Combinatorics

For the first time in 30 years, computer scientists have found a better way to allocate objects evenly between two groups.

AI’s greatest mathematical successes have come from answers to problems posed by a mid-20th century iconoclast. By examining what makes the Erdős problems unique, mathematicians are trying to understand how AI might change the rest of math.

Before he won a Fields Medal for his pioneering work balancing randomness and order, Yu Deng first had to achieve equilibrium in his own life.

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.

Lauren Williams tells 'The Joy of Why' how studying a fundamental object in algebraic combinatorics led to a career full of surprises.

A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day.

A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem in decades.