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It's not really number theory, it's just numbering.
I really liked this video by Veritassium.
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I had read that before but I’ve still not looked at how he actually did it.
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The article does a decent job explaining. Pretty cool stuff
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Huh, I had heard a lot about Godel's Incompleteness Theorem, but I never realized that he proved it by turning mathematical statements into unique numbers, thus connecting the study of formal logic into number theory. Brilliant.