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 ...

Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...

After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

An AI from Google DeepMind can solve some International Mathematical Olympiad (IMO) questions on geometry almost as well as the best human contestants. How does ChatGPT work and do AI-powered chatbots ...