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

How the number 15 solved a longstanding math challenge

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer—only 15. While...

Watch the iterative process of successfully printing a slice of vegan cheesecake

3D printing food requires integrating ingredients with a variety of properties, which may not all resist the physical stress of stacking. This means successful 3D printing of food may require rethinking how ingredients are layered and modifying ratios of each, potentially sacrificing taste for structural integrity.

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.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

In 2018, it took about 2.3 years to develop a way to exploit a software bug for malicious purposes, but as of 2026, AI tools have reduced this time to about 20 hours.

In 2000, the Clay Mathematics Institute placed million-dollar bounties on seven unsolved problems in mathematics—the Millennium Prize Problems—in the hopes of spurring solutions.

Google’s quantum computer completes a 10,000-year task in about 3 minutes

Google used its 53-qubit processor on an extremely difficult problem for traditional computers to simulate to showcase quantum supremacy. IBM later challenged Google’s claim by arguing that its Summit supercomputer could solve the same problem in just 2.5 days using a more efficient method.

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.

Cookies were originally used as low-stakes ways to test the temperature of an oven

In 7th century Persia, bakers used small mounds of dough to test the heat in ovens before baking larger cakes. Afterward, they'd add honey, nuts, and other items to the small mounds, creating early cookies.

Quantum computers use qubits to solve problems much faster than classical machines

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Visualize how data becomes organized through a variety of sorting algorithms

This interactive shows how different algorithms shift elements in a randomized set to order them from smallest to largest. By comparing the different procedures and their corresponding functions, users can explore how runtimes vary across algorithms that complete the same task.

How algorithmic redistricting works

Computational methods are convincing a number of judges that some state district maps are drawn illegally. Here's a simple overview of how it works.

Pizza boxes are square for practical reasons

Although circular pies have sometimes appeared in circular boxes, they usually travel in square, cardboard boxes. That's because the cardboard industry manufactures them with edges so they can be made in one piece and be easily stacked.

Grace Hopper warned against prioritizing hardware purchases in future computing

Foreseeing the rising volume of data and the increasing demand for its processing and access, she advocated that organizations first map the total flow of information they require and then choose infrastructure to support it, rather than wastefully spending on the fastest computing technology and forcing software to compensate for unnecessary hardware or incorrect data.

The first algorithmic random number generator was developed in 1946

Although previous methods of randomness involved physical tools with limited outcomes, such as dice, or relied on chaotic variables for number generation, such as electronic noise, John Von Neumann's middle-square method turned the problem into a mathematical computation. It has since been replaced by methods that generate numbers from unique initial values, such as the time on a clock.

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

Understanding the Diffie-Hellman key exchange, an example of public key cryptography

Published in 1976 by Whitfield Diffie and Martin Hellman, the system involves two parties combining each of their unique private keys with a public key using a mathematical function. The combinations are exchanged and mixed to establish a common key that no third party can determine. The Diffie-Hellman system underlies many encryption protocols for internet traffic.

Moore's Law came from observing exponential computing growth in the 1960s

In 1965, Gordon Moore, cofounder of Intel Corporation, observed a four-year trend of constant growth rate in computing power. Hypothesizing the trend would continue, his observation became the benchmark that the computing industry has worked to maintain for 60 years.

Explore a visual guide to how quantum computers can crack RSA encryption

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

DNA computing allows for storage and processing of massive amounts of data

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

Unsatisfied with the designs provided by an Apple engineer, Steve Jobs designed the original Mac calculator in about 10 minutes.

NSF-funded research into matching algorithms improved the success of organ transplants

Investigations in game theory, including concepts focused on creating mutually beneficial partnerships—matching theory—led to the design of computer systems that efficiently matched kidney recipients and live donors, resulting in higher-quality matches. By 2019, these matching algorithms were used for multi-organ exchanges.

Learn the history of food science breakthroughs from the 20th century

Long after humans developed the means to produce sufficient food to feed civilizations, scientific research focused on a wide variety of objectives, such as developing methods to preserve food quality (accomplished via frozen food), speeding up cooking (leading to the microwave), and lowering the cost of sweetening food, which high fructose corn syrup provides.

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.

The origin of shortest-path algorithms and how they became optimized for navigation apps

In 1956, Dutch programmer Edsger Dijkstra spent about 20 minutes developing an algorithm to demonstrate how computers could quickly determine the shortest route between Rotterdam and Groningen. Since then, modified versions of Dijkstra's formulation comprise the processing backbone of systems such as Google Maps and Apple Maps.

Can animals understand fairness?

Academics have long wondered if fairness is solely a concern of humans. In the largest meta-analysis to date, UC Berkeley researchers tested whether monkeys felt jealousy after receiving unequal rewards. The patterns showed low evidence for inequity aversion and instead frustration due to their expectations not being met by humans. These findings suggest that pursuing fairness and equality is uniquely human.

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.

Purdue students' robot solves a Rubik's cube faster than most people can blink

The solution time of 0.103 seconds is a Guinness World Record. A robot created by Mitsubishi Electric engineers held the previous record of 0.305 seconds.

Computer scientists first started trying to optimize dating using computers in the 1950s.

Against his wishes, Albert Einstein's brain was removed before his cremation, and the pathologist responsible stored it for decades in mason jars within a beer cooler.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Why did the US make it illegal to sell sliced bread during WWII?

Pre-sliced bread has only been with us for almost 100 years, but during the course of World War II it was briefly banned to save on supplies like wax paper and stainless steel for the war effort. This Atlas Obscura article explores this amusing (though not at the time) bit of food during wartime history.

Only allowing three recipients causes the Nobel Prize to overlook team discoveries

While science has grown more inclusive and collaborative, the Nobel Prize system still struggles with outdated practices, such as secrecy and a rigid limit on awardees. This restriction sidelines many deserving scientists, especially in complex projects like the human genome or gravitational waves.

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.

'All the world is birthday cake, so take a piece, but not too much.'

- Musician George Harrison (1943–2001)

Misunderstandings about how quantum computing works may have overhyped their ability

Quantum computers are often viewed as machines that can solve all problems instantly by trying every solution simultaneously. Instead, they amplify correct answers and cancel out wrong ones, which only works for specific kinds of problems with special structures.

Algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

Married computer scientists at Stanford University built the router that became the foundation for Cisco

Len Bosack and Sandy Lerner were both computer scientists at Stanford University in 1984 when the pair created a router that connected computers on different networks. The pair asked for Stanford's permission to manufacture the router, but the university declined, and the couple decided to leave their jobs to launch Cisco, one of the tech companies that powers the internet.

The internet explained at five levels of difficulty, from protocols to internet flattening

Resembling a roadway with traffic laws that all cars must follow, the internet is the hardware that connects a source to a destination, and these connections must follow specific software rules. Although data had to travel through about 10 networks to reach a destination in the past, data centers increasingly consolidate traffic, just as a highway does for cars, to improve data speeds.

Later in life, the clock in Grace Hopper's office ran counterclockwise

Acknowledging that most people have "an enormous tendency to resist change," Hopper's clock served as a reminder for the computer scientist that just because things have been done a certain way does not mean they should forever remain that way: "They love to say, 'We've always done it this way.' I try to fight that." (Some users may experience a paywall.)

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

One of the Widow Clicquot’s many innovations was the process of riddling

Riddling involves storing Champagne bottles at an angle and methodically turning them in order to collect any sediment in the neck of the bottle. The technique—which was kept a strict secret—cut down on both time and waste, allowing the House of Clicquot to outsell its competitors for decades until word inevitably leaked and riddling became the standard.

How to cook food with lasers

Creative Machines Lab at Columbia Engineering have developed a system of software-controlled lasers to cook food with precision, retain moisture with the final-cooked product, brown food within its original packaging, and create an entirely new meal creation process for a consumer. Watch this three-minute video to see for yourself.

A breakdown of algorithms, how they are constructed, and their applications

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

IBM developed a benchmark to measure the usable performance of a quantum computer

Dubbed "quantum volume," the benchmark tests how well a quantum computer runs complex tasks. It stops when the computer can no longer correctly select the most likely answers, called "heavy outputs," more than two-thirds of the time.

All computers are defined by their ability to input, store, process, and output data

From wooden machines to wearable tech, computers have changed a lot in appearance, but they all still perform the same essential tasks. Early computers were made of wood and metal—some were so big that they filled entire rooms just to solve simple math problems.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

Researchers once thought Stonehenge functioned as a precise astronomical computer

In the 1960s, scientists used early computers to analyze the stone layout at Stonehenge, arguing it could predict eclipses and other celestial events. This BBC Sky at Night Magazine piece explains how the theory arose—and why scholars now doubt it.

The first compiler to facilitate communication with computers was developed by Grace Hopper

The A-0 program linker automatically translated mathematical symbols into machine-readable binary code. Although it took two years for computer executives to get on board with the idea, the technology was foundational to future programming languages that allowed computers to understand commands written in word-based languages.