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From one piece Gowers's Weblog 2 beliefs, in the piece's order there
Their words
the 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.
Their words
I agree with Jacob that mathematicians have the sort of training that makes them well suited to contribute.
From one piece Gowers's Weblog 3 beliefs, in the piece's order there
korrents.com
The survival of human mathematical tradition may depend on the motivation of young people to solve problems.Their words
I 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.
Their words
Very 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.
Their words
indeed one of my worries at the moment is that the mathematical community might become bitterly divided, something I would very much like to avoid.
From one piece Gowers's Weblog 3 beliefs, in the piece's order there
korrents.com
Humans are currently better at finding surprising and conceptual mathematical arguments.Their words
Humans 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.
korrents.com
LLMs are likely to be good at problems where the best method is to try many ideas until one succeeds.Their words
Very 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.
Their words
it still doesn't seem to be the case that LLMs are better than all humans at all aspects of mathematics.
From one piece Gowers's Weblog 3 beliefs, in the piece's order there
Their words
I think there is simply no point in hoping that our current system of incentives will not be disturbed - it obviously will.
Their words
I 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.
Their words
For 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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