AlphaProof's Greatest Hits

Why have they still not released a paper aside from a press release? I have to admit I still don't know how auspicious it is that running google hardware for three days apiece was able to find half-page long solutions, given that the promise has always been to solve the Riemann hypothesis with the click of a button. But of course I do recognize that it's a big achievement relative to previous work in automatic theorem proving.

I don't know why so few people realize this, but by solving any of the problems their performance is superhuman for most reasonable definitions of human.

Talking about things like solving the Reimman hypothesis in so many years assumes a little too much about the difficulty of problems that we can't even begin to conceive of a solution for. A better question is what can happen when everybody has access to above average reasoning. Our society is structured around avoiding confronting people with difficult questions, except when they are intended to get the answer wrong.

We know that any theorem that is provable at all (in the chosen foundation of mathematics) can be found by patiently enumerating all possible proofs. So, in order to evaluate AlphaProof's achievements, we'd need to know how much of a shortcut AlphaProof achieved. A good proxy for that would be the total energy usage for training and running AlphaProof. A moderate proxy for that would be the number of GPUs / TPUs that were run for 3 days. If it's somebody's laptop, it would be super impressive. If it's 1000s of TPUs, then less so.

> We know that any theorem that is provable at all (in the chosen foundation of mathematics) can be found by patiently enumerating all possible proofs.

Which computer science theorem is this from?

It’s just an obvious statement. If a proof exists, you will eventually get to it.