I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs.
Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications of things. It is just a set of abstract rules, perfect for a computer.
And remember computer science was initially a sub-discipline of mathematics. So after Claude/Codex conquer writing code, it makes sense to move on to mathematics.
Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite of Ai making mathematicians obsolete.
> Terrance Tao's career trajectory has reached new highs due to AI.
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.
To the credit of the original commenter, that is why they said "give it one or two years". _Right now_ we need the experts to formalize/check. They're saying they think LLMs will reach a point in the near future where that won't be necessary.
All we need experts for right now is verifying the formalization of the statement of the problem is correct. The proof itself, that formalization is checked automatically.
So there is no getting around the fact that someone has to verify something. my point still stands.
I’m not sure about this. Anthropic’s AI constructed complex structures on S^6 and wrote a 108 page paper about it, and a few days later there was already a 250k line lean program claiming to verify it.
an obvious question would be if 250k loc is what is required for the proof or if it can be shortened massively, is this essentially going to be AI trying to search for a smaller proof or is it that a human being would be beneficial in that loop.
It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.
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.
> It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.
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.
Human verification of the Lean program only requires verifying that the theorem itself is represented correctly. The theorem will only make up a very small part of the entire Lean program.
honestly curious question: do you expect this to remain true? If so, for how long? I can think of two potential reasons why it might not stay true.
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.
> honestly curious question: do you expect this to remain true? I
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.
> do you expect this to remain true? If so, for how long?
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.
> 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.
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...
One can tell how much you hate all human skill and beauty. I also think your one of these AI booster people who don't know anything about formal verification and methods or it prerequisites, but are 100% sure it's going to get rid of human talent, beauty, only brutish concerns with what the market demands. May this reality come but only for you and you can occupy your place in the bowels universe as a contemptible slave.
Don’t confuse loving AI with recognizing its capabilities. Know thine enemy