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 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 ...

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 ...

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

In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future. In May, a ...

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 ...