3 ms·
Many folks would say that's not a proof, because it's not efficiently checkable. To tell whether it actually proves the thing, I have to go off and check every
by rntz 10y ago
Many folks would say that's not a proof, because it's not efficiently checkable. To tell whether it actually proves the thing, I have to go off and check every number, which takes an enormous amount of time compared to the length of the "proof".
Of course, the solution of listing every single case seems about equally unhelpful. The whole thing leads one to question whether proofs are really the goal of mathematics, or just a useful proxy.
- jobigoud 10y agoI think it's checkable. You just have to write another program to check the proof, and maybe a meta program that checks that your proof-checking program is correct. I think there is a good chance that in the future we have computers coming up with and proving theorems that we don't fully understand (but for which we understand the practical value) and the human contribution will be to write a program that verifies that the proof is indeed correct.