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 ...

DeepMind, the Google AI R&D lab, believes that the key to more capable AI systems might lie in uncovering new ways to solve challenging geometry problems. To that end, DeepMind today unveiled ...

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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 ...

Researchers at DeepMind, the artificial intelligence research division of Alphabet Inc., have created software that’s able to solve difficult geometry proofs that are often used to test the brightest ...

Combinatorial geometry and density problems form a dynamic field at the intersection of discrete mathematics and geometric analysis. Research in this area explores the intricate arrangements of points ...

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 ...

The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an ...

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 ...

A system developed by Google’s DeepMind has set a new record for AI performance on geometry problems. DeepMind’s AlphaGeometry managed to solve 25 of the 30 geometry problems drawn from the ...

Computers are working to solve an age-old geometry problem. Humans can’t “square the circle” by hand, which was proven in the 1800s. Computer solutions involve infinity, complexity, and some ...

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 ...