How the number 15 solved a longstanding math challenge

It took 70 years for computer scientists to determine how to cut a cake fairly

The cake-cutting problem explores how to divide something fairly, which is not solely about cutting evenly-sized pieces. A protocol that accounted for personal preferences (e.g., a corner piece) between just three people took 16 years to develop.

Figuring out how to get a sofa around a corner has been a math problem since 1966

A sofa with the largest possible area that can make a 90-degree turn is known as Gerver's sofa, named after the mathematician who determined the shape in 1992. In 2025, a 119-page paper provided the proof confirming this shape.

A 14-year-old "human calculator" shatters six mathematical world records in one day

A teenage prodigy from Maharashtra, India named Aaryan Shukla set the record for the fastest time to mentally add 50 five-digit numbers. He did so in just 25.19 seconds–roughly equivalent to one addition every 0.5 seconds. The math whiz said he practices calculations for around five to six hours a day.

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

Explore over 30,000 Olympiad-level math problems

Users can browse questions from 47 countries and 17 languages, sorted by topic across categories that include algebra, geometry, discrete mathematics, and number theory. Each problem is accompanied by at least one solution, with both authored in LaTeX that can be copied over to other platforms.

Mathematicians often solve problems using wordless mental processes

It's a common technique among expert mathematicians, where thinkers rely on intuition, blurry perceptions and subconscious work—no writing, no formulas. The state is distinct from daydreaming, and often relies on sudden illuminations stemming from extended periods of subconscious reflection.

The Millennium Prizes were created to spur solutions to seven unsolved problems

In 2000, the Clay Mathematics Institute brought public attention to the frontiers of mathematics by establishing $1M prizes for some of the most challenging problems mathematicians faced. As of 2025, only one problem has been solved, but the reward was turned down.

Traffic flow can be improved through research into card shuffling

Card-shuffling mathematics has been applied to solving problems in biology to estimate the evolutionary distance between organisms and in computer science to determine the optimal distribution of files and folders in databases.

The Koch snowflake has an infinite perimeter enclosing a finite area

Counterintuitively, although it would be impossible to build a fence along the edges of the shape because it would require an infinite amount of materials, this perimeter can be contained in a larger shape with a finite perimeter and limited area. This is equivalent to enclosing an infinitely long spiral that never reaches the center within a circle.

One reason Americans are bad at math

The president of Barnard College explains why we need to better understand the links between math anxiety, math avoidance, and the US’s dismal test scores.

It took a month for the Rubik's Cube inventor to solve the cube

The Rubik's Cube is the most popular puzzle toy in the world, with over 350 million sold since its invention in 1975. Originally created as a tool to teach three-dimensional movement, the colorful problem-solving game skyrocketed in popularity, spawning speedcubing competitions and becoming a fixture of global toy culture.

Test your gerrymandering skills with this interactive game

This simulation demonstrates how packing and cracking alter election outcomes. See how shifting district lines can change representation—regardless of the overall makeup of the electorate.

The odds of a perfect March Madness bracket are worse than finding one specific grain of sand on Earth

With 63 games to predict, random guessing produces odds of 1 in 9.2 quintillion. Even an informed picker who gets 67% of games right faces odds of about 1 in 120 billion, meaning if every American filled out a unique bracket, we'd expect a perfect one in roughly 366 years.

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

Efforts to find Majorana particles may finally lead to reliable quantum computers

Though the particle—which is its own antiparticle—remains theoretical, scientists from Microsoft to Google continue developing systems to mimic this property towards building error-resistant quantum computers. Scientists at UCSB have been attempting to get the particle using just pencil lead and Scotch tape.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Five charts that changed the world

Data visualization helps us understand the world, providing a powerful way to communicate complicated information in a quick and efficient way. There are many different ways to create graphs, and these five examples—the pie chart, geographic dot...

Tetrachromacy allows humans to observe 10 times the normal amount of colors

Resulting from a mutation on the X chromosome, the rare genetic condition causes individuals to possess an additional type of photoreceptor cell, typically sensitive to the orange range, located between the standard red and green cones. This enables the perception of approximately 100 million colors.

The 15-minute city lets residents meet their daily needs within 15 minutes on foot

Many cities have been designed with inefficient layouts that waste time and lower the quality of life of those who live there. In the 15-minute city, essential services—including work, food, education, and health—should all be located within a short walk or bike ride from where people live.

The missing continent that took 375 years to find

It took scientists 375 years to discover the eighth continent of the world, which had been hiding in plain sight all along. But mysteries still remain.

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

The mathematically correct way to tie your shoes

Tying shoelaces involves three important decisions that determine whether a good knot (reef knot) or a bad knot (granny knot) is formed. The first decision is to criss-cross and tuck the laces, either with the left lace over the right or the right...

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

'No big challenge has ever been solved, and no lasting improvement has ever been achieved, unless people dare to try something different.'

- Apple CEO Tim Cook (1960 - present)

Electrical grids worldwide must double their power delivery capacity by 2050 to meet surging demand from AI and electric vehicles.

The long-lost art of coded postage stamps

In the 1800s, the postcard was a relatively new phenomenon, as was the post office. In the burgeoning system, recipients of mail had to sometimes pay prohibitively costly fees to receive it. So to get around the fees, a system of placing stamps on the envelopes in specific ways to communicate—a simple yes or no—was devised by clever mailers and expanded and codified by postcard companies into guides. Learn about the fascinating system here.

Chess is played on an 8×8 board with 16 pieces per side

Chess begins with two players facing off on a checkered 64-square board. Each controls 16 pieces—king, queen, rooks, bishops, knights, and pawns—with the goal of checkmating the opposing king.

13 unconventional ways to stay cool during heat waves

While air conditioning is the default solution for many in a heat wave, it can get expensive while requiring the consumption of fossil fuel energy. So, how else can you stay cool during a heat wave? This list compiles some practical, at times quirky, suggestions, including an ice-pack-filled aubergine hat.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Cells cannot grow forever due to escalating inefficiency in transporting chemicals

As cells get larger, their volume grows much faster than the surface area through which nutrients and waste products pass, creating a bottleneck that eventually causes cells to die. This forces nearly all organisms visible to the naked eye to comprise enormous numbers of smaller cells, such as the approximately 30 trillion found in the average adult human.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

Explore our favorite visualization of the immense scale of space, from an astronaut to the size of the observable universe

Explore fun facts from the USPS, including unique post office buildings, a stamp that traveled past Pluto, and more.

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

Larger animals like giraffes, elephants, and blue whales have developed a unique defense against cancer, a phenomenon known as Peto's Paradox

See how fireworks are made and learn how metals like magnesium and copper are responsible for different colors.

Exploring the Larry Bird punch that almost changed March Madness

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'

Mid-century modern graphic designers, known for their bright colors and bold lines in advertising, also found success with children's books.

Dorothy's famous entrance into Oz in 'The Wizard of Oz' relied on analog tricks, including a body double and sepia-toned paint, as much as it did on technology

Double world record holder Hunter Ewen helped conquer his fear of balloons, called globophobia, by training to win Guinness World Record titles for balloon inflation.

In 2026, Finland was named the world's happiest country for the ninth consecutive year based on its wealth, social safety network, and high life expectancy, among other factors.

Up to a million Girl Scouts sell about 200 million cookie boxes every spring, generating $800 million, largely because refusing a child is frowned upon

Use this tool to calculate the dollar value of your parental mental load, from meal planning to coordinating after-school care, then see resources that help generate solutions.

In 1963, a basement renovation in Turkey revealed a passageway to a hidden, multilevel underground city that once housed as many as 20,000 people

Watch this video that uses Lego bricks to explain how venture capital works.

Art theft is the third-largest source of criminal revenues worldwide, thanks in part to the subjective nature of valuing a work of art.

Meet the 56 signers of the Declaration of Independence—most of whom didn't put pen to paper until August 2, 1776—and see their original signatures.

A 2019 Facebook event called on attendees to "Storm Area 51, They Can't Stop All of Us," resulting in countless memes, the creation of a music festival, and eventually the arrests of those who did try to approach the area.

The Nasdaq's 'Magnificent 7' companies are responsible for roughly 40% of the Nasdaq 100 index's gains, while the remaining 93 companies account for the other 60%.