Mathematics and AI

Mathematical research (including research in theoretical computer science) is being shaken up by developments in generative AI. The question for us now is – how can we change the publishing/hiring/tenuring trends in our field so that maths doesn't just die. I explain my view of the problem below. But first, here are some writings on the topic that I particularly like:

A Severe Misalignment of AI in Mathematics Written by 25 Fields Medallists and released on 11 Sept 2026. Available here. This letter explains the misalignment and the harm that it causes to mathematics as a discipline. It is now up to all of us to figure out what to do about it. Un-inventing AI is not an option. The responsibility now lies with our community. We must change the metrics that we use to assess progress in our field.
Mathematics in the age of AI. Public lecture by Terence Tao at the 2026 ICM on 24 July 2026. I agree with this analysis. Here is an ArXiv paper based on the talk and here are the slides. All mathematicians should read this. (It is much more important to read Tao's article than to continue reading this page!) You can also read Tao's writings on mathstodon (without joining any social media).
Leiden declaration on AI and Maths. This is a thoughtful declaration, released on 2 June 2026, which includes positive suggestions about how to address these new challenges. Details are here.

The recent rush by some mathematicians to feed so many of our problems into generative AI models is leading to an odd situation where humans are currently becoming line-checking referees for machines. This way of working is likely to lead to decreased human understanding in the long run. It is easy to line-check a proof without really understanding the essence of it, and the essence is what is important. As a side note, this way of working also takes the joy out of mathematics – line-checking is one of the least enjoyable parts of being a mathematician – the best part is working together to generate understanding and solve problems.

The combination of the new availability of AI tools and the existing culture in mathematics causes a particular problem for young researchers. Traditionally, PhD supervisors find "somewhat easy" problems for PhD students. The student works on these problems (with the supervisor) – learning along the way. It takes a long time because there is a lot to learn. After that, the student's track record of "problems solved" is the credential that leads to postdoctoral research positions (and to permanent positions). With the availability of AI tools, it is increasingly difficult to find suitable "somewhat easy" problems. A problem that can be solved by a new PhD student is likely to be solvable using current AI models. Recent developments (including the announcement of the solution of the Navier-Stokes problem) make it clear that AI models can already do substantially more.

It is now apparent that the "track record of problems solved" is going to be a bad metric for judging mathematicians in the future, at least in the near future. I agree with Tao that the best solution for the mathematical community may be to put more emphasis on exposition and much more emphasis on high-level understanding.

Mathematics is cumulative, so it is important to keep the literature from being cluttered with incorrect proofs. However, the increasing volume of AI-generated proofs is a real problem – the community can't keep up with checking them or understanding them. Work on formalisation (checking proofs using Lean, or other theorem provers) and AI-based auto-formalisation is useful for this. Two caveats:

Formalisation cannot completely solve the correctness problem – humans would still need to verify that the problems are correctly translated into Lean. Also, Lean and Mathlib can have bugs. Here is an example.
Formalisation is not enough. The ultimate purpose of maths is not just to produce solutions to problems – it is to produce understanding. Formal proofs do not do this. In fact, they are particularly difficult to read because they miss essential intuitive explanation.

Going beyond mathematics, I am worried about the impact on society of the cognitive outsourcing that is occurring.

In any case, (like so many other people!) I think it is time for the maths community (including Theoretical CS) to think about our objectives. AI is a useful tool, which is clearly here to stay. We need to think about the culture and working practices of our field in order to figure out how to use it wisely.

Further related links, questions, and thoughts

Proofs and Prompts is a communal blog on this topic.
The true cost of LLM use: The true cost (including energy for training) of using generative AI to solve maths problems is not currently publicly available. Are the energy costs excessive (for individuals or for the world)?
Should journals accept papers (by human authors) when the ideas came from LLMs? I think not, even though that causes an incentive problem – I don't think it is immoral to use AI for doing maths, but I do think it is immoral to use AI without disclosing it.
I don't agree with the conclusions of this paper by Max Weinreich. It doesn't seem plausible to me that the maths community could (or should) resolve not to use an available (and useful) technology. Nevertheless, I think he is brave to put it out there, and he raises important concerns. Also, my current stance on AI use in my own collaborations (see below) is a little bit aligned with his thinking, even though my justification is personal, and more pragmatic.
Steven Kelk makes lots of interesting and thoughtful posts on this topic – see his page here. (This page is accessible without joining social media.)
Alberto Romero's blog The Algorithmic Bridge has some thought-provoking articles, including The Month AI Conquered Math: The Full Story and Millennium Pastimes: Has math been solved by AI?
I did not address here the question of why society should want to keep human mathematicians and not just to rely on AI. I think this is clear, not just because of the issue of verification (correctness), but also because I'm a strong believer in the unpredictable and huge benefits of curiosity-driven research (I don't believe that AI can achieve these benefits). Boaz Barak says more about this in his blog post here.
Po-Ling Loh from Cambridge Statistics has written an interesting article about this topic on pages 12-14 here. Since my work definitely comes under "Combinatorics" I was struck by her initial remark that, three months ago, she had thought "maybe it was just combinatorics or number theory on the chopping block" but that she had come to see that the whole of maths was at risk. She also believes that the solution is to change the culture of mathematical research. I think so too - in fact, I don't see any other solution. Her proposal is to move to an extremely collaborative publication model where papers are required to have "enough experts in a sub-area". I think perhaps we should instead de-emphasise the importance of papers altogether, but I am not sure. Po-Ling charts her progress from not being worried (because early state-of-the art LLMs weren't really all that good at maths, despite media hype) to becoming very worried. My path is the same. I didn't become very worried until the end of July 2026, when I first had one of my own research projects killed by somebody's one-shot AI solution (I quit the project at that point - I have no interest in joining an AI-based collaboration). Shortly after that, I started seeing one-shot papers solving problems that I'd actually worked on (without success).

We don't get to choose what is true, we just get to choose what to do about it. So it is a very important time for the mathematics community.

AI use in my own current projects

Despite the fact that I don't agree with Weinreich's full solution (as mentioned above), I don't want substantial AI use in my own collaborative projects. My reason for this is that, although I'm interested in the problems that we work on, I care more about the process of working together, coming up with ideas, and generating understanding than I do about the one-bit answers to the questions themselves. I continue to believe that human understanding is the purpose of mathematics – I did not become a mathematician in order to spend my time as a line-checking referee for a machine.

Not everybody agrees about this, so it seems that collaborators should now agree an "AI policy" before beginning to work together. Here is the policy that I currently propose for my collaborations. I don't really view this as any kind of ideal solution. It is just how I am doing it, for now.

Obviously, any collaborator may use LLMs as search engines, to learn things. Learning is good. Generative AI is excellent for search (it enables looking things up without even knowing what they are called!) It is obviously very sensible to use generative AI for boring routine tasks like making latex pictures and diagrams.
I don't join projects without checking first that co-authors don't plan to send the actual research question to an LLM, or to ask a machine to produce the main proof or proof idea. (This is not a moral statement - I just don't want to be involved in such a project.)
There are many grey areas: What if you just want to speed up the proof of a routine easy lemma by using an LLM? In my view this is OK, but I prefer to work in situations where co-authors would check with each other before doing this. Also, I'm not going to do it myself. What is the point? We are mathematicians because we want to think - why outsource the fun part?

I plan to update this page as frequently as I can – feel free to send me your ideas and thoughts.

Leslie Ann Goldberg, 13 Sept 2026.