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 ...
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, ...
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 ...
Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...
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 ...
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 ...
On Thursday, Google DeepMind announced that AI systems called AlphaProof and AlphaGeometry 2 reportedly solved four out of six problems from this year’s International Mathematical Olympiad (IMO), ...
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 ...
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