:/

IMO that there is any work at all to build from is the result of a long tradition of taking the next step. Professor to student and so on. The danger of AI here is we get to take a leap, say, 10 steps - but then there is no more tradition to have the fortitude and mentoring necessary to continue the progress.

It all gets derailed while betting on RSI and never having to do math research again (but if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter that we get to call it solved?)

Other mathematicians have done the work of writing out and publishing these proofs, OpenAI has published Lean certificates.

The first type of work pushes the field of mathematics further, the second kind strip-mines the sense of discovery and accomplishment and replaces it with math homework for high level mathematicians, because in order for it to be useful, it still needs to be turned into a human readable proof.

It's imho not valid to say OpenAI is "building off" other mathematicians work, in the same way as humans, do.

I think the question is rather, what will happen to human beings when any possible personal intellectual accomplishment will no longer be seen as interesting or relevant by other human beings when AI can do most of it?

It's all well and good to say that we should just go on these journeys for our own enrichment, but even so they will just be doing it alone...or else not do it at all because they need a shared human effort surrounding them to do it, and therefore end up depressed and immersed in drugs or media all day.

Of course we're awed at what AI can do now, because all of us observing it have had the luxury of having such opportunities before AI. I got my PhD before AI and I found satisfaction in participating in a shared math community, which I wouldn't have done if I were starting my PhD now, because I would find the current academic environment unacceptable and useless.

That would be a very exciting experiment. I doubt you could find enough vintage training data to train a LLM enough to do it without it being contaminated by anachronistic data in the weights, but I would be absolutely amazed if it could reproduce that.

> Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.

I don't think so, it was a big leap forward in terms of creativity, imagination, rigor and experimentation. Einstein was able to "run" visual thought experiments inside his mind

whether the original authors would have produced their work without building off from the work of other mathematicians.

That's rhetorical, right? Of course mathematicians built on what older mathematicians built and OpenAI's machine built on that. The real question whether OpenAI's machine has contributed something others will in turn build on.