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I'm impressed but only a little surprised an AI reasoning model could help with Aaronson's proof. The reason I'm only a little surprised is that it's the kind

I'm impressed but only a little surprised an AI reasoning model could help with Aaronson's proof. The reason I'm only a little surprised is that it's the kind of question I would expect to be in the literature somewhere, either as stated or stated similarly, and I suspect this is why GPT5 can do it. I am impressed because I know how hard it can be to find an existing proof, having spent a very long time on a problem before finding the solution in a 1950 textbook by Feller. I would not expect this to be at all easy to find. I can see this ability advancing science in many areas. The number of published papers on medical science is insane. I look forward to medical researchers questions being answered by GPT5 too, although in that case it'd need to provide a citation since proof can be harder to come by. Also, it's a difficult proof step and if I'd come up with it, I'd be /very/ pleased with myself. Although I suspect GPT5 probably didn't come up with this based on my limited experience using it to try and solve unrelated problems.

gsf_emergency_2 1y ago
As someone who has worked in adjacent areas, I guessed that one might find it in random matrix pedagogy, but only after reading Sam (B) Hopkin's comment was I able to get google to give a source for something close to that formula: https://mathoverflow.net/a/300915 https://mathoverflow.net/a/300915 (In particular, I had to prompt with "Stieltjes transform". "Resolvent" alone didn't work.)
- bgwalter 1y ago
  The question was asked May 23, 2018 at 12:42, the answer came May 23, 2018 at 14:51. That is a very quick response time. OpenAI took the answer from here or elsewhere, stripped attribution and credit and a tenured professor celebrates the singularity. If there is no pushback from ethics commissions (in general), academia is doomed.
katzenversteher 1y ago
To me it seems a bit like rubber ducking with extra features. However, I believe in rubber ducking and therefore approve of this approach.

gsf_emergency_2 1y ago

As someone who has worked in adjacent areas, I guessed that one might find it in random matrix pedagogy, but only after reading Sam (B) Hopkin's comment was I able to get google to give a source for something close to that formula: https://mathoverflow.net/a/300915 https://mathoverflow.net/a/300915 (In particular, I had to prompt with "Stieltjes transform". "Resolvent" alone didn't work.)

bgwalter 1y ago
The question was asked May 23, 2018 at 12:42, the answer came May 23, 2018 at 14:51. That is a very quick response time. OpenAI took the answer from here or elsewhere, stripped attribution and credit and a tenured professor celebrates the singularity. If there is no pushback from ethics commissions (in general), academia is doomed.

katzenversteher 1y ago

To me it seems a bit like rubber ducking with extra features. However, I believe in rubber ducking and therefore approve of this approach.