.

You probably haven’t heard of the math subject Knot Theory . It ’s taught in virtually no high schools, and few colleges. The idea is to try and apply formal math ideas, like proofs, to knots, like … well, what you tie your shoes with.

For example, you might know how to tie a “square knot” and a “granny knot.” They have the same steps except that one twist is reversed from the square knot to the granny knot. But can you prove that those knots are different? Well, knot theorists can.

✅ Up Next: The Amazing Math Inside the Rubik’s Cube

Knot theorists’ holy grail problem was an algorithm to identify if some tangled mess is truly knotted, or if it can be disentangled to nothing. The cool news is that this has been accomplished! Several computer algorithms for this have been written in the last 20 years, and some of them even animate the process .

But the Unknotting Problem remains computational. In technical terms, it’s known that the Unknotting Problem is in NP, while we don ’ t know if it’s in P. That roughly means that we know our algorithms are capable of unknotting knots of any complexity, but that as they get more complicated, it starts to take an impossibly long time. For now.

If someone comes up with an algorithm that can unknot any knot in what’s called polynomial time, that will put the Unknotting Problem fully to rest. On the flip side, someone could prove that isn’t possible, and that the Unknotting Problem’s computational intensity is unavoidably profound. Eventually, we’ll find out.

The Large Cardinal Project

If you’ve never heard of Large Cardinals , get ready to learn. In the late 19th century, a German mathematician named Georg Cantor figured out that infinity comes in different sizes. Some infinite sets truly have more elements than others in a deep mathematical way, and Cantor proved it.

There is the first infinite size, the smallest infinity , which gets denoted ℵ₀. That’s a Hebrew letter aleph; it reads as “aleph-zero.” It’s the size of the set of natural numbers, so that gets written |ℕ|=ℵ₀.

Next, some common sets are larger than size ℵ₀. The major example Cantor proved is that the set of real numbers is bigger, written |ℝ|>ℵ₀. But the reals aren’t that big; we’re just getting started on the infinite sizes.

✅ More Mind-Blowing Stuff: Mathematicians Discovered a New 13-Sided Shape That Can Do Remarkable Things

For the really big stuff, mathematicians keep discovering larger and larger sizes, or what we call Large Cardinals. It’s a process of pure math that goes like this: Someone says, “I thought of a definition for a cardinal, and I can prove this cardinal is bigger than all the known cardinals.” Then, if their proof is good, that’s the new largest known cardinal. Until someone else comes up with a larger one.

Throughout the 20th century, the frontier of known large cardinals was steadily pushed forward. There’s now even a beautiful wiki of known large cardinals , named in honor of Cantor. So, will this ever end? The answer is broadly yes, although it gets very complicated.

In some senses, the top of the large cardinal hierarchy is in sight. Some theorems have been proven, which impose a sort of ceiling on the possibilities for large cardinals. But many open questions remain, and new cardinals have been nailed down as recently as 2019. It’s very possible we will be discovering more for decades to come. Hopefully we’ll eventually have a comprehensive list of all large cardinals.

What’s the Deal with 𝜋+e?

Given everything we know about two of math’s most famous constants, 𝜋 and e , it’s a bit surprising how lost we are when they’re added together.

This mystery is all about algebraic real numbers . The definition: A real number is algebraic if it’s the root of some polynomial with integer coefficients. For example, x²-6 is a polynomial with integer coefficients, since 1 and -6 are integers. The roots of x²-6=0 are x=√6 and x=-√6, so that means √6 and -√6 are algebraic numbers.

✅ Try It Yourself: Can You Solve This Viral Brain Teaser From TikTok?

All rational numbers, and roots of rational numbers, are algebraic. So it might feel like “most” real numbers are algebraic. Turns out, it’s actually the opposite. The antonym to algebraic is transcendental, and it turns out almost all real numbers are transcendental—for certain mathematical meanings of “almost all.” So who’s algebraic , and who’s transcendental?

The real number 𝜋 goes back to ancient math, while the number e has been around since the 17th century. You’ve probably heard of both, and you’d think we know the answer to every basic question to be asked about them, right?

Well, we do know that both 𝜋 and e are transcendental. But somehow it’s unknown whether 𝜋+e is algebraic or transcendental. Similarly, we don’t know about 𝜋e, 𝜋/e, and other simple combinations of them. So there are incredibly basic questions about numbers we’ve known for millennia that still remain mysterious.

Is 𝛾 Rational?

Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers.

Rational numbers can be written in the form p/q, where p and q are integers. So, 42 and -11/3 are rational, while 𝜋 and √2 are not. It’s a very basic property, so you’d think we can easily tell when a number is rational or not, right?

Meet the Euler-Mascheroni constant 𝛾, which is a lowercase Greek gamma. It’s a real number, approximately 0.5772, with a closed form that’s not terribly ugly; it looks like the image above.

✅ One More Thing: Teens Have Proven the Pythagorean Theorem With Trigonometry. That Should Be Impossible

The sleek way of putting words to those symbols is “gamma is the limit of the difference of the harmonic series and the natural log.” So, it’s a combination of two very well-understood mathematical objects. It has other neat closed forms, and appears in hundreds of formulas.

But somehow, we don’t even know if 𝛾 is rational. We’ve calculated it to half a trillion digits, yet nobody can prove if it’s rational or not. The popular prediction is that 𝛾 is irrational. Along with our previous example 𝜋+e, we have another question of a simple property for a well-known number, and we can’t even answer it.

Dave Linkletter is a Ph.D. candidate in Pure Mathematics at the University of Nevada, Las Vegas. His research is in Large Cardinal Set Theory. He also teaches undergrad classes, and enjoys breaking down popular math topics for wide audiences.

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5 Global Crises the world can't ignore in 2021

In some of the world’s most dangerous and complex places, COVID-19 has reversed decades of progress, with the  aftershocks  of the pandemic threatening more children’s lives than the virus itself .  COVID-19 magnified the effects of poverty - as conflict, political unrest, food insecurity and violence made children and families increasingly vulnerable. These are five crises the world can’t ignore in 2020.  

1. Food Insecurity

Food is more than a meal. it’s survival. .

If hunger does not kill a child, severe acute malnutrition at an early age can cause lifelong physical and mental damage. The world is not on track to achieve the targets it has set itself to improve nutrition by 2030 with 50.5 million children under five acutely malnourished.  

These children are concentrated in some of the most dangerous places in the world, with conflict and war largely contributing to hunger . In 2021, the effects of the global pandemic, ongoing conflict, and climate change are steadily increasing food insecurity for families and children.  

2. Refugees 

In 2021, more children will be on the move than ever before in history.  .

Last year more than 80 million people around the world were forced to flee their homes , around half of whom are under the age of 18. Violence and conflict are the main reasons people flee.

Families risk everything, undertaking long and dangerous journeys in the hope of finding safety and stability. By far the most affected group are children, who are often separated from their parents, lose access to education and healthcare, and become victims of early marriage and child labour.

3. Climate Change  

The weather on our planet is becoming more extreme, with direct impacts on the poorest and most vulnerable children. Parents struggle to feed their children when rains are late or non-existent. On the other end of this scale are deadly floods and landslides that destroy crops and communities, and become a breeding ground for disease.

Increasingly, severe droughts and floods drive rural families to new towns, cities, and countries which can trigger tension and conflict with host communities. 

Climate change is affecting the future of the most vulnerable children. With millions of families rely on farming for their families and an income, no income means no money for school fees, health, rent or stability.  

4. Child Marriage/Gender Discrimination 

COVID-19 has created a crisis for girls around the world. As vulnerable families lose their incomes, girls are being sold into child marriage just to make ends meet. We believe that as many as 13 million extra child marriages will occur in the years immediately following the pandemic, with at least four million more girls married in the next two years.  

The global pandemic has also created an education disaster for vulnerable girls. COVID-19 lockdowns, meant to keep children and families safe from the pandemic, have seen teen pregnancy rates spike. In sub-Saharan Africa where as many as one million girls may be blocked from returning to school due to becoming pregnant during COVID-19 school closures, 17-year-old Efua's* community in Ghana has seen a 9-fold increase in teen pregnancies. Child marriages and teen pregnancies exacerbate the cycle of poverty for girls growing up in the toughest places to be a child. 

5. Child Labour and Trafficking

The number of children experiencing physical, emotional and sexual violence, both now and in the months and years to come is set to rise.   As COVID-19 puts strain on family incomes, children are being forced to beg in the streets, or sent to work instead of going school just to help their families get by. 

In Asia alone, as many as 8 million children are being forced into begging and child labour  because parents cannot afford to buy enough food. 

At World Vision, we have been walking alongside vulnerable children, their families and communities for more than 70 years. The issues may change overtime, but we remain committed to helping all children experience fullness of life.

Top 20 Current Global Issues We Must Address

What are the most pressing issues in the world today? What will demand the most attention in the next 5, 10, and 20+ years? In this article, which frequently refers to the World Economic Forum’s 17th Edition of the Global Risks Report, we’ll highlight 20 current global issues we must address, including issues related to climate change, COVID-19, social rights, and more. While it’s hardly a comprehensive discussion, it’s a solid introduction to the kinds of concerns facing our world today.

#1. Poverty

In fall 2022, the World Bank will update the International Poverty Line from $1.90 to $2.15. This means anyone living on less than $2.15 is in “extreme poverty.” Why the change? Increases in the costs of food, clothing, and shelter between 2011-2017 make the “real value of $2.15 in 2017 prices equal to $1.90 in 2011 prices. As for the World Bank’s goal to reduce extreme poverty to 3% or less by 2030, the pandemic has made it even harder. Extreme poverty isn’t the only poverty we have to contend with. 62% of the global population lives on less than $10/day. While there’s been progress over the years, the end of poverty is still far off.

Learn more about tackling poverty with an online course: Poverty & Population: How Demographics Shape Policy (Columbia University)

#2. Climate change

The IPCC released its sixth report in 2022. In its summary for policy-makers, the report’s authors outlined a series of near-term, mid-term, and long-term risks. If global warming reaches 1.5°C in the near term (2021-2040), it would cause “unavoidable increases in multiple climate hazards,” as well as “multiple risks to ecosystems and humans.” In the long term, climate change will present major health issues, premature deaths, risks to cities and settlements , and other dangers. Mitigation is desperately needed – and fast. Because of climate change ’s connection to other issues on this list, it’s one of the most serious challenges facing humanity.

Learn more about climate change with an online course: Science and Engineering of Climate Change (EDHEC Business School)

#3. Food insecurity

According to the 2022 Global Report on Food Crises , which is produced by the Global Network against Food Crises, the number of people in crisis or worse is the highest it’s been in the six years since the report has existed. Close to 193 million people were experiencing acute food insecurity in 2021, which is an increase of almost 40 million since 2020. This represents a staggering 80% increase since 2016. Causes include “economic shocks,” like an increase in global food prices. Domestic food price inflation in low-income countries also rose a lot. “Weather-related disasters” are also a big driver. For 15.7 million people in 15 countries, it was the primary driver of acute food insecurity.

Learn more about food insecurity with an online course: Feeding the World (University of Pennsylvania)

#4. Refugee rights

According to UNHCR, the war in Ukraine sparked the fastest-growing refugee crisis since WWII. Almost 6 million (as of May 10, 2022) people have fled. The UNCHR’s Refugee Brief , which compiles the week’s biggest refugee stories, has recently described situations in places like Somalia, where thousands of people were displaced due to severe drought. Between January and mid-April, more than 36,000 refugees from Nigeria, Mali, and Burkina Faso arrived in Niger. These are only a few examples of the refugee crises, which endangers already marginalized groups – like women and children – and puts them at an increased risk of trafficking , violence, and death.

Learn more about refugee rights with an online course: Refugees in the 21st Century (University of London)

#5. COVID-19

The WHO declared COVID-19 a pandemic in March 2022. It will continue to be a major issue for the world. The WEF’s Global Risks Report 2022 discusses COVID’s effects at length , including major economic recovery disparities and social erosion. According to a January 2022 article from NPR , there are also issues with vaccinations as many countries continue to have trouble getting doses. Distribution, vaccine hesitancy, healthcare systems, and other problems also factor into low vaccination rates. While we may never know the exact impact, the WHO estimates that between 1 January 2020 and 31 December 2021, there were around 14.9 million excess deaths linked to COVID-19.

Learn more about the impact of COVID-19 with an online course: Life After COVID-19: Get Ready for our Post-Pandemic Future (Institute for the Future)

#6. Future pandemic preparation and response

COVID-19 taught the world the importance of prepardeness. In a Harvard blog , Dr. Tedros Adhanom Ghebreyesus, director-general of the WHO, outlined the lessons the world should take to heart. The first: science has to guide policy. The politicization of the pandemic led to a lot of unnecessary damage. Another lesson is that science must pair with equity or it can actually make inequalities worse. This is obvious when looking at how low-income countries struggled to get the vaccines while wealthier countries stocked up. More resilient healthcare systems are also a must, as well as more coherent, global plans on how to respond. The world must also invest in research on contagious diseases, zoonotic diseases, the effectiveness of outbreak responses, and more.

Learn more about future pandemic response with an online course: Pandemic preparedness, prevention, and response (Politecnico di Milano)

#7. Healthcare

The healthcare industry has experienced major shifts due to the COVID-19 pandemic. According to the World Economic Forum, there’s been new investments and innovations, especially from the technology and telehealth sectors. In 2021, $44 billion was spent on health innovation. The world will be seeing the effects of these innovations for years to come, though equity will no doubt be a major issue. In places like the United States, the pandemic also reaffirmed how broken healthcare systems can be. In an MIT News blog , Andrea Campbell, a professor of political science, says the pandemic revealed a “dire need” for investments in public-health infrastructure, as well as a need to expand healthcare access and insurance coverage.

Learn more about health inequity issues with an online course: Addressing Racial Health Inequity in Healthcare (University of Michigan)

#8. Mental health

Globally, almost 1 billion people have some form of mental disorder. The pandemic made the world’s mental health worse. According to a scientific brief from the WHO , there’s been a 25% increase in anxiety and depression worldwide. Causes include social isolation, fear of sickness, grief, and financial anxieties. Health workers were also severely impacted, as well as young women and girls. The brief also highlights how the pandemic disrupted many mental health services, including services for substance abuse. Countries need to ensure access to mental health services as part of their COVID-19 recovery plans and beyond. It’s an economic decision, as well. The Lancet states that anxiety and depression alone cost the global economy around $1 trillion a year.

Learn more about mental health with an online course: The Science of Well-Being (Yale University)

#9. Disability rights

According to the WHO , over 1 billion people have some form of disability. Half can’t afford healthcare. They’re also more likely to live in poverty than those without a disability, have poorer health outcomes, and have less access to work and education opportunities. Human Rights Watch lists other discriminations disabled people face, such as an increased risk of violence. There’s been progress regarding disability rights, but many countries lack strong protections. The world still has a long way to go to ensure equality for those with disabilities.

Learn more about disability rights with an online courses: Disability Awareness and Support (University of Pittsburgh)

#10. LGBTQ+ rights

Members of the LGBTQ+ community face discrimination in many forms. According to Amnesty International , discrimination can target sexual orientation, gender identity, gender expression, and sex characteristics. Even in more progressive countries like the United States, people face violence and discrimination. According to the Human Rights Campaign, more than 300 anti-LGBTQ+ bills were proposed in 2022. At least a dozen states are considering legislation that forbids schools from discussing or using a curriculum that covers sexual orientation and gender identity. Considering the United States’ influence in the world, this attack on LGBTQ+ rights will likely have consequences that need to be addressed.

Learn more about LGBTQ+ issues with an online courses .

#11. Reproductive justice

Reproductive justice – which encompasses more than just abortion rights – is threatened by legislation, lack of funding, lack of education, and restricted healthcare access. In most places, wealth is a big determinant of whether a person can access reproductive services. It’s better in some places than others, but as we’ve seen with other issues on this list, even “progressive” countries like the United States are experiencing major shifts. In June 2022, the Supreme Court is expected to overrule Roe v. Wade , a milestone court case that protected a pregnant woman’s right to abortion. The impact would be immediate and will likely influence other countries.

Learn more about reproductive justice and women’s rights: International Women’s Health and Human Rights (Stanford University)

#12. Children’s rights

Children are a very vulnerable group. In 2019, around 5.2 million children under five from mostly preventable and treatable causes. 2.4 million were newborns under 28 days old. Leading causes include preterm birth complications, pneumonia, and malaria. According to UNICEF, the climate crisis also represents a severe threat to kids. Around 1 billion kids live in “extremely high-risk countries” that are hit by the worst effects of climate change. 920 kids have trouble accessing clean water and 600 million are exposed to vector-borne diseases like malaria. Child labor also remains an issue. At the beginning of 2020, around 160 million were forced into labor while COVID-19 put 9 million more kids at risk. That’s almost 1 in 10 children globally. Almost half are in dangerous environments. As is often the case, the other issues on this list – climate change, poverty, COVID, gender equality, etc – factor into children’s rights.

Learn more about children’s rights: Children’s Human Rights – An Interdisciplinary Introduction (University of Geneva)

#13. Gender equality

Global gender equality has gradually improved over the years, but data from the 2021 Global Gender Report shows that the end of the global gender gap is still 135 years away. The pandemic played a huge role in reversing positive trends as women were hit harder financially. According to Oxfam , women experienced a 5% job loss while men experienced 3.9%. That means women lost about $800 million in 2020. This is a low estimate since it doesn’t count the informal economy, which includes millions of women. Women are also more likely to live in poverty, more affected by gender-based violence, and more affected by climate change.

Learn more about gender equality: Gender Analytics: Gender Equity through Inclusive Design (University of Toronto)

#14. Cybersecurity

The WEF’s Global Risks Report 2022 (page 9) listed cybersecurity vulnerabilities as a concern. The reason is rapid digitalization, which was triggered in part by COVID-19. Many “advanced economies” are now at a higher risk for cyberattacks. GRPS respondents identified cybersecurity failure as a critical short-term risk. In 2020, malware and ransomware attacks went up by 358% and 435%. There are a few reasons for this, including better (and easier) attack methods and poor governance. Cyberattacks have a swath of serious consequences and erode public trust. As countries become more dependent on digitalization, their cybersecurity needs to keep up.

Learn more about cybersecurity: IBM Cybersecurity Analyst Professional Certificate (IBM)

#15. Disinformation

Rapid digitalization comes with many issues, including the lightning-fast spread of disinformation. The WEF report describes deepfakes, an accessible AI technology, and its potential to sway elections and other political outcomes. Disinformation doesn’t need to be sophisticated to be successful, however. Through social media posts and videos, twelve anti-vax activists were responsible for almost ⅔ of all anti-vaccine content on platforms like Facebook and Twitter. Their content flooded the internet with the type of harmful, fear-mongering disinformation that played a significant role in vaccine hesitancy and political radicalization. Because disinformation travels faster online than the truth, it’s a global issue that should be addressed.

Learn more about tackling disinformation: Communicating Trustworthy Information in the Digital World (University of Rotterdam)

#16. Freedom of the press

According to the Varieties of Democracy Institute (as reported in The Economist ), about 85% of people live in a country where press freedom has gone down in the past 5 years. After peaking at .65 in the early 2000s and 2011, the global average dropped to .49 in 2021. Major countries like China, India, Russia, Brazil, and Turkey saw significant declines. Journalists and news organizations face threats like violence, imprisonment, lack of funding, and coordinated online attacks and harassment. A free press is essential to a functioning democracy. Without press freedom, all human rights are at risk.

Learn more about freedom of expression: Human Rights for Open Societies (Utrecht University)

#17. Debt crises

In the WEF Global Risks Report (page 7), respondents named debt crises as one of the most pressing issues over the next decade, though respondents believe they will become most serious in just 3-5 years. COVID-19 is a big reason why. Government stimulus was necessary, but many countries are now left with debt burdens. For corporate and public finances in large economies, debt burdens can lead to defaults, bankruptcies, insolvency, and more. This is a far-reaching issue as it affects budgets for areas like healthcare and green energy.

Learn more about the debt: Finance for everyone – Debt (McMaster University)

#18. Corruption

Corruption encompasses a host of actions such as bribery, election manipulation, fraud, and state capture. The World Bank Group names corruption as a barrier to ending extreme poverty and “boosting shared prosperity” for the poorest populations. When it comes to addressing poverty, climate change, healthcare, gender equality, and more, corruption gets in the way. Because corruption is a global problem, global solutions are necessary. Reform, better accountability systems, and open processes will all help.

Learn more about tackling corruption: What is Corruption: Anti-Corruption and Compliance (University of Pennsylvania)

#19. Authoritarianism

According to Freedom House, global democracy is eroding. That includes countries with long-established democracies. In their 2022 report, the organization reveals that global freedom has been declining for the past 16 years. 60 countries faced declines in the last year. Only 25 saw improvements. Only 20% of the global population lives in Free countries. China, Russia, and other authoritarian countries have gained more power in the international system, while countries with established democracies – like the United States – are losing their freedoms. What can be done? Freedom House says success “requires a bold, sustained response that establishes support for democracy and countering authoritarianism.” Governments and citizens engage and stand for democracy.

Learn more about tackling authoritarianism: Citizenship and the Rule of Law (University of London)

#20. Global cooperation

Addressing the issues in this article is not an easy task. True progress is only possible through global cooperation, a fact which is woven through the WEF report. Everything from addressing cybersecurity threats to humanitarian emergencies to protecting democracy depends on strong cooperation between countries. As the report says in its preface: “Restoring trust and fostering cooperation within and between countries will be crucial to addressing these challenges and preventing the world from drifting further apart.” The challenges threatening global cooperation are just as clear as the need, however, which makes it one of the most serious issues of the day.

Learn more about global cooperation: Global Diplomacy: the United Nations in the World

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About the author, emmaline soken-huberty.

Emmaline Soken-Huberty is a freelance writer based in Portland, Oregon. She started to become interested in human rights while attending college, eventually getting a concentration in human rights and humanitarianism. LGBTQ+ rights, women’s rights, and climate change are of special concern to her. In her spare time, she can be found reading or enjoying Oregon’s natural beauty with her husband and dog.

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When it comes to everyday problems in your life, some are easier to fix than you might think, like not having enough lighting in your kitchen or losing items in your purse. Amazon is a handy site when looking for solutions, as they have tons of products to help solve those pesky common issues.

In this list, you’ll find a bunch of simple life solutions , at home and on the go. In the kitchen, you can improve your dish-drying setup with this silicone drying mat that’s easy to clean. Make it easier to add sugar to your coffee or tea with this glass container that dispenses from the bottom.

Forgetting where to be and when? Keep your appointments and events more organized with this magnetic whiteboard calendar that’s perfect for attaching to your fridge. Is your closet becoming an issue? You can better organize your shoes with this bamboo shoe rack that looks great wherever it’s placed.

Whether your problems are in the kitchen, the closet, or your own purse, you’ll find plenty of solutions that make your life just a little bit easier in this list.

Problem: You Can’t Reach The Candle Wick

After you’ve burned a candle for a while, it can be tricky to light without burning your hand. This electric lighter has a long, bendable neck, so you can adjust it based on the size and depth of your candle. Since it’s electric, the lighter is rechargeable using a USB charging port and doesn’t use lighter fluid.

Problem: Your Half-Eaten Bag Of Chips Went Stale

Keep your snacks fresh with this mini bag sealer . The device uses heat to reseal the packaging of chips, cookies, and other snacks, so they don’t go stale. It heats up in just a few seconds and seals almost instantly. It’s also lightweight, so you can take it to work or while traveling.

Problem: Necklaces Are Getting Tangled

A layered necklace look is always chic — unless, of course, your necklaces get tangled. This clasp allows you to clip three necklaces onto little rings that keep the chains separated. It clasps together with a magnet, so it’s easy to take on and off. It’s also great for bracelets and comes in silver and gold.

Problem: Inside Your Bag Is A Mess

Having an organized purse is a rare skill that most of us don’t possess — it doesn’t help that many bags (looking at you totes!) don’t even have any inner pockets or storage. This purse organizer insert has 10 pockets, including a zippered one, so you can keep your wallet, makeup, gum, and other items in their own pockets. The organizer is made from a sturdy felt material and comes in 19 colors and designs, including snakeskin and polka dot.

Problem: Burning Your Fingers & Forearms

When it comes to kitchen tools, oven mitts are not somewhere you want to skimp, since they protect you from burning yourself. These silicone oven mitts have an extra thick padded lining, so they keep your hands and arms safe, but they also have a silicone layer on the outside which makes them heat resistant up to 450 degrees. Aside from the brilliant red shade featured, you can also buy them in aqua, gray, and black.

Problem: Charging Cables Everywhere

Keep all your devices at 100% with this 3-in-1 charging station. With a spot for your phone, smartwatch, and earbuds, this charging station is perfect for keeping in your home or office. It uses wireless charging, so it also means you won’t have a huge mess of cords. It’s compatible with most smart devices, including Apple, Android, and Samsung.

Problem: Poorly Lit Cabinets & Closets

Add more light to your closets, cabinets — or anywhere that needs a little extra light — without having to install a whole light fixture. These under the cabinet lights come with adhesive tape, so they’re easy to install. A remote is included, so the brightness can be easily adjusted.

Problem: Bugs Getting In The House

When the weather’s nice out, it’s the perfect time to leave your door open to let the warm breeze in. Of course, the open air comes with bugs — unless you have one of these magnetic screen doors . Made from a fine mesh, the screen lets air in but keeps bugs and debris out. It also has a magnetic closure so you can enter and exit even if your hands are full.

Problem: Running Out Of Paper Towels

Paper towels are handy, but they eventually run out. These Swedish dishcloths , on the other hand, are machine washable and reusable up to 100 times. Plus they come in a pack of 10, so they can take the place of several paper towel rolls. The cloths are stiff when dry but become soft and pliable when wet.

Problem: Overbooking Your Schedule

If you have a hard time keeping track of your schedule, then this magnetic whiteboard calendar will come in handy. The calendar is ideal for attaching to the fridge, or any other magnetic surface. It can be filled in and erased each month to keep track of appointments and events. You can use it immediately, as it comes with six dry erase markers.

Problem: Having Noisy Housemates

Keep your room quiet with this door draft stopper that blocks out noise and insulates. This stopper has a velcro strip that makes it more adjustable. It also helps keep cold air out and keep heat in. For those with noisy roommates, this can offer a bit more peace at a low price.

Problem: Losing Your Luggage

It can be hard to keep track of your luggage when so many suitcases look alike. Set yours apart with this luggage tag that has a big colorful letter on it to match your initial on your first or last name. The tag is made of rubber, so it won’t be easily damaged, and includes a card for writing down your contact information in the chance your luggage gets misplaced.

Problem: Not Being Able To Properly Clean Your Reusable Straws (Or Not Having Them At All)

Reusable straws are great for reducing single-use plastic, but they can be a pain to clean. These silicone straws come with their own cleaning brush that gets into the narrow cavity of the straws. They can be used for hot and cold drinks and are safe to throw in the dishwasher. They also come in a 2-pack, with 20 straws total.

Problem: Breaking Dishes Because You Don’t Have A Proper Place To Dry Them

If you’re playing Jenga with your dishes when you’re setting them on your counter to dry then chances are you’ve broken more than a few. But that is where this silicone dish drying mat comes in: It’s soft but non-slip so you can set your wet dishes on it without them slipping around, cracking, and shattering. It is easy to clean, so it won’t build up dirt and grime like a cloth drying mat. It’s dishwasher safe and heat-resistant, so you can also use it to support hot plates.

Problem: Getting Syrup Or Honey All Over Your Hands

When it gets on your hands, syrup seems to multiply — making everything you touch sticky for the rest of the day. But with this syrup/honey dispenser , you can keep your hands clean. The dispenser has a lever you can pull that releases syrup from the bottom of the bottle. Dispensing from the bottom also means you’ll be able to get every last drop of the sticky sweet liquid sugar without having to shake the bottle or awkwardly balance it on its head while it slowly drips towards the opening at the top. This dispenser comes with a stand with a reservoir to catch any syrup drips.

Problem: Running Out Of Aluminum Foil

Never worry about running out of foil or plastic wrap again with this reusable food wrap made from beeswax. These wraps are moldable to your needs, so they can cover a large bowl of salad or wrap around a leftover piece of fruit. They’re washable and reusable, plus biodegradable, so they’re better for the environment.

Problem: Your Rugs Are Sliding Around

Keep your rugs from slipping around the floor with this rug pad that can be cut to fit any size you need. The pad is made from a non-slip foam that can be used on wood floors, tile, and other materials. It automatically sticks to the rug and the floor, so there’s no special installation required.

Problem: There’s Not Enough Storage Space In The Living Room

Use this storage ottoman to hold blankets, books, pillows, and other items that don’t necessarily have a good home in your living room. The ottoman has a faux leather cushioned top, which is perfect for resting your feet on. The lid is removable with a collapsible base.

Problem: Figuring Out Where To Put Your Phone During Workouts

Workout clothes don’t always have pockets for holding your phone the way a pair of jeans does. Luckily, these high-waisted leggings have pockets on the thigh, so your phone will be safe and secure while you’re going on a walk or run. They’re made from a soft, stretchy fabric made from a spandex and polyester blend for maximum comfort.

• Available sizes: One Size and One Size Plus
• Available colors: 51

Problem: It’s Too Bright To Nap

Darken your room without the hassle of professionally installing shades. This set of six window shades comes with sticky adhesive for easy installation. They can also be cut to size, so you can fit them exactly to your window. They also come with clips to help you easily adjust the height.

Problem: You’re Not Able To Find Your Keys After Dropping Them

Dropping your keys in the dark can be a huge pain, but this magnetic pickup tool will help save the day. The tool has a long arm, bright flashlight, and magnetic surface to pick up whatever you dropped. Use it to safely collect anything metal, or magnetically attach it to a metal surface, like the hood of your car, for better vision.

Problem: There’s No Way To Store Canned Pet Food

I recently started feeding my dog canned wet food, and having can covers makes it so much easier. This set of five covers is made from food-safe silicone and fits three different sizes of cans. They’re dishwasher safe and come in an array of colors. They also have a cute paw tab that makes removal a breeze.

Problem: You Slept In And It’s Too Late To Get Coffee

We can’t all get up early to make it to the coffee shop before work. Make your own fancy latte at home with this milk frother . The lightweight device is easy to use and turns milk into foam in just a few seconds. It’s portable, so you can even take it with you to work or on vacation. It also comes with its own metal stand.

Problem: There’s Nowhere To Put Your Essentials When Going For A Walk

Sometimes you want to go on a walk or hike, but don’t want to drag around a heavy backpack. Did you know that fanny packs are back in style? This fanny pack is the perfect option for holding your phone, wallet, keys, and other essentials. The fanny pack is made from durable nylon that is water-resistant. It has six zippered pockets, so your things will be safe and sound.

Problem: Breaking Eggs When Storing Them In The Fridge

Cardboard egg cartons are flimsy — stack them in your fridge and chances are you’re probably going to end up breaking an egg or two — which is why these plastic egg cartons are so genius. They’re sturdy and stackable, so you can organize your fridge and protect your eggs. The trays come in a pack of two and hold 12 eggs each.

Problem: You’re Dropping Nails & Screws While Working

If you like to spend time working on DIY projects or doing repairs, then this magnetic wristband will come in handy. The wristband attaches with velcro and is handy for holding screws, nails, or other tools you’re using while working. The wristband is equipped with 10 strong magnets, but it’s still lightweight.

Problem: You’re Spending Too Much On Cold Brew

Save yourself time in the morning and ditch the coffee shop. This cold brew maker has a stainless steel filter and holds up to 12 cups, so you can make cold brew for the whole week. Just put your favorite coffee grounds in the filter, add water, and put it in the fridge to steep. It can also be used for making iced tea. It comes in two sizes — two liters and a gallon.

Problem: You Always Drop Your Soap In The Shower

A bar of soap can be hard to hold onto in the shower, but these soap saver bags are easier to grip. The five-bag set is made from natural sisal plants, which help the soap lather and produce foam. The bags are also ideal for when the bar of soap gets too small, but you’re not ready to throw it out just yet.

Problem: There’s Nowhere To Store Leftover Food

A good set of food containers serve as one of the most useful tools in any kitchen. These glass storage containers come in a set of 24, with a range of sizes to fit everything from leftover salmon to half a lemon. The containers have an airtight seal that is leakproof, so it’s perfect for storing leftovers to take for lunch.

Problem: The Sheets Keep Coming Off The Bed

It’s a pain when your fitted sheets don’t stay fitted. These sheet holder straps clip onto the corner of your sheets, holding them in place so they don’t slip off. The straps have metal clips and elastic bands, which are easy to install. They’re basically like little suspenders for your sheets.

Problem: You Can’t Find Your Shoes

If you have a habit of misplacing your shoes around the house, then this shoe shelf will help keep them organized. Made from sturdy bamboo, the shelf holds three or four pairs of shoes on each tier and is perfect for keeping in the entryway or bedroom. If you need three or more tiers, Amazon offers those options as well.

Problem: Misplacing Your Keys

Attach this Tile Bluetooth tracker to your keyring and you won’t have to dig through all your purses to find your keys. The small, lightweight tracker connects to the Tile app on your phone, so it can help you find your keys in your home, or if you left them in your bag somewhere while out and about. It’s incredible how much time you’ll save (and how many appointments you’ll be on time for.)

Problem: Uneven Winged Eyeliner

Unless you’re a professional makeup artist, getting the perfect winged eyeliner can be tricky. This eyeliner stamp makes it so much easier by literally stamping the shape of the wing on the corner of your eye. Each liner has two ends, one for the stamp and one with a fine point for refining the edges. It’s also waterproof and smudge-proof.

Problem: Forgetting A Good Pillow While Traveling

One of the worst feelings in the world is needing a pillow, but not having a pillow. Luckily, you can prep ahead of time by storing this compressible memory foam pillow in the trunk of your car. It doesn’t take up a lot of room but will offer a ton of comfort in a pinch. It’s also machine washable.

Problem: Getting Sauce On The Counter

The problem with most spoon rests is that they only hold one spoon. This silicone utensil rest has four slots, which is perfect if you’re the kind of cook (like me) who cooks with a spatula and two spoons at the same time. The utensil rest has a large drip pad to catch any sauce or liquid that drips off. The best part is that you can easily throw it in the dishwasher to clean.

Problem: Avocados Going Bad Too Quickly

Avocados are an odd shape, so they don’t always fit in a typical storage container. This avocado saver is designed to preserve the fruit with an indent designed to fit around the pit (leaving the pit in helps it from going brown) The container also has an adjustable strap to keep the avocado in place, like a little seatbelt.

Problem: Having Too Much Produce You Didn’t Finish

These silicone food huggers are a versatile kitchen accessory and can be used to preserve half an apple, a partially used onion, or as a replacement lid on a jar. They come in a set of five of varying sizes, and are a great solution for replacing plastic wrap or foil, and help reduce single-use plastic in your home.

Problem: You Can’t Get All The Toothpaste Out

Get the most out of your toothpaste with these tube squeezers . Just like the name implies, these handy tools squeeze out every last drop from the tube, and can also be used for makeup, lotion, or anything else that comes in a tube. They come in a pack of four, so you’ll have plenty at hand.

Problem: You Can’t Find Your Earrings

Make it easier to find the pair of earrings or that necklace you want to wear with this jewelry organizer . With 80 clear vinyl pockets, this organizer makes it easy to find the piece you’re looking for while also keeping them from getting tangled with each other. The organizer also has a hook at the top, making it easy to hang.

Problem: The Duvet Getting Scrunched Up In Its Cover

Keeping your duvet in place inside a duvet cover is no easy feat. Luckily, these magnetic duvet clips are an easy solution. The clips secure your duvet with a magnetic pin, and each pin can secure up to 10 pounds. They come in a set of eight, so you can secure the whole edge.

Problem: Accidentally Shrinking Cotton Clothes

Not all fabrics are suitable for a dryer. This Amazon Basics laundry rack is perfect for hanging shrinkable fabrics like cotton, delicate undergarments, or other items that you want to air-dry. The steel rack can support up to 32 pounds and is collapsible, so you can store it away when not in use.

Problem: Leaving The Lights On

Once you leave the house, there’s no way to know whether or not you left any lights on. That is, unless you use these smart lightbulbs that you can control from your phone. These bulbs connect to an app (and can even connect to Alexa and Google Home) where you can turn them on and off, adjust the brightness, and even change the color of the light.

Problem: Losing Jewelry While Traveling

If you take your favorite jewelry with you on a trip, then you’re gonna want a safe place to store it. This travel jewelry organizer has compartments to hold rings, necklaces, and other assorted jewelry. It has a zipper closure and is compact enough to fit in a purse. Plus, it comes in 17 colors.

Problem: Pants That Are Too Long

Adjust the length of your pants without going to a tailor using this double-sided clothing tape . It’s safe to use on both your skin and clothing without damaging either. It can also be used to keep clothing in place, like a dress strap or a low-cut blouse. Each pack comes with 50 pieces of tape.

Problem: Wrinkly Clothing

It can be a whole ordeal to pull out the iron just to remove a few wrinkles. This crease release spray works without an iron. Just spray it on the fabric and smooth your hand over it to remove the wrinkles. Plus, it has a clean, fresh laundry scent.

The World's Biggest Problems Are Interconnected. Here's How We Can Solve Them This Decade

T wo decades ago, people around the world rang in the new millennium with a growing sense of optimism. The threat posed by the Cold War was fading slowly in the rearview mirror. Leading thinkers like Francis Fukuyama touted the benefits of globalization , saying it would bring democracy and prosperity to the developing world. The nascent Internet economy promised to bring us closer together.

The following 20 years took some of the air out of the assumption of steady progress, but when future historians assess the 21st century, the year 2020 is likely to serve as the point at which the optimism bubble burst. The COVID-19 pandemic has exposed a complex web of interlocking problems that have morphed into full-blown crises. The coronavirus laid bare the dangers of endemic poverty not only in the developing world but also in rich countries like the U.S., where millions lack health care and are one paycheck away from living on the street. Around the world, racial and ethnic minorities have demanded justice after centuries of structural discrimination. Woven through it all, the earth’s climate is increasingly unstable, posing an existential threat to human society as we know it. In the next decade, societies will be forced to either confront this snarl of challenges, or be overwhelmed by them. Our response will define the future for decades to come.

The recognition that these challenges are fundamentally linked isn’t new. Activists and academics have for many years pointed to the cascading effects of various social ills. Whether it’s the way racism contributes to poor health outcomes or gender discrimination harms economic growth , the examples are seemingly endless. But this understanding has made its way into the conversation about solutions too.

Notably, for the past five years, the U.N. has touted 17 interrelated sustainable development goals, objectives for building a more viable world, and called for a push to achieve them by 2030. The goals, which cover environmental, social and economic progress, are nonbinding but have become key benchmarks for commitments at a national and corporate level. Countries from China to the Maldives, as well as companies like Amazon , Microsoft and PwC, have committed to rolling out policies over the next decade that will set them on a path to eliminate their carbon footprints.

The understanding that these problems require holistic solutions has only grown amid the pandemic and its fallout. President Joe Biden has referred to four urgent crises—the pandemic, the economic crisis, racial injustice and climate change—and promised a push to tackle them all together. The European Union’s program to propel the bloc out of the COVID-19 crisis targets climate change, while incorporating equity concerns. As stock markets soared last year, institutions with trillions of dollars in assets demanded that their investments deliver not only a good return for their wallets but also a good return for society.

All these developments and many more have created new opportunities for bold ideas . These new ways of thinking will come from government leaders, to be sure, but also from activists, entrepreneurs and academics. Here, our eight inaugural members of the 2030 committee offer their own specific solutions—and in them, perhaps, the seeds of 21st century optimism.

This appears in the February 1, 2021 issue of TIME.

• Succession  Was a Race to the Bottom , And Everybody Won
• What Erdoğan’s Victory Means for Turkey—and the World
• Why You Can't Remember That Taylor Swift Concert All Too Well
• How Four Trans Teens Threw the Prom of Their Dreams
• Why Turkey’s Longtime Leader Is an Electoral Powerhouse
• The Ancient Roots of Psychotherapy
• Drought Crisis Spurs U.S.-Mexico Collaboration 
• Florence Pugh Might Just Save the Movie Star From Extinction

Write to Justin Worland at [email protected] .

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10 Math Equations That Have Never Been Solved

By Kathleen Cantor, 10 Sep 2020

Mathematics has played a major role in so many life-altering inventions and theories. But there are still some math equations that have managed to elude even the greatest minds, like Einstein and Hawkins. Other equations, however, are simply too large to compute. So for whatever reason, these puzzling problems have never been solved. But what are they?

Like the rest of us, you're probably expecting some next-level difficulty in these mathematical problems. Surprisingly, that is not the case. Some of these equations are even based on elementary school concepts and are easily understandable - just unsolvable.

1. The Riemann Hypothesis

Equation: σ (n) ≤ Hn +ln (Hn)eHn

• Where n is a positive integer
• Hn is the n-th harmonic number
• σ(n) is the sum of the positive integers divisible by n

For an instance, if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1?

This problem is referred to as Lagarias’s Elementary Version of the Riemann Hypothesis and has a price of a million dollars offered by the  Clay Mathematics Foundation  for its solution.

2. The Collatz Conjecture

Equation: 3n+1

• where n is a positive integer n/2
• where n is a non-negative integer

Prove the answer end by cycling through 1,4,2,1,4,2,1,… if n is a positive integer. This is a repetitive process and you will repeat it with the new value of n you get. If your first n = 1 then your subsequent answers will be 1, 4, 2, 1, 4, 2, 1, 4… infinitely. And if n = 5 the answers will be 5,16,8,4,2,1 the rest will be another loop of the values 1, 4, and 2.

This equation was formed in 1937 by a man named Lothar Collatz which is why it is referred to as the Collatz Conjecture.

3. The Erdős-Strauss Conjecture

Equation: 4/n=1/a+1/b+1/c

• a, b and c are positive integers.

This equation aims to see if we can prove that for if n is greater than or equal to 2, then one can write 4*n as a sum of three positive unit fractions.

This equation was formed in 1948 by two men named Paul Erdős and Ernst Strauss which is why it is referred to as the Erdős-Strauss Conjecture.

4. Equation Four

Equation: Use 2(2∧127)-1 – 1 to prove or disprove if it’s a prime number or not?

Looks pretty straight forward, does it? Here is a little context on the problem.

Let’s take a prime number 2. Now, 22 – 1 = 3 which is also a prime number. 25 – 1 = 31 which is also a prime number and so is 27−1=127. 2127 −1=170141183460469231731687303715884105727 is also prime.

5. Goldbach's Conjecture

Equation: Prove that x + y = n

• where x and y are any two primes

This problem, as relatively simple as it sounds has never been solved. Solving this problem will earn you a free million dollars. This equation was first proposed by Goldbach hence the name Goldbach's Conjecture.

If you are still unsure then pick any even number like 6, it can also be expressed as 1 + 5, which is two primes. The same goes for 10 and 26.

6. Equation Six

Equation: Prove that (K)n = JK1N(q)JO1N(q)

• Where O = unknot (we are dealing with  knot theory )
• (K)n  =  Kashaev's invariant of K for any K or knot
• JK1N(q) of K is equal to N- colored Jones polynomial
• We also have the volume of conjecture as (EQ3)
• Here vol(K)  =  hyperbolic volume

This equation tries to portray the relationship between  quantum invariants  of knots and  the hyperbolic geometry  of  knot complements . Although this equation is in mathematics, you have to be a physics familiar to grasp the concept.

7. The Whitehead Conjecture

Equation: G = (S | R)

• when CW complex K (S | R) is aspherical
• if π2 (K (S | R)) = 0

What you are doing in this equation is prove the claim made by Mr.  Whitehead  in 1941 in  an algebraic topology  that every subcomplex of an  aspherical   CW complex  that is connected and in two dimensions is also spherical. This was named after the man, Whitehead conjecture.

8. Equation Eight

Equation: (EQ4)

• Where Γ = a  second countable   locally compact group
• And the * and r subscript = 0 or 1.

This equation is the definition of  morphism  and is referred to as an assembly map.  Check out the  reduced C*-algebra  for more insight into the concept surrounding this equation.

9. The Euler-Mascheroni Constant

Equation: y=limn→∞(∑m=1n1m−log(n))

Find out if y is rational or irrational in the equation above. To fully understand this problem you need to take another look at rational numbers and their concepts.  The character y is what is known as the Euler-Mascheroni constant and it has a value of 0.5772.

This equation has been calculated up to almost half of a trillion digits and yet no one has been able to tell if it is a rational number or not.

10. Equation Ten

Equation: π + e

Find the sum and determine if it is algebraic or transcendental. To understand this question you need to have an idea of  algebraic real numbers  and how they operate. The number pi or π originated in the 17th century and it is transcendental along with e. but what about their sum? So Far this has never been solved.

As you can see in the equations above, there are several seemingly simple mathematical equations and theories that have never been put to rest. Decades are passing while these problems remain unsolved. If you're looking for a brain teaser, finding the solutions to these problems will give you a run for your money.

See the 11 Comments below.

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Posted in Mathematics category - 10 Sep 2020 [ Permalink ]

11 Comments on “10 Math Equations That Have Never Been Solved”

But 2(2127)−1 = 340282366920938463463374607431768211455 is not a prime number. It is divisible by 64511.

Hello I am explorer and i type on google search " unsolvable mathematical formulas ", and I first find this syte. I see you are good-math-guys. Do you know what is this formula means:

π × ∞ = " 5 "

If you happen to have a quantum computer, I am not kidding be smart and don't insert this formula: [π × ∞ = " 5 "] into it please.

Maybe only, if you know meaning of this three symbols up writen and connected together.

(x dot epsilon)

I can explain my theory if you want me to spoil the pleasure of solving the equation. And mathematics as a science too or " as well " sorry i am not good in English, and google translate is not exelent.

8.539728478 is the answer to number 10

8.539728478 is the answer to number 10 or 8.539734221

Equation Four: Solved

To determine whether the number 2(2^127)-1 – 1 is a prime number, we first need to calculate its value. The expression 2(2^127) can be simplified as follows:

2(2^127) = 2 * 2^127 = 2^128

Therefore, the expression 2(2^127)-1 – 1 can be written as 2^128 – 1 – 1. We can then simplify this further to get:

2^128 – 1 – 1 = 2^128 – 2

To determine whether this number is prime, we can use the fundamental theorem of arithmetic, which states that every positive integer can be written as a product of prime numbers in a unique way (ignoring the order of the factors). This means that if a number is not prime, it can be expressed as the product of two or more prime numbers.

We can use this theorem to determine whether 2^128 – 2 is prime by trying to express it as the product of two or more prime numbers. However, it is not possible to do this, because 2^128 – 2 cannot be evenly divided by any prime number (except for 1, which is not considered a prime number).

Therefore, we can conclude that 2^128 – 2 is a prime number, because it cannot be expressed as the product of two or more prime numbers.

Equation Ten: Solved

The sum of π and e is equal to π + e = 3.14159 + 2.71828 = 5.85987.

To determine whether this number is algebraic or transcendental, we first need to understand the difference between these two types of numbers. Algebraic numbers are numbers that can be expressed as a root of a polynomial equation with integer coefficients, while transcendental numbers cannot be expressed in this way.

In this case, the number 5.85987 can be expressed as the root of the polynomial equation x^2 - 5.85987x + 2.71828 = 0. Therefore, it is an algebraic number.

In conclusion, the sum of π and e is equal to 5.85987, which is an algebraic number.

Equation 2: SOLVED

The equation 3n + 1 states that a positive integer n should be multiplied by 3 and then 1 should be added to the result. If the resulting value is then divided by 2 and the quotient is a non-negative integer, the process should be repeated with the new value of n.

To prove that this equation always results in a repeating sequence of 1, 4, 2, 1, 4, 2, 1, ... if n is a positive integer, we can start by substituting a value for n and performing the calculations as specified in the equation.

For example, if n is equal to 1, the sequence of values will be: n = 1 3n + 1 = 3(1) + 1 = 4 n = 4/2 = 2 3n + 1 = 3(2) + 1 = 7 n = 7/2 = 3.5

Since n must be a non-negative integer, the value of n becomes 2 when the result of the previous calculation is divided by 2. The sequence then becomes: n = 2 3n + 1 = 3(2) + 1 = 7 n = 7/2 = 3.5

The value of n becomes 3 when the result of the previous calculation is divided by 2. The sequence then becomes: n = 3 3n + 1 = 3(3) + 1 = 10 n = 10/2 = 5

The value of n becomes 5 when the result of the previous calculation is divided by 2. The sequence then becomes:

n = 5 3n + 1 = 3(5) + 1 = 16 n = 16/2 = 8 n = 8/2 = 4 n = 4/2 = 2 n = 2/2 = 1 n = 1/2 = 0.5

Since n must be a non-negative integer, the value of n becomes 1 when the result of the previous calculation is divided by 2. The sequence then becomes: n = 1 3n + 1 = 3(1) + 1 = 4 n = 4/2

To complete the proof that the equation 3n + 1 always results in a repeating sequence of 1, 4, 2, 1, 4, 2, 1, ... if n is a positive integer, we can continue the process of substituting values for n and performing the calculations as specified in the equation.

If n is equal to 4, the sequence of values will be: n = 4 3n + 1 = 3(4) + 1 = 13 n = 13/2 = 6.5

Since n must be a non-negative integer, the value of n becomes 6 when the result of the previous calculation is divided by 2. The sequence then becomes:

n = 6 3n + 1 = 3(6) + 1 = 19 n = 19/2 = 9.5

Certainly! To complete the proof that the equation 3n + 1 always results in a repeating sequence of 1, 4, 2, 1, 4, 2, 1, ... if n is a positive integer, we can continue the process of substituting values for n and performing the calculations as specified in the equation.

If n is equal to 4, the sequence of values will be:

n = 4 3n + 1 = 3(4) + 1 = 13 n = 13/2 = 6.5

Since n must be a non-negative integer, the value of n becomes 9 when the result of the previous calculation is divided by 2. The sequence then becomes:

n = 9 3n + 1 = 3(9) + 1 = 28 n = 28/2 = 14 n = 14/2 = 7 n = 7/2 = 3.5

The value of n becomes 3 when the result of the previous calculation is divided by 2. The sequence then becomes:

n = 3 3n + 1 = 3(3) + 1 = 10 n = 10/2 = 5 n = 5/2 = 2.5

Since n must be a non-negative integer, the value of n becomes 2 when the result of the previous calculation is divided by 2. The sequence then becomes:

n = 2 3n + 1 = 3(2) + 1 = 7 n = 7/2 = 3.5

As we can see, the sequence of values becomes repetitive

The Riemann Hypothesis

This equation states that the sum of the positive integers divisible by n (σ(n)) is less than or equal to the n-th harmonic number (Hn) plus the natural logarithm of the n-th harmonic number (ln(Hn)) multiplied by the n-th harmonic number (Hn) raised to the power of Hn.

To solve this equation, you would need to substitute a specific value for n and determine the value of Hn and σ(n) for that specific value. You can then substitute these values into the equation and see if it holds true.

For example, if n = 5, the sum of the positive integers divisible by 5 (σ(5)) is 15 (1 + 5 + 10 + 15 + 20 + 25), the 5th harmonic number (H5) is 2.28, and the natural logarithm of the 5th harmonic number (ln(H5)) is 0.83. Substituting these values into the equation, we get:

σ(5) ≤ H5 + ln(H5)eH5 15 ≤ 2.28 + 0.83 * 2.28^2.28 15 ≤ 4.39

Since 15 is less than or equal to 4.39, the equation holds true for this specific value of n.

Equation #9

In the equation y = limn→∞(∑m=1n1m−log(n)), y is the limit of the sequence (∑m=1n1m−log(n)) as n approaches infinity.

The Euler-Mascheroni constant is defined as the limit of the sequence (∑m=1n1m−log(n)) as n approaches infinity, and it has a value of approximately 0.5772. Therefore, y is equal to the Euler-Mascheroni constant, which is a rational number.

Rational numbers are numbers that can be expressed as the ratio of two integers, such as 3/4, 7/11, or 2/5. They can be written as a finite or repeating decimal, such as 0.75, 0.636363636..., or 1.5.

Irrational numbers are numbers that cannot be expressed as the ratio of two integers, and they cannot be written as a finite or repeating decimal. Examples of irrational numbers include √2, π, and e.

Since y is equal to the Euler-Mascheroni constant, which is a rational number, y is a rational number.

The equation G = (S | R) is a definition of a CW complex, where S and R are subcomplexes of G. A CW complex is a topological space that can be built up from cells, where each cell is homeomorphic to a closed ball in Euclidean space.

The statement "when CW complex K (S | R) is aspherical" means that the complex K (S | R) does not contain any non-trivial loops, i.e. loops that cannot be continuously contracted to a point. This implies that the fundamental group of K (S | R) is trivial, which means that π1(K (S | R)) = {e}.

The statement "if π2 (K (S | R)) = 0" means that the second homotopy group of the complex K (S | R) is trivial, which means that there are no non-trivial 2-dimensional holes in K (S | R).

Together, these statements imply that the CW complex K (S | R) is a topological space with no non-trivial loops or holes. This is a strong condition that is satisfied by very few spaces, and it is a necessary condition for a space to be aspherical.

In summary, the statement "when CW complex K (S | R) is aspherical" and "if π2 (K (S | R)) = 0" implies that the complex K (S | R) is a topological space with no non-trivial loops or holes, which is a necessary condition for a space to be aspherical.

#3 Erdos Strauss Conjecture:

To solve the equation 4/n = 1/a + 1/b + 1/c where n ≥ 2, a, b and c are positive integers, we can first multiply both sides of the equation by nabc to get rid of the fractions:

4abc = nab + nbc + nac

We can then group like terms:

4abc = (n + a)(b + c)

Now we can use the fact that n, a, b, and c are positive integers to make some observations:

Since n, a, b and c are positive integers, n, a, b and c must be factors of 4abc. Since n is greater than or equal to 2, it must be one of the factors of 4abc. The other factors of 4abc are (n + a), b, and c. So, to find all the possible values of n, a, b, and c, we must find all the ways to factorize 4abc such that one of the factors is greater than or equal to 2.

4abc = 4 * 1 * 1 * 2 * 3 * 5 = 120

Some possible factorizations are:

n = 2, a = 1, b = 5, c = 12 n = 2, a = 3, b = 5, c = 8 n = 2, a = 4, b = 3, c = 15 n = 2, a = 6, b = 2, c = 20 n = 4, a = 1, b = 3, c = 30 So, the possible solutions to the equation are: (n,a,b,c) = (2,1,5,12), (2,3,5,8), (2,4,3,15), (2,6,2,20), (4,1,3,30)

It's worth noting that this is not an exhaustive list, but just some of the possible solutions, as there could be infinitely many solutions to this equation.

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There Are No Easy Answers for Our Biggest Global Problems

• Andrew King,
• Kenneth P. Pucker,
• Auden Schendler

Real change takes hard work and sacrifice.

Too many academics, commentators and experts have fallen victim to magical thinking regarding our ability to tackle the major societal challenges facing humanity. To wit: many of the signatories to a recent pledge to find societal purpose in business are furloughing employees during the Covid-19 pandemic, paying dividends to shareholders and provoking complaints from workers that they aren’t adequately protected from danger. It is time to give up on hopeful stories and get back to basics.   If the global pandemic can teach us something, it is to remind us to return to those ideas, like regulation and good governance, that we know work, even if they are obvious or dull. Taxing carbon is not a shiny new idea, but it would redirect investment and effort to low carbon solutions.  Mandating accounting and reporting standards for non-financial measures sounds like an notion from a previous century, but it works. Nobel Laureate James Heckman long ago showed that investing in early childhood education improves social justice and economic productivity. But it has upfront costs. Maybe it is time we listened to him, despite our dislike of taxes. For other global problems, proven interventions are available, but they require effort and sacrifice to deliver results.

In these difficult times, we’ve made a number of our coronavirus articles free for all readers. To get all of HBR’s content delivered to your inbox, sign up for the Daily Alert newsletter.

If ever there was a time to remind us of the futility of magical thinking, this is it.  In real time, we watched the hopeful promise of easy solutions to the Covid-19 pandemic evaporate when confronted by unforgiving reality. Thinking the virus will “just go away” didn’t work, nor did a travel ban, warm weather, or hydroxychloroquine. For the foreseeable future, what will likely work best will be boring and costly solutions such as requirements to social distance and wear a mask. There’s a broader lesson here that we hope we remember after Covid-19 has been vanquished. The desire for sexy and easy solutions can be harmful if it preempts the implementation of homely but proven ones.

The flea-market in magical nostrums for global problems did not start with Covid-19. Before the pandemic, the most seductive new idea was that major societal challenges, such as climate change and inequality, could be solved at a profit. Capitalism was to be reinvented, we were told, by and for a new type of business leader. The Business Roundtable (led by Jamie Dimon, CEO of JP Morgan) and Larry Fink, CEO of Blackrock, both recently announced a visionary new theory of business, one in which taking care of the environment, communities, and workers would yield bottom-line profits. According to this new line of thinking, capitalism was being redefined and our problems soon would be solved. This talk then crashed against the pandemic, and as is often the case, the need for purpose proved less durable than the need for profits In April, the New York Times reported that signatories to the Business Roundtable statement “are furloughing employees, paying dividends to shareholders and provoking complaints from workers that they aren’t adequately protected from danger.”

Further Reading

Coronavirus: Leadership and Recovery

Over our more than 25 years working as business professors or corporate managers, we have observed journals, sustainability consultants, executives, and academics (including, at times , ourselves ) peddle magical solutions: to address poverty, companies can access huge, untapped markets by selling products to poor people; to solve climate change, we just need to encourage the use of more efficient gadgets; to eliminate waste and address resource scarcity, we can profitably recycle and reuse everything; and to solve remaining social and environmental challenges, we only need executives to realize they can grow profits by doing good.

We were once enthusiastic about such ideas, but now believe that many win-win solutions have been dangerously oversold. Cherry-picked case studies can suggest what might be possible, but not what happens on average. Patagonia, the privately- held poster-company for delivering social purpose and profit, may use organic cotton and recycle its products, but very few companies can follow their lead. Yes, corporations can be part of the solution, as many promise, but asking them to solve enormous societal problems by going beyond established rules, has not, and will not, achieve social stability or environmental balance. Consider that in the last 20 years, the number of corporate sustainability reports has grown exponentially, yet so too has atmospheric CO 2 .

It is time to give up on hopeful stories and get back to basics. When U.S. citizens faced dirty rivers and piles of trash in the 1970s, they didn’t expect executives to re-imagine capitalism, they demanded that pollutants be regulated. When smog overcame U.S. cities, activists didn’t invite heroic CEOs to create win-win solutions; they called for emission standards. When toxic chemicals turned up in Love Canal, citizens did not ask for a circular economy, they demanded regulations that tracked the location and use of dangerous chemicals; and when the world faced its first global threat to our shared atmosphere (damage to our ozone layer), citizens and lawmakers did not ask for companies to create “social purpose” charters — they forced global leaders to negotiate a worldwide ban. As a result, our rivers are healthier, our air is safer, and the hole in the ozone layer is closing.

Hope is not a strategy. If the global pandemic can teach us something, it is to remind us to return to those ideas, like regulation and good governance, that we know work, even if they are obvious or dull. Taxing carbon is not a shiny new idea, but it would redirect investment and effort to low carbon solutions.  Mandating accounting and reporting standards for non-financial measures sounds like a notion from a previous century, but it works. Nobel Laureate James Heckman long ago showed that investing in early childhood education improves social justice and economic productivity. But it has upfront costs. Maybe it is time we listened to him, despite our dislike of taxes. For other global problems, proven interventions are available, but they require effort and sacrifice to deliver results.

We can reject such awkward solutions and look for slicker ones, or we can heed Thomas Edison’s warning that real opportunities, unlike magical thinking, often come dressed in overalls, and look like work.

If our content helps you to contend with coronavirus and other challenges, please consider subscribing to HBR . A subscription purchase is the best way to support the creation of these resources.

• Andrew King is the Questrom Professor in Management, Strategy and Innovation at Boston University.
• Kenneth P. Pucker is a professor of practice  at the Fletcher School . He is an advisory director at Berkshire Partners and was formerly the chief operating officer of Timberland. kpucker31
• Auden Schendler is author of the book Getting Green Done and has 25 years of experience in sustainable business. He is an emeritus board member and advisor to the nonprofit Protect Our Winters .

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24 Problems We Should Have Solved By Now

We've explored every corner of the planet. We've used technology to create a global community. We've even put a man on the moon. But we still haven't figured out how to make fitted sheets stay put? Really?

BuzzFeed Staff

1. Reese’s Peanut Butter Cups first came out 86 years ago. THIS STILL HAPPENS EVERY SINGLE TIME!

2. You want a pen? Fine, BUT YOU’RE GOING TO WORK FOR IT.

3. That’s not an eraser on the end of your pencil; IT’S A GODDAMNED LIE.

4. THIS ISN’T CONVENIENCE; THIS IS JUST THEATER!

5. NAILED IT, Netflix! I’m DEFINITELY trying to watch my favorite show, “Movies, supernatTV shows, actors, directors.”

6. Did you think you could defy gravity? HUBRIS! THESE ARE THE CONSEQUENCES!

7. God forbid you CHOOSE A SPELLING AND STICK WITH IT, iTUNES.

8. I sure hope your SHOES AND BACKPACK ARE COMFORTABLE, YOU MONSTER!

9. Your computer will select EVERY PIECE OF TEXT OTHER THAN WHAT YOU WANTED. EVERY. TIME.

10. thanks for the reminder, asshole.

11. “Click to enlarge”?! I TRUSTED YOU, WEBSITE! THIS IS HOW YOU DO ME?!

12. Nothing makes you feel cleaner than your knuckles RUBBING AGAINST THE BACK OF A FILTHY SINK. DO YOU HAVE ANY IDEA HOW MANY OTHER KNUCKLES HAVE RUBBED THAT SINK?! MILLIONS, PROBABLY!

13. GODDAMNIT BUTTER! YOU’RE USELESS!

14. JUST LOOK UP! IT’S RIGHT THERE! YOU’RE DOING THE THING!

15. Your bowl has no problem ferrying whatever slop you're eating from your table to your face, but the second it’s empty IT JUST FOLDS UNDER THE PRESSURE OF YOUR STUPID SPOON.

16. You wanted a receipt? HAVE THIS YARD OF USELESS BULLSHIT INSTEAD!

17. Sweet dreams! Don’t worry about your fitted sheet. It’ll just be over there in the corner MAKING YOUR LIFE A LIVING HELL.

18. CAN WE ALL JUST AGREE TO STOP PUTTING STICKERS ON THINGS?!

19. Oh! That’s convenient! Now you don’t need to calculate the tip. EXCEPT THAT $10.25 ISN’T A 20% TIP — IT’S LIKE A 50% TIP.

20. Great textbook design. IT’S NOT LIKE YOU NEED TO STUDY OR ANYTHING.

21. oh perfect that’s exactly where a shoe tongue belongs you stupid piece of shit shoe.

22. WHY DOES THIS ALWAYS HAPPEN?! WHERE DO THESE LITTLE HOLES COME FROM?!

23. Need to erase some text? HOW ABOUT SHUTTING DOWN YOUR COMPUTER INSTEAD?!

24. There’s a special place in hell for book publishers that REFUSE TO LINE UP THE SPINES OF BOXED BOOK SETS.

Via /r/mildlyinfuriating

Share this article.

CNN values your feedback

Wind energy has a massive waste problem. new technologies may be a step closer to solving it.

Wind turbines are built to last. Their tall bodies are topped with long fiberglass blades, some more than half a football field in length, made to withstand the harshest, windiest conditions .

But this sturdiness brings a big problem: What to do with these blades when they reach the end of their lives.

While about 90% of turbines are easily recyclable, their blades are not. They are made from fiberglass bound together with epoxy resin, a material so strong it is incredibly difficult and expensive to break down. Most blades end their lives in landfill or are incinerated.

It’s a problem that’s vexed the wind energy industry and provided fodder for those who seek to discredit wind power.

But in February, Danish wind company Vestas said it had cracked the problem.

It announced a “breakthrough solution” that would allow wind turbine blades to be recycled without needing to change their design or materials.

The company said the “newly discovered chemical technology” breaks down old blades in a liquid to produce high quality materials, which can eventually be used to make new blades, as well as components in other industries.

Claire Barlow, a sustainability and materials engineer at Cambridge University, told CNN that if this kind of technology can be scaled up, it “could be a game changer.”

A new method for a big problem

In 2019, an image from Casper Regional Landfill in Wyoming showing piles of long, white blades waiting to be buried went viral, prompting criticism of the environmental credentials of wind power.

Wind energy has been growing at a fast pace . It is the world’s leading renewable energy technology behind hydropower, and plays a vital role in helping countries move away from fossil fuel energy, which pumps out planet-heating pollution.

But as the first generation of wind turbines start to reach the end of their service lives , while others are replaced early to make way for newer technology – including longer turbine blades that can sweep more wind and generate more energy – the question of what to do with their huge blades becomes more pressing.

The future of wind energy in the US is floating turbines as tall as 30 Rock

Blade waste is projected to reach 2.2 million tons in the US by 2050. Globally, the figure could be around 43 million tons by 2050.

There are few easy ways to deal with it.

Current options are not only wasteful but have environmental drawbacks. Incineration brings pollution and, while wind companies say there is no toxicity issue with landfilling blades, Barlow said that’s not yet totally clear.

“That’s not as benign as you might think,” she said.

Turbine blade materials make recycling hard and costly. The epoxy resins used to make turbine blades are called “thermosets.”

“If you heat them up, they don’t change their properties until they just burn,” Barlow said. “You can’t just scrunch them up and recycle the material into something easily reusable.”

That’s why Vestas hopes its new technology could hold real promise.

“This has been the key sustainability challenge in the industry. And so we’re of course very excited to have found a solution,” Lisa Ekstrand, the head of sustainability at Vestas, told CNN.

'The sound of money': Wind energy is booming in deep-red Republican states

The process, which the company has been working on in partnership with Aarhus University, the Danish Technological Institute and US-based epoxy company Olin, uses a liquid chemical solution to break down the blade into epoxy fragments and fibers. The epoxy resin is then sent to Olin which can process it into “virgin-grade” epoxy, Ekstrand said.

The process uses inexpensive, non-toxic chemicals that are readily available in large quantities, she added. “We expect this to be a low energy consuming, low CO2-emitting technology.”

The company remains tight-lipped on further details, including the chemicals involved and how many times the process can be repeated.

Ekstrand said they are filing patents and the plan is eventually to license it to other companies.

So far, Vestas has tested the technology in a lab but is now building a pilot facility to test it on a bigger scale for two years, after which it hopes to commercialize it.

Gummy bears from turbine blades

Vestas is far from the first to try to tackle this knotty problem. Companies and scientists have been working on different approaches for years, although many potential solutions are nascent or remain small scale.

One approach is to grind blades up and use the material in other industries. The downsides are that the enormous blades are tricky to transport and crush. “Because the material isn’t worth very much, it’s not really worthwhile doing it,” Barlow said.

But some companies say they’re making it work.

Veolia, a resource management company headquartered in France, turns old blades into an ingredient for cement production.

It shreds, sorts and blends blade materials before sending them to cement kilns. Using this blend reduces the planet-heating pollution produced in cement manufacturing by 27%, according to Veolia. The program has processed 2,600 blades so far.

Carbon Rivers, a Tennessee-based company, has worked with the US Department of Energy to help scale up its “pyrolysis” technology – a form of chemical recycling that uses very high heat in an oxygen-free environment.

What's killing whales off the Northeast coast? It's not wind farm projects, experts say

The company’s process produces glass fibers, which can then be used in new wind turbine blades, as well as in the automotive and shipping industries, it says. It also produces oil that can be used in energy production, David Morgan, chief strategy officer at Carbon Rivers, told CNN.

The technology allows them “to fully and completely upcycle wind turbine blades” in a process that is “net positive energy,” Morgan added.

Carbon Rivers has so far upcycled 41 blades weighing 268 tons and is building recycling facilities and with the aim of scaling up to more than 5,800 blades a day.

Other efforts focus on changing the materials used to make turbines, to create a new generation of blades that are easier to recycle.

In 2022, researchers at the University of Michigan announced they had made a new resin for blades by combining glass fibers with a plant derived polymer and a synthetic one, which could be recycled into ingredients for products, including new turbine blades, laptop covers, power tools – and even gummy bear candies .

'Beginning of the end' for fossil fuels: Global wind and solar reached record levels in 2022, study finds

“We recovered food-grade potassium lactate and used it to make gummy bear candies, which I ate,” John Dorgan, a professor of chemical engineering at Michigan State University, said in a statement.

For those concerned about eating an old turbine, Dorgan said: “A carbon atom derived from a plant, like corn or grass, is no different from a carbon atom that came from a fossil fuel. It’s all part of the global carbon cycle, and we’ve shown that we can go from biomass in the field to durable plastic materials and back to foodstuffs.”

Of course, this won’t help with the blades being decommissioned now.

The reason Vestas’ discovery could be so compelling, said Barlow, is that it’s promising a process to recover reusable materials from current turbine blades, without using noxious chemicals and huge amounts of energy. “That’s a real winner,” she said.

Now the company has to scale up.

“There will be all sorts of problems which they haven’t conceived of. So it may be slow, but this is a good starter for ten,” Barlow said.

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10 major engineering challenges of the next decade

1. Upgrading the sagging U.S. infrastructure. The American Society of Civil Engineers gives our aging infrastructure a D+ grade and estimates that $3.6 trillion dollars must be invested by 2020 to bring our roads , bridges , water , electrical and sewage systems to proper safe working order.

2. Educating first world engineers to understand how to solve third world problems . The Renewable Resources Journal reports that the world’s population will grow by 2 billion over the next two decades, 95% of this in developing or underdeveloped countries. Engineers must learn new ways to solve problems in these countries.

3. Promoting green engineering to improve sustainability and reduce the carbon footprint in manufacturing . According to the U.S. Office of Energy Efficiency & Renewable Energy, manufacturing in the U.S. produced 19,237 trillion BTUs and 1,071 million metric tons of carbon dioxide .

4. Identifying viable alternative energy sources. The contributions to our energy production from renewables and other new fuel sources are growing at 6% per year according to BP and will contribute 45% of the increment in energy production by 2035.

5. Rethinking how the city looks and works. 54% of the world’s population lives in cities. Europe leads the way in sustainability , with seven out of the world’s top 10 most sustainable cities, according to the ARCADIS Sustainable Cities Index.

6. Making STEM more appealing to young students. By 2018, the United States will have more than 1.2 million unfilled STEM jobs. Meanwhile, according to a UCLA study, 40% of students enrolled as STEM majors switched subjects or failed to get a degree.

7. Safeguarding our personal data and wealth from cyberattacks . 34% of data breaches happen at financial institutions; 11% target retail companies; while 13% target government institutions , according to the 2014 Data Breach Investigation Report.

8. Addressing climate change through engineering innovation. Six of the 10 cities with the largest annual flood costs by 2050 are in India and China. Three are in the U.S.: New York, Miami and New Orleans.

9. Feeding our growing population through cutting-edge bio-engineering and agricultural innovations . The U.N. warns that we must produce 60% more food by 2050 to keep up with demand, but how do we do this sustainably? Food and water access will be major issues in the future, and research must begin now.

10. Improving our health and well-being through life sciences, nanotechnology & bio-engineering . Administration on Aging, by 2060 the population of Americans aged 65 and older will have more than doubled in size from 2011. This puts a lot of pressure on new drug creation and also on innovative engineering techniques to deliver drugs .

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100+ global problems worth solving

Of course this list is far from being complete. It’s just a tiny start.

CONTRIBUTE And you can add to this list of “global problems worth solving” on our Google Drive . Feel free to add yourself to the contributor list. Do not spam it – please. We will update this post once in a while.

(1) Building a platform that collects problems, anybody can contribute and be curated by the community.

ENVIRONMENT

(2) Inventing new material or techniques to replace plastic (3) Inventing new techniques, and materials to replace paper (4)Inventing new techniques and products, recycling any given material (5) Inventing new materials replacing plastic bottles and cups (6) Creating new ways to package food (100’s of varieties of food) environmentally friendly (7) Finding artificial, yet environmentally friendly replacement for wood to reduce deforestation (8) Inventing new motors that neither use electricity nor fuel

(9) Finding ways to augment education in conventional schools and universities with highly relevant education (10) Creating social education programs that can run in parallel to schools, universities or jobs (11) Offering classes for undergrads, how to get successful and rich (12) Providing better base education programs on political know how (13) Providing better education programs on the general concept of economies (14) Providing better education on how wars are started and how peace is achieved and maintained today (15) Creating more tangible lifelong learning concepts (16) Creating more universally applicable career guidance mechanisms or platforms (17) Creating solutions to shift from an “all learn – all work” model to a more balance model

(18) Exploring new ways to generally reduce and safe energy (19) Providing a more transparent and plausible energy consumption prediction for the scenario that most people on earth are out of poverty, living in newly developed countries (20) New ways to harvest energy from bio thermal energy sources (21) New ways to harvest solar energy (22) New ways to harvest hydro energy (23) Finding ways to transmit energy created on the moon, down to earth (24) Identifying new ways to harvest energy from unidentified sources (25) Finding all new ways to store electric energy in bigger volume and less in size and weight (26) Smart energy re-distribution for those who produce excess energy that can be provided to others

PRODUCTS & TECHNOLOGY

(27) Lower cost reliable Internet connections (28) Independent and reliable “News & Information Publishing” organization (29) Better, social media integrated search engines (30) All new and modern operating systems (31) Fully integrated business application tools (32) Meteorology technology provider not only for weather forecasts but for everything agricultural (33) Generally available intelligent traffic lights, connected to a traffic flow system, but autonomous features (34) Low cost mini satellites to explore earth and space, provide data hubs, accessibility and more (35) Omnipresent, inexpensive and easy mobile payment system (36) Building robots for all kinds of dedicated tasks such as cleaning shoes, planting crops, cleaning windows, etc. (37) The whole range of wearable products counting, watching, recording, measuring all kinds of things underway (38) Situation dependent automatically changing materials to turn a lofty t-shirt into a rain covering shirt (39) Smart materials that change their behavior based on environmental conditions i.e, taking the carbon out of carbon dioxide and returning the dioxide back to air (40) Smart Contract development for cryptocurrency agnostic blockchain like media (41) Universal low voltage power connection system that handles everything from a single wall plug to staggering distribution (42) Creating universal ultra small IOT devices that allows any product to be programmed by a smartphone including remote controls, refrigerators, heaters, air conditioner, lights – anything. One interface for any product in the future. (43) New better zipper that do not stuck, break or derail WATER & SANITATION

(44) New ways to get to clean water (45) Better ways to turn salt water into sweet water (46) New ways to manage waste water in rural areas (47) Cheaper ways to produce sanitation products i.e. toilets (48) All new toilette models alleviating paper use (49) More efficient ways for flushing toilets than using precious water (50) New product for cleaning replacing bathtubs and showers or make their use a less used luxury (51) More water consumption sensitive products such as water cranes, showers, garden watering systems

FOOD & DIET 

(52) New ways to offer unified insights into the ingredients of food in any supermarket (53) Ways to eradicate factory farming (mass animal farming) (54) More scientifically proven and generally understood advice to a healthy diet (55) New ways to provide food portions in smaller sizes to stimulate reduction of food consumption and reduction of food waste RESEARCH, DATA & INFORMATION

(56) Finding new ways to research all the facts and sources of climate change (57) Finding new ways to deal with climate change and leverage the development so far (58) Finding ways to predict climate change more precisely for the next 50 years and provide meaningful indications for the agricultural industry (59) Better ways to organize research in general, creating more unbiased data. (60) Catalog of things that could be done with AI and inspires developer (61) An AI development system that could be used by virtually anybody (62) Research for a more rational view of the evolving powers of Artificial Intelligence (63) Creating algorithms that focus on environmental dependencies of new technologies (64) Identify new ways that help certain countries to get off of the data protection hysteria (65) New suggestions for data privacy models that give more power to the individual (66) Developing ways to deal with the general risk of eradicating life through asteroids (67) Developing scenarios to evacuate earth if needed, even though we would probably take 1,000 years to find the technical possibilities. (68) New tools and platforms to interact with governments and communities (69) New apps that cover all of the problems, allow to contribute in all kinds of ways and see reports (70) 3-D printing companies, producing unique products, spare-parts, artificial organs, and more (71) Cyber security improvements to significantly reduce or even alleviate hack attacks (72) Data ownership mechanisms, rules and technology that makes sure that personal data are controllable by its owner

(73) Providing better technology for customer experience management (74) Providing a new value system for corporate balance sheets involving employee contribution (75) Providing new ways to offer equity to highly innovative employees (76) Develop new systems that can track the degree of innovation development (77) Design new systems for customer interaction with corporations (78) Design new corporate employee education systems including lifelong learning (79) Create a fortune 100,000 leader board with indexes addressing environmental, employee and other key aspects (80) Creating all new insurance business models that provide much more contract transparency and easier to deal with (81) Online grocery stores with home delivery like a few in Germany or Switzerland (82) New media business models, disrupting the user unfriendly monopolies (83) Much easier booking systems for public transportation anywhere in the world (84) Creating systems that alleviate waiting (in line, at doctors, at shops, at bus stops….)

(85) More effective ways to deal with birth control in times where we help more people to survive (86) Starting large scale research that can only be done with tens of thousands of supporters (87) Finding better ways to deal with migration, integration and return mechanisms (88) Finding ways to replace prisons with socially effective methods of societal reintegration (89) Finding new policies to deal with people ignoring the generally accepted rules of societal coexistence (90) Finding solutions to get to a broader reach of well being for all humans (91) Developing new political concepts or new varieties of democracy that is more applicable in today’s world (92) Developing new job concepts for people who work on social or macro economic solutions to be financed (93) Developing new concepts for city creation addressing the bigger problems of today’s cities (94) Developing new and holistic ways to reduce traffic congestion in larger cities (95) Developing new logistical concepts to bring the huge amount of products directly to the citizens (96) Developing new techniques to transport the remaining waste to the designated areas without the current waste disposal chain (97) Finding new methods to alleviate corruption in government and other large organizations (98) Finding new mechanisms to make governments more accountable, providing rewards and punishment solutions based on their achievements relative to their promises

(99) New ways to provide a more balanced healthcare for the various developed nations (100) New ways to provide healthcare in the first place for developing nations (101) New ways for mental health care (102) New ways to produce cheaper medicine or secure living without medicine

This list of “global problems worth solving” will sooner or later grow much bigger. We are looking forward to your inputs.

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How To De-Risk Supply Chains In An Unpredictable World

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Supply chain collaboration is one of those every day business terms that’s easy to dismiss until a catastrophic disruption strikes like material shortages, product design flaws, production delays, and more. But what if organizations across the supply chain could quickly huddle to pinpoint problems and take action together, staving off anything from minor setbacks to potential disaster? This is the concept behind Inspectorio , a cloud-based solution designed to help suppliers, manufacturers, brands, and retailers work together to reduce supply chain risk through digitalized quality management, ESG compliance, production tracking, and lab testing.

After digitalizing manual product inspection activities on Inspectorio, organizations have averaged 95% time savings in administrative data entry, and 100% time savings in reporting.

“Automating activities on a centralized data platform helps companies make fast and strategic adjustments in a way that is incredibly collaborative with their supplier base,” said David Klein, president and co-founder of Inspectorio. “Organizations can become more agile and resilient to supply chain disruptions, able to shift sources, product materials, and production locations to address problems and improve productivity and efficiencies.”

After digitalizing manual activities on Inspectorio, Klein said that organizations have averaged 95% time savings in administrative data entry, and 100% time savings in reporting. Customers have improved quality pass rates by approximately 8% on average. Some have reduced defect rates by 14% on average.

Digitizing quality control for accuracy and efficiency

Quality management spans numerous groups, including factories that conduct self-inspections and third-party inspectors who visit facilities. According to Klein, digitizing quality management activities helps suppliers, retailers, and others work together on standardized quality control. Inspectorio incorporates artificial intelligence to monitor facility risk, leading to valuable business insights and cost-savings.

“With data integrity, you can better understand your supplier base and benchmark their performance,” said Klein. “When you designate factories and products by risk factor, you can adapt quality controls appropriately. For example, maybe lower-risk factories can manage self-inspections on their own. High-risk factories producing high-risk products require tighter controls. Over time, you're able to maximize your resources and lower costs while increasing quality outcomes.”

Antidote for sustainability audit fatigue

Rising sustainability regulations are also stressing modern supply chains. Centralized data gives companies and their partners a single view into accurate information for informed decisions. Regulations are constantly changing by in-country policymakers, spanning an ever-expanding circle of partners and auditors across the supply chain.

“Many customers experience audit fatigue because they track and report the same data for multiple partners and regulators,” said Klein. “Inspectorio helps centralize ESG-related information, allowing companies to capture and act on a holistic understanding of sustainable performance metrics. The data helps organizations better assess risk, manage corrective actions with suppliers along the value chain, and prove regulatory compliance as they often produce goods in one part of the world for commercialization elsewhere.”

From boutique sourcing to global supply chain power

Inspectorio’s roots are in a Latin American-based boutique sourcing startup that Klein co-founded with his current partners. As the original startup grew, customers added quality activities to the scope of work. After experiencing first-hand the inefficiencies of manually collected data that was disconnected from performance-based metrics, Klein said the team decided to build a digital inspection management solution.

“When our clients received inspection reports in hours instead of days, and saw the performance of their far flung facilities in one dashboard at the click of a button, we knew that we were on to something very special and powerful,” said Klein. “We have expanded the digitalization of quality inspections to automation that supports sustainable business and production.”

SAP.iO teamwork builds expertise

Inspectorio participated in the Sustainability in Retail and Consumer Industries cohort of SAP.iO Foundry New York, the company’s global network of B2B startup accelerators. Klein appreciated the practical go-to-market advice he received from SAP experts, as well as the opportunity to develop targeted use cases where Inspectorio can complement the company’s solutions, including SAP S/4HANA .

“We found the experience with SAP.iO particularly informative and inspiring because supply chains are all about teamwork – no single company can solve problems on its own,” said Klein. “Our capabilities can be integrated with quality and sustainability-related data from customer purchase orders in the SAP system.”

Inspectorio is available on the SAP Store .

Supply chain resilience from intelligent data

Supply chain management data transparency is valuable in a turbulent market. Inspectorio has assembled a noteworthy database of information capturing root causes of quality and sustainability-related problems, along with effective preventive and corrective actions. Looking ahead, Klein saw new possibilities in using that data intelligence for business value.

“We can help companies build best-in-class quality, sustainability, compliance, and production programs layering intelligent predictions and suggestions on top of data from our centralized platform,” said Klein. “Think of it as a company’s smart intelligent advisor, able to offer predictive and prescriptive guidance from a global supply chain management playbook of real-world scenarios.”

Learn more about the SAP.iO Foundries program supporting B2B technology startups worldwide.

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Top Problems in the World That Can Be Solved

Top Problems that can be Solved

The Copenhagen Consensus Center, a think tank that researches the smartest solutions to global issues, organized a panel of five distinguished economists in 2012 to set priorities for fighting the 10 top problems in the world that can be solved:

• Armed Conflict
• Chronic Disease
• Infectious Disease
• Population Growth
• Biodiversity
• Climate Change
• Hunger and Malnutrition
• Natural Disasters
• Water and Sanitation

The panel was asked to describe the best ways to advance global welfare, specifically that of developing countries. The experts then assembled a prioritized list of thirty solutions.

Solutions to the World’s Issues

The number one solution was “bundled interventions to reduce undernutrition in pre-schoolers” and addressed the challenge of hunger and education. Some other proposals high on the list were subsidies for malaria combination treatment and expanding childhood immunization coverage.

The group of experts covered topics besides health, with solutions ranging from investing in early warning systems for natural disasters to increased funding for green energy.

With this list in mind, world leaders at the U.N. Sustainable Development Summit adopted the 2030 Agenda for Sustainable Development in Sept. 2015. On Jan. 1, 2016, the 17 Sustainable Development Goals (SDGs) replaced the eight Millennium Development Goals of 2015.

The new 17 SDGs were to:

• End poverty
• End hunger and improve nutrition and sustainable agriculture
• Promote well being for all ages
• Ensure equitable and quality education
• Achieve gender equality
• Ensure water and sanitation for all
• Ensure access to modern energy for all
• Promote sustainable economic growth and productive employment
• Build resilient and innovative infrastructure
• Reduce inequality
• Make settlements safe, resilient and sustainable
• Ensure sustainable consumption and production patterns
• Take urgent action to combat climate change
• Conserve and sustainably use Earth’s water
• Promote sustainable use of terrestrial ecosystems and forests, and halt and reverse land degradation and biodiversity loss
• Promote peaceful societies, provide access to justice and build effective, accountable institutions
• Implement and revitalize the Global Partnership for Sustainable Development

A New Set of Problems

80,000 Hours, an independent nonprofit organization that researches how graduates can make the biggest difference possible with their careers, came up with another list defining problems in the world that can be solved. Drawing from research from groups such as the University of Oxford’s Future of Humanity Institute and the Copenhagen Consensus Center, 80,000 Hours created a framework to rate global issues.

The organization based its scoring on how solving the problem would reduce the risk of extinction , raise the global economic output, increase the income among the world’s poorest 2 billion people and save years of healthy life. It also used factors like the amount of good done compared to the percent of the problem solved and the number of resources required.

Risks from artificial intelligence topped 80,000 Hours’ list  out of 11. Also on the list were biosecurity, developing world health and climate change. Other issues 80,000 Hours has yet to rate include science policy and infrastructure, cheap green energy and promoting human rights. The group indicates that improving health would be more beneficial than topics like empowering the poor and education.

Due to how differently each solution overlaps with others there are various ways to rank a list of top problems in the world that can be solved. Thankfully, experts are doing their best to target issues to focus on and world leaders are taking calculated steps to implement solutions to such issues.

– Connie Loo

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Feinstein Suffered More Complications From Illness Than Were Publicly Disclosed

Senator Dianne Feinstein, 89, whose recent bout with shingles included contracting encephalitis, is frailer than ever. But she remains unwilling to entertain discussions about leaving the Senate.

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By Annie Karni and Carl Hulse

Reporting from Capitol Hill

When she arrived at the Capitol last week after a more than two-month absence recovering from shingles, Senator Dianne Feinstein, Democrat of California, 89, appeared shockingly diminished.

Using a wheelchair, with the left side of her face frozen and one eye nearly shut, she seemed disoriented as an aide steered her through the marble corridors of the Senate, complaining audibly that something was stuck in her eye.

Ms. Feinstein’s frail appearance was a result of several complications after she was hospitalized for shingles in February, some of which she has not publicly disclosed. The shingles spread to her face and neck, causing vision and balance impairments and facial paralysis known as Ramsay Hunt syndrome . The virus also brought on a previously unreported case of encephalitis, a rare but potentially debilitating complication of shingles that a spokesman confirmed on Thursday after The New York Times first revealed it, saying that the condition had “resolved itself” in March.

Characterized by swelling of the brain, post-shingles encephalitis can leave patients with lasting memory or language problems, sleep disorders, bouts of confusion, mood disorders, headaches and difficulties walking. Older patients tend to have the most trouble recovering. And even before this latest illness, Ms. Feinstein had already suffered substantial memory issues that had raised questions about her mental capacity.

The grim tableau of her re-emergence on Capitol Hill laid bare a bleak reality known to virtually everyone who has come into contact with her in recent days: She was far from ready to return to work when she did, and she is now struggling to function in a job that demands long days, near-constant engagement on an array of crucial policy issues and high-stakes decision-making.

In the statement provided after The Times’s article was published on Thursday, Ms. Feinstein’s spokesman acknowledged that the senator continued to suffer the effects of Ramsay Hunt syndrome. Her office declined to comment further for this article, beyond a statement from Ms. Feinstein saying: “I’m back in Washington, voting and attending committee meetings while I recover from complications related to a shingles diagnosis. I continue to work and get results for California.”

Many people close to Ms. Feinstein, a six-term senator, described seeing her operating in the Senate in her current state as “frightening,” a tragic end to a formidable career in politics that they worry is casting a shadow over her legacy and her achievements. More immediately, it has resurfaced questions about whether Ms. Feinstein, who has announced she will retire when her term ends in January 2025, is fit to continue serving even for that long.

Ms. Feinstein, a pioneering woman in Democratic politics who was once a major party power broker and a legislative force in the Senate, has stubbornly refused to consider leaving. The same force of will that led her nearly a decade ago to resist pressure from the Obama administration to keep secret a damning torture report still rears its head when she is confronted with calls to step down. The senator still sees the job as her calling and is no more receptive to a conversation about stepping aside than she was in 2018, when she decided to seek another term despite questions about her mental acuity.

People close to her joke privately that perhaps when Ms. Feinstein is dead, she will start to consider resigning. Over the years, she and many Democrats have bristled at the calls for her to relinquish her post, noting that such questions were rarely raised about aging male senators who remained in office through physical and cognitive struggles, even after they were plainly unable to function on their own.

But after her latest illness, even some of Ms. Feinstein’s longtime allies have grown deeply uneasy about her situation.

“I admire the senator deeply, and I am sorry she is so not well,” said Susie Tompkins Buell, a major Democratic donor and a longtime Feinstein supporter. But she added: “The Senate has critical, challenging work to do, and as the stakes are so high and she is not able to be present, to be informed and active, let alone have the rest she needs in order to recover, I feel she needs to step down. And yet she isn’t willing in this state of mind.”

Ms. Buell said Senator Chuck Schumer, Democrat of New York and the majority leader, or Gov. Gavin Newsom of California, who would appoint a successor should Ms. Feinstein resign before the end of her term, have “the responsibility to do something.”

Neither has directly implored her to leave, as the senator has deflected almost every effort to have a serious discussion about her future.

At home in San Francisco during her recovery, Ms. Feinstein refused to have contact with California lawmakers who tried checking in with her. A call from Mr. Newsom on her personal phone was answered by an aide and went unreturned. An offer of an in-person visit from Senator Alex Padilla, Democrat of California, was flatly rejected. Even some family members who wanted to see her were turned away.

Throughout her latest health ordeal, Ms. Feinstein remained adamant about her need to return to work. She agitated to return to Washington as pressure mounted for her to step aside or physically show up to vote so that Democrats could advance President Biden’s judicial nominees and move ahead with their agenda in the closely divided Senate.

One person whose call she would take was Mr. Schumer, who in multiple conversations with Ms. Feinstein encouraged her to listen to the advice of her doctors. But when it became clear that she had no desire to discuss leaving office, Mr. Schumer began planning for her to return to Washington, according to several people familiar with the conversations.

“After talking with her multiple times over the past few weeks, it’s clear she’s back where she wants to be and ready to deliver for California,” Mr. Schumer said in a statement on the day of Ms. Feinstein’s return. He greeted her in front of the Capitol as an aide helped her from a car into her wheelchair.

With Ms. Feinstein’s return, Senate Democrats were able to advance three of Mr. Biden’s judicial nominees whose approval by the Judiciary Committee had been delayed because of her absence, which deprived her party of the majority it needed to move forward in the face of Republican opposition. Democrats greeted her in the committee with a standing ovation.

But Ms. Feinstein appeared confused about the warm greeting when a small group of reporters asked about it days later.

“I haven’t been gone,” she said . When pressed on whether she meant that she had been working from home, she pushed back in a manner that suggested she might not have been aware of her long and politically charged absence. “I’ve been here,” she said, appearing to grow agitated. “I’ve been voting. Please, either know or don’t know.”

Aides who themselves have come under criticism for allowing her to continue in her current state described Ms. Feinstein as still engaged and ultimately in charge of decisions that come out of her office. She reviews and approves work that her staff brings her, they say, and they do not shield her from the toughest news clips about her condition and the calls for her to step aside. But they have also acknowledged that she is not fully up to her senatorial duties; Ms. Feinstein has missed several votes since her return, and aides issued a statement saying she would be working on a “lighter schedule” given her continuing health challenges.

Ms. Feinstein flew on a chartered private plane last week to return to Washington, accompanied by her dog, her longtime housekeeper and Nancy Corinne Prowda, the eldest daughter of Representative Nancy Pelosi of California, the former House speaker who has been a longtime friend of Ms. Feinstein’s and has been practically living at her house during her recovery.

The senator’s relationship with Ms. Pelosi’s daughter goes back decades. The Pelosi family grew up across the street from Ms. Feinstein, people close to her said, and Ms. Prowda has been close with Ms. Feinstein since she was a child, looking up to her as a maternal figure.

But the senator’s condition and the political drama surrounding her fate has drawn so much scrutiny that even the presence of one of her closest friends during her convalescence has drawn speculation. Some have read Ms. Prowda’s involvement as a tacit endorsement by Ms. Pelosi of Ms. Feinstein’s decision to stay on, reasoning that it could give Representative Adam B. Schiff, Democrat of California and Ms. Pelosi’s chosen candidate in the crowded race to replace Ms. Feinstein in 2024, a leg up. Mr. Newsom has committed to appointing a Black woman to the seat should it become vacant.

But Ms. Prowda is not involved in politics at all and is as close to Ms. Feinstein as family.

Since Ms. Feinstein’s return to Washington, several of her colleagues have privately acknowledged that she is obviously diminished. She should probably not be in the Senate, they said, though Democrats are happy to have her vote when she can.

Ms. Feinstein was ailing before her latest setback. For years, she has sometimes struggled to recall the names of colleagues, frequently had little recollection of meetings or telephone conversations that just took place, and at times walked around in a state of befuddlement. Some lawmakers who have interacted with her have come away with serious concerns that she is mentally incompetent to serve. Others have hung up the phone after conversations in which she repeated the same comments several times in a row with no apparent awareness that she was doing so.

Shingles can potentially contribute to cognitive decline in a number of ways, including by damaging blood vessels of the brain, said Dr. Sharon E. Curhan, a physician and epidemiologist at Brigham and Women’s Hospital and Harvard Medical School who is studying the link between shingles and changes in cognition.

But there are few people in Ms. Feinstein’s circle who can persuade her that it is time to step down. A longtime friend, former Representative Ellen Tauscher of California, who was known as a “Feinstein whisperer,” died in 2019. Her husband, Richard C. Blum, passed away last year, a major setback for Ms. Feinstein.

Some current and former colleagues said the situation was alarming to watch and blamed Senate Republicans — who blocked Ms. Feinstein’s request for a temporary replacement on the Judiciary Committee — for upsetting images and sound bites of an infirm and confused senator trying to navigate the Capitol.

“Republicans are responsible for this nightmare scenario that’s unfolding,” said former Senator Barbara Boxer, who made history with Ms. Feinstein in 1992 as the first female senators elected from California. “I am sick at heart at that. I blame them for being mean to her and spinning it to blame the Democrats.”

Shawn Hubler contributed reporting from Sacramento, Thomas Fuller from San Francisco, and Benjamin Mueller from New York.

An earlier version of this article misstated the end date of Senator Dianne Feinstein’s current term. It is January 2025, not 2024.

How we handle corrections

Annie Karni is a congressional correspondent. She was previously a White House correspondent. Before joining The Times, she covered the White House and Hillary Clinton's 2016 presidential campaign for Politico, and spent a decade covering local politics for the New York Post and the New York Daily News. @ AnnieKarni

Carl Hulse is chief Washington correspondent and a veteran of more than three decades of reporting in the capital. @ hillhulse

Screen Rant

Thor 5 being darker doesn't actually solve the mcu's biggest problems.

Thor 5 could be a far darker movie than previous Thor installments - but this doesn't actually solve the series' problems, or the wider MCU's.

Thor 5 could well be darker given reactions to Thor: Love & Thunder - but this wouldn't necessarily help the MCU's biggest problems with the character, and its tone overall. The Thor series has received some of the most complicated reception of the MCU's main movie roster, with reception for the first two Thor movies being mixed, the reception for Thor: Ragnarok being positive, and then the reaction to Love & Thunder also seeing more criticisms steep back in. Though all of the series maintains a relatively positive score on Rotten Tomatoes, it is notably the lowest MCU series Rotten Tomatoes average, which strongly suggests changes need to be made in the future.

In many ways, the criticisms of Thor: Love & Thunder are emblematic of larger issues within the MCU. One of the major shared complaints between Thor: Love & Thunder and the MCU in general is an overly comedic tone, meaning it would make most sense to ensure the next installment is a darker movie - especially since Chris Hemsworth also wants a Thor 5 tone change . However, while this would alleviate a major criticism for the next Thor movie, it wouldn't automatically fix things either.

Related: Thor 5: Story, Setting, Cast, & Everything We Know

Thor 5 Being Darker Only Solves The Comedy Thor Issue

A lot of Thor: Love & Thunder was either set-ups for jokes, or the jokes themselves, which divided audiences. Thor 5 's potential tone problems in terms of following Love & Thunder would be solved by a darker movie, but the perception of the most recent MCU Thor being too comedic isn't where the battle starts or ends. Love & Thunder 's more serious Gorr scenes also received flack, and while part of this was the tonal whiplash reported by viewers, a chunk of criticism was also directed at the lack of real set up for the character, and a lack of time dedicated to Gorr and Thor's dynamic, despite how emotionally impactful their intertwined comic storyline is.

Thor 5 can begin to address all of these issues, and create a new path for the hero. However, it can't change previous movies' stories, and with Gorr's death in Thor: Love & Thunder , there's a limit to how much it can resolve, especially regarding people's current complaints about Thor and his place in the universe. This is something the larger MCU also has to navigate, as previous movies have created complicated scenarios to address - like the Hulk's somewhat stagnant MCU story compared to other heroes - which need to be course corrected now, or else they risk becoming bigger problems down the line.

If Thor Isn't Funny, What Is He? The MCU Has No Real Idea

Making a more serious Thor 5 comes with many benefits, but also creates a new problem for the MCU, in that the franchise's iteration of the character has always been an inherently comedic figure. As such, the challenge for a darker Thor movie is twofold, as it has to recalibrate the character and decide what he will look like from that point of the MCU, but do so in a way that audiences don't find a jarring alteration of a beloved figure. This is vital, as Thor would pave the way for other characters who will also need to change tone or purpose in the MCU's new era.

Key Release Dates

The marvels, captain america: new world order, marvel's thunderbolts, marvel's fantastic four, avengers: the kang dynasty, avengers: secret wars.