New research has found ChatGPT-5.2 can generate original mathematical proofs, introducing “vibe-proving” as a new AI ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

The International Mathematical Olympiad (IMO) is a prestigious competition featuring talented high school students from around the world, in which competitors solve complicated mathematical problems.

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 ...

Decades of data have suggested the universe is flat, much like an infinite plane. But a new analysis reveals deep flaws in ...