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Mathematical proofs and computer programs are isomorphic, so it's not unreasonable to start from the premise that with the right guidance, many skills would tra

• Tainnor 4y ago
  > Mathematical proofs and computer programs are isomorphic I've heard this multiple times and it always misses the point. Isomorphisms exist whenever we focus on particular structural features of mathematical objects, to the exclusion of irrelevant characteristics. For example, all completions of "the" rational numbers are isomorphic with respect to the structure of ordered fields, be they equivalence classes of Cauchy sequences, Dedekind cuts or something else. But they're clearly not isomorphic as sets. Similarly, all n-dimensional F-vector spaces, for fixed n and a field F, are isomorphic as vector spaces. That doesn't mean they're all the same - 4-dimensional vectors and 2x2 matrices are very different things, for example. Mathematical proofs and computer programs are isomorphic from a very specific point of view, namely type theory (which doesn't even apply to dynamically typed languages). That doesn't translate into mathematics necessarily being useful for all other aspects that are important in computer programs, nor into computer programmers having a good understanding of how proofs work.
• wombatcringe 4y ago