An interesting (unscientific) experiment on #MathOverflow from a few months ago, where a user gave 15 different MO problems for o1 to answer, with the aim of verifying and then rewriting the answer into a presentable form if the AI generated answer was correct. The outcome was: one question answered correctly, verified, and rewritten; one question given a useful lead, which led the experimenter to find a more direct answer; one possibly correct answer that the experimenter was not able to verify; and the remainder described as "a ton of time consuming chaos", in which the experimenter spent much time trying to verify a hallucinated response before giving up. https://meta.mathoverflow.net/questions/6114/capabilities-and-limits-of-ai-on-mathoverflow This success rate largely tracks with my own experience with these tools. At present this workflow remains less efficient than traditional pen-and-paper approaches; but with some improvement in the success rate, and (more importantly) an improved ability to detect (and then reject) hallucinated responses, I could see one soon reaching a point where a non-trivial fraction of the easier problems in MO could be resolved by a semi-automated method.

I found the discussion for possible AI disclosure policies for MO in the post to also be interesting.

In the spirit of old questions, here's another one without an answer: can we get a "holomorphic model" for a K(Z,2)?

https://mathoverflow.net/q/237837/4177

A recent answer by Simon Henry about coproducts of C*-algebras in a certain category reminded me of this old question on pushouts in the same category, which is still unanswered:

https://mathoverflow.net/q/372841/4177

An anecdote that I shared about rolling around on the floor back in 2000 to solve a math problem, both in my #Masterclass at https://www.masterclass.com/classes/terence-tao-teaches-mathematical-thinking/chapters/transforming-problems , and on #MathOverflow at https://mathoverflow.net/a/38882/766 , as well as the #NewYorkTimes https://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html , has for some reason recently gone viral on various social media. Just for the record, I wanted to add some mathematical background behind the story, which eventually led to my paper https://arxiv.org/abs/math/0010068 . At the time, I was trying to construct solutions to an equation known as the wave maps equation on the sphere: the solution was like a solution to the wave equation, except being forced to take values in a sphere rather than in a vector space.

I was trying to solve the equation iteratively, breaking up the solution to a low frequency base solution and a high frequency correction. As a first approximation, the low frequency base could also be assumed to stay on the sphere and solve the wave maps equation, so the main problem was to work out what the high frequency correction was doing.

Because the high frequency correction also had to keep the solution on the sphere, one could assume as a first approximation that the high frequency correction was tangent to the low frequency base. So, at any given point in space and time, the low frequency base solution was located on some point on the sphere, and the high frequency correction basically lived on the tangent plane to the sphere at that point. But because the base solution evolved (slowly) in space and time, this tangent space kept rotating around the sphere.

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I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

https://mathoverflow.net/questions/454096/lattice-point-counts-on-determinant-variety

Please look at my question. Boost it, and if possible, answer it!

As an experiment, I recently tried consulting #GPT4 on a question I found on #MathOverflow prior to obtaining a solution. The question is at https://mathoverflow.net/questions/449361/elegant-recursion-for-a301897 and my conversation with GPT-4 is at https://chat.openai.com/share/53aab67e-6974-413c-9e60-6366e41d8414 . Based on past experience, I knew to not try to ask the #AI to answer the question directly (as this would almost surely lead to nonsense), but instead to have it play the role of a collaborator and offer strategy suggestions. It did end up suggesting eight approaches, one of which (generating functions) being the one that was ultimately successful. In this particular case, I would probably have tried a generating function approach eventually, and had no further need of GPT-4 once I started doing so (relying instead on a lengthy MAPLE worksheet, and some good old-fashioned hand calculations at the blackboard and with pen and paper), but it was slightly helpful nevertheless (I had initially thought of pursuing the asymptotic analysis approach instead to gain intuition, but this turned out to be unnecessary). I also asked an auxiliary question in which GPT-4 pointed out the relevance of Dyck paths (and some related structures), which led to one of my other comments on the OP's question. I decided to share my experience in case it encourages others to perform similar experiments.

I don't post on #mathoverflow , but when i do
https://mathoverflow.net/questions/434279/two-credible-references-seem-to-differ-on-the-equivalence-of-induction-and-well
#linearorder #newfoundations #axiomofchoice #zornslemma #induction

A surprisingly "soft" question in #Mathoverflow, answered by the hardest of the hard:

https://mathoverflow.net/a/366118

First time I venture into #MathOverflow, with a relatively undergraddy question:

https://math.stackexchange.com/a/3188720/664348

I wonder my answer will survive.