Given he is uniquely brilliant, he is likely one of the very last mathematicians to be rendered obsolete for his skills. But AI is pretty unstoppable here, so I would give him maybe another year compared to pretty much all the just really good / great mathematicians.
I guess it could be AI turtles checking and summarizing all the way down, but is that any more credible than a single AI checking it? I doubt it.
Generally you only need to look at 10-100 lines (unless you have a highly novel theorem that essentially invents a new field of math or builds on a field that has never been worked on in Lean before) of the 250k to verify what it claims. This is why there is excitement around formal verification. The rest of it is perhaps useful to read to figure out why the proof works, but is not necessary for checking.
1. The very best humans remain able to understand/check the proofs, but we go for so long with every proof checking out that society more broadly just decides to trust. We are already doing that with human mathematicians. I can't verify what Terence Tao tells me is correct, I just trust that it is because he (and other human mathematicians) tell me it is. How many proofs/years of them checking out before we reach this point? I don't know, but history suggests that eventually, humans might keep checking, but they will do so only as a hobby. For any purpose that actually matters, we will just start to trust and use it.
2. The proofs that AI comes up with become too difficult/complex for even the very best human mathematicians to understand, and our options become to either trust or to not use at all.
Obviously it's possible that neither of these happens if AI capabilities stall out not too far beyond where we are now, but if they keep progressing at the current rates for another few years, I expect at least one, and maybe both, to eventually come to pass.
For the foreseeable future. Left to their own devices current LLMs kinda wander off into outsider art territory. They aren’t grounded in the real world and they need that feedback loop to stay within the category of relevant ideas. I haven’t seen anyone working on fixing that.
Regarding 1, the same is true of every other scientific field. Verifying some tidbit of knowledge for yourself as an individual isn’t optimally useful in all circumstances.
Regarding 2, if the proof isn’t understandable then it probably isn’t useful. Many people today work in the hypothetical world where the Riemann Hypothesis is true, and many work in the hypothetical world where it is false. If it takes decades to validate that some horrifically complex AI proof of either fork is true, people will probably continue working on the other fork just in case.
I have. DataAnnotation and these other AI-training piecework companies are pretty much the backstop now against total navel-gazing model collapse. With the Dead Internet Theory now pretty much reality, it's not like there is, or is going to be, gobs of untainted human-generated data out there ripe for the harvesting so it's going to take active human effort to keep the models grounded. That is, of course, until they start inhabiting robot bodies so they can live and move around in the real world, and thereby achieve their grounding, as in GitS or Ex Machina...
It's already the case that it's becoming not true. For example see this post from Lin Yang: https://x.com/lyang36/status/2092092709251293611
"Throughout the process, I felt that my only role was to teach the AI how to write things in a way that I could understand. Its initial language was extremely condensed—so compressed that I could barely follow it—but somehow the AI agents themselves seemed to understand it perfectly well."
It won't take much longer before AI is consistently better at validation than humans, and at that point, why continue to have humans do the validation? I think we're being naive about the end game - admittedly I don't know what it is though.