Despite their wide variety of sizes, niches and shapes, sharks scale geometrically, pointing to possible fundamental ...

To see how one cube can pass through another, imagine holding a cube over a table and examining its shadow (assuming it’s ...

The recent paper studies algorithmic pricing through the lens of game theory, an interdisciplinary field at the border of ...

Neuroscientists probing the boundary between sleep and awareness are finding many types of liminal states, which help explain ...

The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major ...

The amplituhedron is a geometric shape with an almost mystical quality: Compute its volume, and you get the answer to a central calculation in physics about how particles interact. Now, a young ...

The Earth’s atmosphere is nothing but freely roaming molecules. Left alone, they would drift and collide, and eventually even out into a mixture that’s dynamic, yet stable and broadly unchanging. The ...

In cellular automata, simple rules create elaborate structures. Now researchers can start with the structures and reverse-engineer the rules. Alexander Mordvintsev showed me two clumps of pixels on ...

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures. Hofstadter was ...

Randomness is a source of power. From the coin toss that decides which team gets the ball to the random keys that secure online interactions, randomness lets us make choices that are fair and ...