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What are some unexpected math proofs?

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I've loved how people find clever ways to apply math. Like washing clothes using less electricity, water, and detergent. (This is more like a programming problem, but who invented the computer? Mathematicians! Charles Babbage, Alan Turing, John von Neumann) What is Fuzzy Logic in a Washing Machine? read more

By unexpected, I mean that the proof is very unusual for that type of problem or for every kind of problem. read more

A classic proof by contradiction from mathematics is the proof that the square root of 2 is irrational. If it were rational, it could be expressed as a fraction a/b in lowest terms, where a and b are integers, at least one of which is odd. But if a/b = √2, then a2 = 2b2. Therefore a2 must be even. read more

In my opinion, all proofs of the infinitude of primes rely on the same core mathematical content, and the rest is just fluff. Take your cited topological proof, for example. read more

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