Mathematics and AI

Mathematical research (including research in algorithms and complexity theory and other areas of theoretical computer science) is being shaken up by developments in generative AI. Here are some writings on the topic that I particularly like:

Leiden declaration on AI and Maths. This is a thoughtful declaration which includes positive suggestions about how to address these new challenges. Details are here.
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.

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 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 may well be solvable using high-end AI models). More generally, it seems 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.

I am somewhat encouraged by current work on formalising mathematics (checking proofs using Lean, or other theorem provers). Since mathematics is cumulative, 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 – not all of these are correct and the community can't keep up with checking them. Work on auto-formalisation is therefore relevant. Two caveats:

Formalisation cannot completely solve the 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 really do this. In fact, they are particularly difficult to read because they miss essential intuitive explanation.

Going beyond mathematics, I am starting to get worried about the impact on society of the cognitive outsourcing that seems to be 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.

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

Leslie Ann Goldberg, 26 August 2026.

Further questions, thoughts, and related links

Here are some related things that I've been wondering about, including good questions raised by friends and colleagues.

Economics of maths research: Is the availability of high-end AI tools (to some researchers, but not to others) causing a new kind of unfairness? Is it significant in the context of all of the other unfairnesses that already exist? If so, what should we do about it? Should researchers be spending their own money on AI tokens?
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 would say no, but that does cause 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.
I don't follow social media, but I have seen that Steven Kelk makes lots of interesting and thoughtful posts on this topic – see his page here. Glancing through as I write this, I was rather struck by his re-post on 7 Aug of a plot enumerating math.CO submissions by year. There are apparently a lot of other blogs about maths and AI, and links to them from Steven's page.
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 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 cause these benefits). Boaz Barak says more about this in his blog post here.

AI use in my own current projects

Despite the fact that I don't agree with Weinreich, 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 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?