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

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

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 ...

Discrete mathematics is about precision in reasoning as much as it is about solving problems. Proof techniques like induction, contradiction, and direct reasoning are used to establish results in ...

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 ...

The race is on to develop an artificial intelligence that can do pure mathematics, and top mathematicians just threw down the gauntlet with an exam of actual, unsolved problems that are relevant to ...