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 ...

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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 ...

Google updated its search engine and Lens tool with new features to help you visualize and solve problems in more difficult subjects like geometry, physics, trigonometry and calculus. The update ...

Google DeepMind has developed an artificial intelligence system that can solve complex geometry problems better than top human minds. Named AlphaGeometry2 (AG2), the AI has outshined International ...

A year ago, AlphaGeometry, an AI problem solver created by Google DeepMind, surprised the world by performing at the level of silver medallists in the International Mathematical Olympiad (IMO), a ...

Einstein's 1917 paper, "Cosmological Considerations in the General Theory of Relativity," applied general relativity to the universe as a whole, establishing a firmer basis for cosmology. To create a ...

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized. Around 450 BCE, Anaxagoras of ...

Crows are able to look at a handful of four-sided shapes and correctly distinguish those that exhibit geometric regularity from those that don't, according to a provocative new study. It's the first ...