"Oh, of course no one ever really *does* it..." A compressed version of my own confusion as a maths student: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/ooasn01bfe
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This sort of feels like "computers can only run machine code, but no-one ever really writes that. It would take forever!" So how does anything run? Because we work in higher abstractions most of the time, with the thing that actually works underpinning them. (Not a mathematician)
Yeah, I'd say the main differences are a) maths had a massive crisis in foundations in the early 20th c, so weird stuff happens in the 'machine code' layer anyway...
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... and more importantly b) proofs mathematicians write are *not* just written in a higher-order language that can be mapped cleanly onto lower-level primitives, they use all kinds of messy human language to explain things.
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