Thank you for replying and for reporting your results. My schtick is AI (i.e. I publish in AI conferences and journals), not maths and I'm interested in the question of autonomy from a professional point of view: how close are we to a machine that can carry out the job of a mathematician like yourself, by itself?

If you, e.g. got an LLM (any one) to one-shot the problem with a prompt that said "solve this problem", then we're much closer to that, than if you spent a year trying with different LLMs and then finally got it to work with a lot of hand-holding and even suggesting the ultimate solution. An autonomous system can't succeed once a year, if it's going to be of any use. It should also be able to identify the right tools on its own, not rely on a human to tell it what to do.

This should also go to address some of the questions you pose on reddit, about the future of mathematics. If LLMs can already do your job fully autonomously (as I would explain the term) then ... you're out of a job. You and all other mathematicians, young or old.

I personally don't think we're there yet.

I hear what you say, btw, about never being able to get there by yourself etc. Maybe you would, maybe you wouldn't. What we know is you used a tool to get there, in fact a series of tools, and it took you many tries before you did. The fact that an earlier LLM tried and failed is interesting, but that may just mean you were capable of crafting a better prompt after your interaction with the earlier LLMs.