seeing more math on the TL recently. i haven't mathposted in a long time but i'm still happy to field math questions from twitter peeps, just reply here or tag me or w/e. big meaty philosophical questions like "wtf are real numbers anyway" would be particularly fun for me rn
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Why are p-adic numbers important? Feels like every phd i know has published on it yet it never came up in my classes
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hmm. i guess the most concrete case you could make is: they let you prove a bunch of useful stuff in number theory, partly using intuitions ported over from analysis. thinking about the p-adic norm as a kind of distance is not an obvious move but turns out to be super fruitful
here's a fun example i ran into when i was 16 and was totally baffled by, involving the patterns that show up when you repeatedly square the number 5
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