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 ...

Paul Erdős, the famously eccentric, peripatetic and prolific 20th-century mathematician, was fond of the idea that God has a celestial volume containing the perfect proof of every mathematical theorem ...

Recently, two American high school students made headlines for discovering a new proof of the Pythagorean theorem. Calcea Johnson and Ne'Kiya Jackson, seniors at St. Mary's Academy in New Orleans, ...

Stanford's Jared Lichtman said ChatGPT's raw proof was poorly structured and required expert interpretation. Tao called it 'a nice achievement' offering a new way to think about large numbers, though ...

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

Keith Devlin is a consulting professor in Stanford's Mathematics Department and a fellow of the American Association for the Advancement of Science. Some biologists recognize his name because there's ...

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 ...

The mathematicians Günter Ziegler and Martin Aigner have spent the past 20 years collecting some of the most beautiful proofs in mathematics. Paul Erdős, the famously eccentric, peripatetic and ...