stackyFACTSIn set theory, this axiom states that given any collection of mathematical sets, each containing at least one object, it is possible to make a selection of exactly one object from each set. It sounds incredibly obvious, but assuming it is true completely breaks other parts of mathematics.
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Instead of appreciating a nice snowflake, mathematicians decided to rigidly define symmetry through abstract algebraic structures. It turns out that rotating…
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The Clay Mathematics Institute isolated seven massive mathematical problems and offered a one million dollar bounty for each. To date, only one has been…
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Albert Einstein gets all the pop-culture glory, but Emmy Noether did the heavy lifting for modern physics. She mathematically proved that every conservation…
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Goldbach's conjecture states that any even number greater than two is just two prime numbers added together. It works for every number we have ever simulated,…
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Weather forecasts fail after about 10 days not because we are stupid, but because the universe itself is touchy. Many systems are chaotic: tiny differences in…
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The Banach-Tarski paradox is a mind-bending mathematical theorem involving infinite sets. It mathematically demonstrates that it is theoretically possible to…
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