Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says ...

"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

Discrete mathematics gets easier when you know how to approach proofs. Direct reasoning, induction, and contradiction each have specific steps that can be learned and practiced. Pairing these methods ...

In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...

Remember that math problem from 2014? A Chinese AI tool cracked it ...

Mathematicians have proved a key building block of the Langlands programme, sometimes referred to as a “grand unified theory” of maths due to the deep links it proposes between seemingly distant ...

"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." Two mathematicians now say they’ve made progress on a very old unsolved math problem. The problem ...