Interesting post. The First Proof experiment really showed us the near future of AI/math interactions, some impressive success, but also lots of extremely hard to verify text, misformulated lean "proofs" etc. but progress on AI does math has indeed been impressive
This is a very interesting contribution to the AI/math space. I hope it can be seen by nonmathematicians interested in this. The mathematicians involved are quite well known (Martin Hairer is a Fields medalist). See https://www.reddit.com/r/math/comments/1qx77l7/a_new_ai_math... for some discussions.
Yes this is the standard proof of infinitely many primes but note that my prompt asked for infinitely many even primes. The point is that GPT would take the correct proof and insert "even" at sensible places to get something that looks like a proof but is totally wrong.
Of course it's much better now, but with more pressure to prove something hard the models still just insert nonsense steps.
This also can be observed with more advanced math proofs. ChatGPT 5.2 pro is the best public model at math at the moment, but if pushed out of its comfort zone will make simple (and hard to spot) errors like stating an inequality but then applying it in a later step with the inequality reversed (not justified).
My favorite early chatgpt math problem was "prove there exists infinitely many even primes" . Easy! Take a finite set of even primes, multiply them and add one to get a number with a new even prime factor.
It's helped, but it's not correct that mathematicians are scoring major results by just feeding their problems to gpt 5.2 pro, so the OP claim that mathematicians are just playing off AI output as their own is silly. Here, im talking about serious mathematical work, not people posting (unattributed AI slop to the arXiv).
I assume OP was mostly joking, but we need to take care about letting AI companies hype up their impressive progress at the expense of mathematics. This needs to be discussed responsibly.
I think a more realistic answer is that professional mathematicians have tried to get LLMs to solve their problems and the LLMs have not been able to make any progress.
I think "pretty soon" is a serious overstatement. This does not take into account the difficulty in formalizing definitions and theorem statements. This cannot be done autonomously (or, it can, but there will be serious errors) since there is no way to formalize the "text to lean" process.
What's more, there's almost surely going to turn out to be a large amount of human generated mathematics that's "basically" correct, in the sense that there exists a formal proof that morally fits the arc of the human proof, but there's informal/vague reasoning used (e.g. diagram arguments, etc) that are hard to really formalize, but an expert can use consistently without making a mistake. This will take a long time to formalize, and I expect will require a large amount of human and AI effort.
I think that (most) mathematicians were not that interested in formal proof until quite recently (as opposed to computer scientists), and most of the interest in lean has been self-reinforcing, namely there is a (relatively speaking) huge library of formally verified mathematics. So now basically anyone who cares about formal verification as a tool for mathematics is working in lean. There are of course numerous techincal differences which you can read about if you google coq vs lean.
Citation based metrics are much more prevalent in physics than in math (at least in the US and most countries in Europe). When compared with physics, my impression is that mathematics has the tradition "slow, long term" over "rapid, incremental." Of course, it's not perfect.
Do we?