> I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
As a mathematician, I am a bit disappointed by my (admittedly illustrious) colleagues.
I get the need to take it slowly (and I am a quite impatient person, so I shouldn't get to decide stuff like this), but everything said feels a bit too sour grapes for my taste.
Ok, maybe AI did not solve the field (I believe it will, btw), maybe there is a need for human "understanding", but:
1) They don't seem to consider even the possibility (not the certainty) that they might be wrong, that math as we know it is gone, and we cannot "adapt"
2) They seem to have been oblivious all these years about AI eventually reaching this point (at least I personally wasn't, I predicted this stage back in 2018)
Regarding 1, it's not clear what you want them to actually do. Would you rather they just gave up, rolled over and died instead of at least trying to rescue their field? What is to be gained from considering this?
I suppose you could say, hypothetically, that if the field were “solved” then the protection of the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide.
The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
> the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide
Wiping out an occupation that people enjoy and that gives them purpose (making them "obsolete") is a public mental health crisis, if anything. It's unclear that the "benefits" of the "solved" field actually outweigh that.
> The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
They aren't in the way. AI labs can do their own math all they want, and nobody is stopping them. Rather, mathematicians are simply speaking about the topic.
So is the answer that they should just shut up?
They absolutely are in the way. We’ve had the most exciting months of mathematical progress since antiquity, and the vast majority of voices from mathematicians have been bitching about one thing or the other, to the extent that they now got themselves a committee that (co-)decides when, how, and possibly if, the next batch of results is made available to the public.
People merely speaking their mind does not constitute getting in the way.
I'm sorry that you personally don't like that mathematicians are "bitching" about OpenAI snaking their work out from under them, and would like to silence them. But if we're going for consistency's sake, maybe consider taking your own advice here before giving it to others.
In the meantime, OpenAI can do whatever they want, mathematically-speaking. Nobody is in their way. If there isn't further meaningful progress from them, that would seem to strengthen the work-product-theft hypothesis.
Please. Have you been doing mathematics ? Yes, some big open problems are solved. I have not seen the ideas therein used to solve related or other problems. That is the point of most mathematics: to develop frameworks and general techniques for understanding and solving problems, not solving one-off problems.
For example, group theory lead to a useful way of thinking about how to solve a wide array of problems. That is what mathematicians are seeking.
If LLMs could both prove any relevant theorem, explain such a theorem cogently and lay the groundwork for further theory, I don't see how any way mathematicians could stand in the way of that.
As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years and now do damage control by nudging everyone to either hypothetical open models paid for by industry or the EU or sitting in a committee that "advises" OpenAI.
No one is saying "Perelman and Wiles didn't need that silly AI and N-S was more of a counterexample". Most people imagine the sky is falling.
What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
> As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years
I did notice, this is why I had thought that they had thought through the consequences. But, unfortunately, it is likely they imagined that AI would plateau somewhere around the "smart undergraduate" level and that they will stay relevant in pure problem solving.
Was there really a choice? What they do or advised others to do would have had no bearing on what is happening.
And why have the Nobel Prize winners been silent (or taken post-Nobel bets contrary to the current consensus ie Hinton-Hassabis)?
Taking GP at his word, I'd be more terrified if Oai had identified one hundred NEW open problems..
In contrast with Fields Medallists, some Nobelists get the prize for something they'd eventually NOT be (in)famous for. Like Josephson. In hindsight, will it be because they found out, as young unknowns, how to explore underappreciated avenues without millions in dedicated funds (uh encouragement).. ??
GP, did you? Get the prize for the question you are most proud of.
> What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
Which is what I think a large chunk of AI progress actually is - people taking the latest models out for a spin, and browbeating them to actually ship code, and RLHFing them to ship better code in the process, either directly or indirectly through Github.
How do you conceptualize mathematics being 'solved' and 'gone'?
How do you reconcile that with incompleteness and undecidability results?
I think I'm mostly on your side (also I believed early it would get here), but what does it mean to "solve the field"? I'm pretty much as bullish as you get on AI but I'm sure I can come up with questions AI cannot solve. I think the space of problems in math is so large and the distribution of proof lengths so heavy-tailed, there's probably no way without dyson-sphereing the sun to solve all easy to state problems.
Without understanding, what are we?
I think it is good people are talking but there seems to be a lot of "forced optimism", especially by people obviously hoping to keep a channel open between themselves and the labs.
I think it isn't true that no one imminent is considering (1). Tsimmerman said he thought the job of math researcher was over as soon as he announced he was leaving the field.
I think the question is so far still open, but it is easy to imagine Tsimmerman was right. I haven't been impressed with the calls for "human understanding" as the really important thing. It seems to miss the point of why math has been funded (not exactly problems, but certainly not to ensure every theorem is understood either).
As a scifi comment, it is now possible to start thinking about some future AI system which decides if it will need to explain certain math to humans and to pick and train young people for that purpose.