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 ...

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 ...

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 ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. The question was proposed by Japanese mathematician Sōichi Kakeya in 1917. It sounds simple: How can you ...

Meta's work made headlines and raised a possibility once considered pure fantasy: that AI could soon outperform the world's best mathematicians by cracking math's marquee "unsolvable" problems en ...

This geometry challenge puts your spatial reasoning and problem-solving skills to the test as you work to find the area using given clues and relationships. The explanation breaks the problem down ...

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 ...

Mathematics of Operations Research, Vol. 34, No. 4 (Nov., 2009), pp. 869-879 (11 pages) Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation ...