This is an updated version of a story first published on Nov. 1, 2024 For centuries, students have learned that in a right triangle, the square of the hypotenuse equals the sum of the squares of the ...

For ages, countless mathematicians have advanced mathematics through proofs. This is because proof is a key tool for developing new theories and solving problems. That’s why a discussion about proofs ...

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 ...

The painstaking process of formalization to verify proofs is starting to surge thanks to AI. That could radically change the ...

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

For centuries, the Pythagorean Theorem has occupied a unique position in mathematics: both elementary and profound. Its equation, a² + b² = c², is taught early and used widely, yet its implications ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

Ananyo Bhattacharya is chief science writer at the London Institute for Mathematical Sciences and the author of The Man from the Future: The Visionary Ideas of John von Neumann. One of the biggest ...