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 ...

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs ...

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 ...

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What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide ...

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 ...

A simple, step-by-step breakdown of two “perfect” math proofs. But which prime number is p? It must be on our list of primes, because our list is complete. But it also can’t be on our list of primes, ...

A few weeks ago, an animated discussion unfolded in a WhatsApp group whose members are mathematicians interested in the Indian Mathematical Olympiad. The spark was a Nature paper that announced a ...

There's a simple way to learn geometry over the summer. It is easy and fun. Imagine Euclidean geometry: the video game. If your experience in high school geometry was anything like mine, it probably ...

The International Mathematical Olympiad (IMO) is probably the most prestigious competition for preuniversity students. Every year students from around the world compete for its coveted bronze, silver ...