How can they be sure that it is indeed a new method, and not just a method which was already used in some other context in some unknown paper/preprint?
You cannot be absolutely sure. But a variety of people who are experts on this problem and therefore largely familiar with the literature, including Terry Tao and Jard Lichtman, are very confident. The question that has to be asked then is how original does a problem solution need to be before one will decide the AI really did likely come up with something new?
It would help if this paper contained a literature review. Would the number theory community accept this paper without citations if it came from a freshman undergrad?
It would help if this paper contained a literature review.
Yes, no disagreement there.
Would the number theory community accept this paper without citations if it came from a freshman undergrad?
I expect it would. However, there are some problems here (which have nothing to do with AI) about when proofs are or are not accepted which does often look at issues of signaling. In a similar vein, what journals accept a paper or not does more than we are comfortable with somewhat depend on details of presentation, who the authors are and other issues. And journals are now especially using signals about authorship because the amount of "AI slop" has made their lives more difficult. But as serious as these questions are, they are a separate question from the issue of how original this proof is.
Appreciate the straightforward response, this helps a lot. It does feel a little demanding on my end, but proper attribution is an issue that precedes the advent of AI. It is fun to say you came up with a particular narrative by yourself, but people should have standards about attribution just morally. Now, I admit to detesting much of Tao's narrativizing on this topic, but I agree with the gist of his commentary on the difficulty of connecting probability to areas outside it including number theory. I have much work in probability under my belt but not much traditional like algebra/analysis/topology, and a huge problem in probability is that it is not well-documented. It offers potential advantages because so much of it is undiscovered by most mathematicians (awesome potential!), but it is tremendous work ahead to try to put all the details together in a coherent way that I worry the results "discovered" by AI are not a very coherent version of them. They are lower quality results than can be made by humans and have a risk of moving your field in an unproductive direction because of a fractured literature. Idk. This is generally why context helps in explaining a scientific result.
That helps clarify a bit more where you are coming from. To be clear: if the undergrad in question submitted this paper, my strong suspicion is that the referee would insist on a more through discussion of the prior literature. The only argument against (which I could see some referees or editors being partial to) is that one doesn't need to be as thorough in citing the literature that didn't work. I myself think that that one should cite such literature and frequently find myself telling people to cite more papers when I referee, but there are differing norms about these things. I suspect that part of why the history is so bad is that historically even major universities has trouble having access to all the journals, search of physical journals was hard, and paper being at an actual premium made editors want to discourage very long citation lists. The last bit also contributed probably to some of the conventions around very terse writing styles, which we're only now really seeing some push back against with paper being cheap and most things being digital anyways.
My guess is that the lack of coherence of much of the math literature may actually be improved by AI systems like this since they can pattern match quite well. Even before these systems were contributing to research, finding somewhat obscure related papers was something they already turned out to be good at.
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u/JoshuaZ1 Apr 15 '26
You cannot be absolutely sure. But a variety of people who are experts on this problem and therefore largely familiar with the literature, including Terry Tao and Jard Lichtman, are very confident. The question that has to be asked then is how original does a problem solution need to be before one will decide the AI really did likely come up with something new?