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 ...

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry. In the mid-1980s, the mathematician Jean ...

A year ago AlphaGeometry, an artificial-intelligence (AI) problem solver created by Google DeepMind, surprised the world by performing at the level of silver medallists in the International ...

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Google's second generation of its AI mathematics system combines a language model with a symbolic engine to solve complex geometry problems better than International Mathematical Olympiad (IMO) gold ...