Math & AI

As is evident by my last blog post, I used an LLM for a preprint recently (with Sam Mattheus). It feels necessary to have a second, short post addressing the wide-spread concerns regardings the usage of LLMs and how much money AI companies are investing to solve prominent open problems in mathematics. This has been very disruptive and the math community needs to partially reassess how it works. In parts, I am (manually, without AI) plagarizing parts of Anurag Bishnoi’s blog post here.

First of all, there are several declerations on AI usage. At the time of writing, I am aware of the Leiden declaration, The Association for Human Mathematics (AHM), \begin{proof}, and Math and AI. The principles of the Leiden decleration I tried to follow so far. The decleration “Math and AI” I just signed. One paragraph that I would like to highlight is the following:

In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas.

As an editor, reviewer, and just regular consumer of the arXiv, I have seen several preprints where it was clear to me that the authors did not develop any understanding of the underlying problem. While often solving prominent problems. Even limited to my core interests, I will need years to digest these and to think about what might be an interesting next question. Otherwise, this does not seem to create any progress. (Of course there are also some AI-assisted preprints which I consider excellent and where I am sure that the authors put much effort into understanding their results. And after reading the preprint, the ideas are quite clear to me.)

Anurag’s post also gives a list of reading recommendations. The article Knowledge Collapse by Micheal Harris I enjoyed a lot. His quotes in the beginning are wonderful. He quotes Stefaan Vaes’ explanation for why we do mathematics: “Omdat wij dit graag doen”. In English: “because we like to do this”.

Finally, for my own research I still have to decide what to do. Now I had one finished project that involves LLM usage. And I have two ongoing projects for which I used LLM (probably, corresponding to three papers). But I do not want to rush any of these. For now, I will also not tell my collaborators or my students what to do. Personally, the main point for me is to keep having fun doing mathematics. In the long run, I will need to get an idea of what I consider an ethical usage of AI. (At least I do not want to stop using it for proofreading. Or for Lean formalizations.)