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248 points rishicomplex | 3 comments | | HN request time: 0.001s | source
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throwaway713 ◴[] No.42167915[source]
Anyone else feel like mathematics is sort of the endgame? I.e., once ML can do it better than humans, that’s basically it?
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margorczynski ◴[] No.42168138[source]
I doubt it. Math has the property that you have a way to 100% verify that what you're doing is correct with little cost (as it is done with Lean). Most problems don't have anything close to that.
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1. AlotOfReading ◴[] No.42169130[source]
Math doesn't have a property that you can verify everything you're doing is correct with little cost. Humans simply tend to prefer theorems and proofs that are simpler.
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2. thrance ◴[] No.42172952[source]
You can, in principle, formalize any correct mathematical proof and verify its validity procedurally with a "simple" algorithm, that actually exists (See Coq, Lean...). Coming up with the proof is much harder, and deciding what to attempt to prove even harder, though.
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3. AlotOfReading ◴[] No.42173253[source]
You can verify it with a simple algorithm, but that verification won't always be cheap. If it was, curry-howard would be incredibly uninteresting. It only seems cheap because we usually have little interest in exploring the expensive theorems. Sometimes we do though and get things like the 4 color theorem whose proof verification amounts to combinatorial search.