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 ...

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 ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved 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 ...

Mathematician Kevin Buzzard of Imperial College London is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem. Resolving the problem isn’t the point.

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 ...