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A beginning for mathematics

I've written an essay on how I think the mathematics profession should adapt to highly capable AI systems. It's hosted here on "Proofs and Prompts": proofsandprompts.com/2026/09/14/a... though you should also feel free to complain/comment on my website here: daniellitt.com/blog/2026/9/...

proofsandprompts.com

Daniel Litt, professor at the University of Toronto Three years ago, AI systems could not reliably add two numbers. A year ago, internal models at OpenAI and DeepMind received the equivalent of a g…

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Joel Dodge @weakthinker.bsky.social · 18/09/2026

Daniel Litt the wise AI commentator? I remember when it was Daniel Litt the S-tier shit poster. Just one more thing AI has taken from us.

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Colin @colin-fraser.net · 18/09/2026

this probably feels so good if you're @littmath.bsky.social

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River_Tam @rivertam.bsky.social · 16/09/2026

"Whatever our goals are, we’ve operationalized them primarily through proving theorems. Almost all papers or PhD theses have a main theorem, and ostensibly a proof of it. But it should be clear that the goal of mathematics is not to prove theorems..." proofsandprompts.com/2026/09/14/a...

proofsandprompts.com

A beginning for mathematics

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Daniel Litt @littmath.bsky.social · 15/09/2026

My worry is that evaluating people based on any written signal will incentivize people to use the AIs for writing (especially once they get better at it).

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Daniel Litt @littmath.bsky.social · 15/09/2026

I do value them! I just think they will carry little signal about the person who wrote them pretty shortly.

Steve Huntsman @stevehuntsman.bsky.social · 15/09/2026

Reposted by Daniel Litt

“I think we are at the beginning of an incredible, wonderful explosion of mathematics, and if we value human understanding, there will be more need for human mathematicians than ever before. But the profession will have to change.”

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I agree with everything you are saying (and also not saying) here.

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Anyway, please let me know what you think!

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On what we want to preserve:

In the course of this change, we will have to decide what to hold on to and what to throw away. Some things I would like to preserve: learning seminars; serendipitous conversations that spark an idea; students knocking on a professor’s door to chat about math. A robust community learning exciting new mathematics. Thousands of people that, together, slowly start to resolve their confusion.

I worry that much of what has been written on this topic, including some of my own past writing, focuses too much on trying to preserve the precise shape of the institutions of academic mathematics, rather than our values. How can we preserve the journal and peer review system?5 How can we protect the arXiv? How can we keep our role as gatekeepers? If you have internalized the fact that existing AI systems can produce relatively high quality results for the marginal cost of a few dollars, the idea that any semblance of the current equilibrium can survive what’s coming is absurd.

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On pushing buttons and what we can and can't do:

As we think about how to reshape our profession, it’s important to understand that, whether one likes it or not,10 it’s impossible to stop people, amateur or professional, from pushing a button to produce mathematics. The idea that we will persuade people not to play around with math, or that we will be able to “reserve” problems for graduate students, is just not realistic.11 And we shouldn’t want to do this!

There is now more interest in math than at any other time in history. We should be ecstatic for mathematics’s sake, even as we are concerned about mathematicians and mathematical expertise. And by and large, the value of this button-pressing comes from the mathematical community. If a conjecture falls in the woods and no one is around to hear it, who cares?12 For the abundance of new mathematics to have value outside application, we will need an abundance of new mathematicians. And for results with applications, we will want people to be capable of understanding their assumptions and consequences.

I wrote above that solving problems and resolving open conjectures is an incomplete operationalization of our values. But nonetheless it is important to solve problems and resolve conjectures! The provenance of such solutions only matters insofar as it intersects with the existing structure of the profession (incentives, prestige, and so on). It is obvious that structure needs to change in any case.

On balance, I think I like it, though I am sometimes annoyed to find slop PDFs in my inbox. It took me some time to understand that these PDFs expressed a need for understanding; a person elicited them, often without being able to meaningfully engage with their contents, and needed to know that someone could engage, and that someone cared.

That we cannot reserve a problem for a graduate student does not mean we can’t give them the opportunity to work on it. This is compatible with the reconceptualization of a PhD outlined previously.

The essay is mostly written for my colleagues but I hope non-mathematicians will get something out of it too. A couple excerpts...

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A beginning for mathematics

proofsandprompts.com

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Reposted by Daniel Litt

Daniel Litt | Working with LLMs to do high quality math

I gave a talk at CMSA on AIxMath on Wednesday. The title ended up a bit unrelated to the content--I rewrote the talk at the last minute for obvious reasons, and talked a bit more about my views on the future of the profession than I expected to. Link: www.youtube.com/watch?v=0wL8...

youtube.com

YouTube video by Harvard CMSA

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Incidentally I think the Q&A starting around minute 52 is arguably more interesting than the talk itself.

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My goal is to spend less time talking about AI and more time talking about math for the next few months, but they pulled me out of retirement for one last job.

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If you're not a mathematician I encourage you to skip the middle part (about math, about minutes 15-34) and just watch the beginning and end.

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Daniel Litt | Working with LLMs to do high quality math

youtube.com

YouTube video by Harvard CMSA

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theseouldan.bsky.social @theseouldan.bsky.social · 11/09/2026

For a much more positive - and frankly much more informed - view than mine on LLMs in maths, this from @littmath.bsky.social is very good youtu.be/0wL8NlhxXcU?...

youtu.be

Daniel Litt | Working with LLMs to do high quality math

YouTube video by Harvard CMSA

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This all seems reasonable to me!

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It makes me worry how they will behave if something more substantial is at stake, and what principles will be sacrificed for that. 12/n, n=12

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While I know many people at the labs care about science and the norms of good science, it seems to me that these norms were sacrificed as soon as there was a hint that there was a (frankly pretty inconsequential, though mathematically cool) prize to be won. 11/n

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On a related note, I find the race dynamics between the labs disturbing. 10/n

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That there is so much jockeying for credit between the labs, and people at the labs, suggests to me that the people closest to the technology might think it still matters. 9/n

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Will credit continue to matter so much as model capabilities increase? I'm not sure; I very much hope not. I think this is more a question about the shape of society than the shape of model capabilities. 8/n

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That some people are motivated by this does not make their work less important, and credit and prestige have historically incentivized good work. Of course I wish that we were all perfect truth-seekers and cared about this less. 7/n

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I wish that science was free from concerns of human ego but it's not. (Maybe it soon will be.) Top scientists mostly forgo substantial monetary compensation for their work, and are instead primarily compensated in credit. 6/n

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The weaker claim that PDFs or announcements put out by labs and lab employees often do not adequately attribute or credit other work seems correct to me. How important is it? 5/n

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And we should also celebrate exciting mathematics, even as we're concerned about mathematicians and mathematical expertise; who are these results for, if not us? 4/n

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Whatever one thinks of the labs, this is exceedingly dangerous to the health of profession; if human mathematics is going to survive we have to face facts about what the models can do. 3/n

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It seems to me that the primary function these claims have is to deny or downplay recent growth in model capabilities. 2/n

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boarders.bsky.social @boarders.bsky.social · 10/09/2026

There's been some recent suggestions that recent AIxMath successes have relied on stealing ideas from mathematicians' work in progress. While we can't know for sure what happened, I think the evidence for this is very weak. 1/n

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mathematics is absolutely enormous and spending any time in any part of it quickly reveals many worthwhile small and interesting questions without immediately satisfying or thorough answers

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Stay tuned, essay on this topic coming out Monday!

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My main point though is that I think that this argument is mostly about a refusal to believe the models are as good as they are. I’m very happy to concede AI companies have acted unethically; but if the profession is to survive we also have to face facts about model capabilities.

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(Not sure how trustworthy this is, of course.) But I also think we can try to evaluate how likely this sort of thing is to have influenced the outcome; from what little I understand about model training my weak sense is “very unlikely.”

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FWIW they have now (in the recent NYTimes article) denied categorically that Buckmaster’s discussions could have been used in training.

I agree that the models and the companies training them are bad at citation etc. and I am certainly not excusing this. If it is true that they took ideas from work in progress that's very bad. Just saying that the evidence for this claim is very weak.

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The issue is that our beliefs about how strong they are affect how we should evaluate the strength of the evidence here.

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They have now denied it categorically.

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What we do have strong evidence for, like it or not, is that the models are very good at math. If you found a good idea there’s a good chance the models can find it too.

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I think what’s happening is that (in these cases) there is a relatively small number of reasonable paths forward and the models try them all in parallel. So the fact that you had one of the ideas too isn’t much evidence.

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No, I don’t think so. The circumstantial evidence seems exceedingly weak to me. In 0/3 cases did the people claiming to have ideas stolen actually prove the theorem that the models did!