We've wondered for centuries whether knowledge is latent and innate or learned and grasped through experience, and a new ...

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"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This ...

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 ...

Professor of Mathematics Jeremy Kahn won the 2012 Clay Research Award — one of the most prestigious awards in mathematics — for his work on hyperbolic geometry. Kahn and his collaborator Vladimir ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

Educational Studies in Mathematics, Vol. 94, No. 1 (January 2017), pp. 37-54 (18 pages) This paper reports the results of an international comparative study on the nature of proof to be taught in ...

J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...