Timothy Gowers
British mathematician; Fields Medal 1998. Professor at the Collège de France and fellow of Trinity College, Cambridge. Started the Polymath collaborative-proof projects and the 2012 Cost of Knowledge boycott of Elsevier. Writes Gowers's Weblog.
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Their wordsI agree with Jacob that mathematicians have the sort of training that makes them well suited to contribute.
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Their wordsJacob is the first to admit that something like an international treaty to slow down AI development is likely to have a far bigger impact on AI safety, especially in the short term, than mathematicians obtaining a better theoretical foundation for talking about it
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Their wordsthe Hugging Face incident and many others like it have shown beyond all reasonable doubt that AI can have wants of the general kind people were worried about: unpredictable wants that we did not intend to give them and that could potentially cause a lot of damage.
- 4 weeks earlier
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Their wordsindeed one of my worries at the moment is that the mathematical community might become bitterly divided, something I would very much like to avoid.
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Their wordsVery soon, the whole "credit system" will surely collapse, since finding an amazing proof will be no more of an intellectual achievement than when a citizen scientist spots through their telescope an object that turns out to be a new comet.
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Their wordsI very much hope that there is a pool of young people for whom it will be a powerful motivation, because I think the survival of a human mathematical tradition may well depend on it.
- 5 weeks earlier
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Their wordsit still doesn't seem to be the case that LLMs are better than all humans at all aspects of mathematics.
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Their wordsVery roughly, LLMs would have the edge when there is more of a probabilistic element to the proof-finding process: they would be good at problems for which the best method is to try a lot of ideas, not necessarily particularly novel, until at some point you get lucky.
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Their wordsHumans on the other hand would be better (for the moment) at finding more "surprising" and "conceptual" arguments, where the appropriate method is to dig deeper and deeper into a problem until the solution reveals itself.
- 2 weeks earlier
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Their wordsFor example, it seems to me that the importance of rigorous proof will be even greater in an AI age than it was before - if the output of AI is not underpinned by rigorous proof, then the kinds of difficulties one already hears about with certain areas of human mathematics (see for example many talks by Kevin Buzzard arguing for the value of formalization) would be hugely magnified.
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Their wordsI think there is simply no point in hoping that our current system of incentives will not be disturbed - it obviously will.
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Their wordsI do think all that will happen at some point, but whereas some people say that it will obviously happen within the next two to three years, I would say that it might happen as soon as that, but I don't rule out that we'll get lucky and find that we can do interesting AI-assisted maths for quite a bit longer than that before AI doesn't need us any more.