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, ...
Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...
Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News. A high school ...
The same branch of mathematics that helped Einstein to formulate his theory of general relativity could now allow scientists to peer with unprecedented accuracy into impenetrable objects—such as the ...
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 ...
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), ...
In 2022, two high school students created a trigonometric proof of the Pythagorean Theorem—something that’s only ever been accomplished by a few professional mathematicians. Now, a new article not ...
Welcome to 2025! A lovely year, filled with excellent things. Obviously, we’re not talking about the state of the planet – ...
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