[rocqua]

It seems to me you hooked onto the wrong part of proofs vs software compared to what OP meant. The difference OP cares about isn’t how much one cares about style. Instead the important difference lies in validation. A proof can be validated as either correct or wrong. That type of hard feedback really helps combat the optimism and desire for shortcuts of modern models.

Now, that still doesn’t help an LLM distinguish between good and bad correct proofs. But it still really helps a lot. On top of that, taste in proofs is a lot more uniform than taste in coding. That helps LLMs be better at judging the quality of a proof, because there’s less disagreement in the wider world.

[sigbottle]

The standards of proof are different from the fundamental operation of "OK, cool, you solved this problem. Why does this problem matter? Isn't it useless? Senseless? Meaningless?" You have this same question whether or not you're in an a priori discipline (mathematics), scientific fields proper, or engineering. "Absolute certainty" has nothing to do with it. I can assure you, people on the job are not looking for The Absolute Truth when doing their jobs, yet they still can question at a solution by asking: are we solving the right problem?

(Although in general, there's no true difference between "I answered the question correctly, but the question was mapped to this thing we call 'reality' wrong", and "I answered the question incorrectly", because you can (try) adding the constraints that you really wanted targeted in case A, to case B, and boom, suddenly a question/answer pair that was "Answered correctly, but question doesn't map to reality" now becomes, "You answered this question wrong". However, individuals generally tend to have some breakpoint to differentiate between the two).

[rocqua]

That's a valuable extra distinction between Mathematics and Software.

In Mathematics there is much more clarity on what question you want to answer. It's much less likely you get an answer to a question, and then realize that the question was useless. Whereas in software its almost guaranteed that your first implementation, correct or otherwise, will solve the wrong problem.

[sigbottle]

Really? Not my experience at all.

If you're saying that math has a consolidating network effect, sure. There are a lot of people who think similar problems are important. I guarantee you that when math was small, that is not the case, and when coming up with new math, that's not the case, and when coming up with sub problems to tackle large problems, that is not the case.

[nicf]

No, what I'm saying is that I don't agree that taste in mathematics is more uniform than taste in coding! Mathematicians argue about taste all the time. Just as you might look at a piece of code and agree that it compiles and doesn't have any fatal bugs but still think it's badly written, hard to follow, hard to modify, or whatever else, mathematicians judge mathematical work using very similar criteria.

[vatsachak]

Maybe a subset of mathematicians, but if someone proved that RH was undecidable we would still give them the millennium prize.