An artificial-intelligence (AI) tool can rigorously prove whether geometric facts — statements about two-dimensional shapes such as triangles or polygons — are true, just as well as competitors in the ...

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 ...

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 ...

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In the ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...