To be fair, what revolution were you expecting to see, exactly? You can 10x a "dashboard but with AI" app all you want but it's only ever going to be a "dashboard but with AI" app. And I note that nobody seems to be claiming that the AI helped them create a brand new kind of app.
>> If future AI systems will produce genuine proofs, logically correct and intelligible, like those produced by “master” mathematicians, it would still be incorrect to think that mathematics would have been “solved” as some say that chess or Go have been solved.
Chess and Go have most definitely not been solved. In AI research when we say that a game (and usually we mean a traditional board game) has been "solved", what we mean is that we can correctly predict the outcome of any game instance from any board position provided both players play perfectly [1]. This can mean we have an algorithm that chooses the perfect play for each player in any position or that we have mapped the entire game tree for that game: every move in every game, from start to finish.
There are games that have been solved this way: tic-tac-toe; connect four; nim; othello, checkers. But not chess and Go.
Rather, what we have for chess and Go are super-human engines, i.e. computer players that no human has ever beaten in the full game. So for example a chess engine like Stockfish can always choose what move to make in order to win against a human player in any board position. However, that is still not the same as knowing how to play perfectly in any board position. Like the old joke with the two guys trying to outrun a bear, a chess engine doesn't have to play perfect chess to be super-human: it just has to play better than any human.
To the extent that chess and Go are games it could be said that winning is the whole point of AI game-playing [2]. But the article above suggests that there is no point of "winning" in maths. In AI chess it is unfortunate that the development of super-human chess engines has ended all research in using AI chess to understand the way that human players play chess (which is to say: not by alpha-beta minimax, or Monte Carlo Tree Search, or anything like that) which was the original reason that luminaries of the field such as Shannon, Minsky, McCarthy, Michie, and even Turing himself were interested in the question in the first place. The concern then for mathematics is that AI "winning" at maths will kill mathematics research and replace it with ... as McCarthy would have it "very fast fruit flies" [3].
Amazing. Comment upon comment, thread upon thread, failing to engage with the substance of the Field medalists' letter and instead going off on tangents about the privileges that mathematicians will lose and how they're bitter about it. There is a shocking inferiority complex on this site towards mathematicians and yet users always seem to think of themselves as smart nerds, all about science and reason and maths and whatever.
I've been disappointed by this community before but this is the first place that there is such unanimous rejection of the very ideals the uses here will claim to represent. The reaction is just... small, tiny, petty.
The difference is that most software engineers don't care about bringing up a new generation to keep their field alive when they retire. Software engineers usually don't give a flying fuck for other software engineers, young or old, nor for software engineering itself. Mathematicians apparently care deeply for their subject, their field, and its future.
>> I’m no big AI cheerleader, but why don’t you try these models to see what they offer - they might suggest some things you haven’t thought of, or save you some time in your research.
One reason not to try is to create an air gap between the OP's ideas and the data that future models can train on. We saw that the mathematicians who trusted OpenAI and Anthropic with their preliminary work found the rug pulled out of their feet by those same companies.
Another reason is to avoid inadvertently plagiarising the work of other mathematicians. Any mathematical insight that comes out of an LLM is the result of training on the entire bibliography of mathematical research, but those insights are spat out of the models without attribution. If you use AI in your matematical research you are only using the work of others without even knowing who they are and what they contributed.
And yet another reason is to avoid polluting your mind with the ideas that come out of the AI. Maybe you get a hint that pushes you to one direction, when you would go into an entirely other direction without that hint. And then maybe that becomes a habit and you can't find new directions without asking the all-knowing oracle.
tl;dr: opsec, integrity and independence are the reasons to not use LLMs in your research. I don't.
Unless you’re very weak-willed, I wouldn’t worry about independence. LLMs make mistakes all the time, they are nothing like an all-knowing oracle nor are they going to replace humans despite the absurd fantasies of LLM fans and those with a vested interest.
Plagiarism is an interesting point, though honestly I think it would be fairly easy to work out who had published similar research if the LLM gives you an idea - personally I see this as the weakest argument against using them, as long as you are strict about attribution - all work like this depends heavily on the research of others - the LLM is just a tool to aid that research IMO.
Opsec is a fair point, and it might be worth avoiding the completely amoral OpenAI at this point for that reason. There are open models though.
Absurd fantasies like solving a Millennium Prize Problem? How is this not prima facie absurd? And if that's come to pass, why should we believe your bar for anything else?
Yes absurd fantasies like it did that without human help and guidance. OpenAI found out there was a solution and humans attempted to brute force generating all possible solutions while threatening the mathematicians involved (generous interpretation), or stole some ideas and took shortcuts to know where to look and brute forced it so they could claim credit.
Neither looks good for OpenAI or those who support them.
Thanks. Regarding plagiarism, I agree that it is possible to check; I don't know how easy it is. But I do note that the mathematicians who complained that their work was plagiarised by AI did not seem to realise that they, themselves, were using a plagiarism machine and were instead quite comfortable admitting that, yeah, we worked our Euler result out together with Sol, Claude and the gang.
To clarify, they do attribute the original ideas to Cordoba and Martinez-Zoroa, but they don't seem to acknowledge that their result which they say was achieved "with a great deal of help from LLMs" is also derivative of others' work.
Independence is about avoiding making errors because of the influence of error-prone models. I guess I didn't explain it well.
I think plagiarism machine is a stretch personally in this domain. In art or writing I could see it persuasively argued (see attempts to generate famous books or imitate illustrators).
Academics and scientists build on the work of many others and always have - their work is not possible without using other’s work.
Attribution is a problem here but I don’t think a new way to reference many others’ research and combine it in novel ways is the problem or should be rejected on that basis alone.
Anyway, Sturgeon's law and all that.
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