In an episode of Math-life Balance, Olga Paris-Romaskevich asks whether she’d be doing mathematics if she were living alone on a deserted island¹. After some deliberation, she says:

I think I do mathematics to share it with other people who do mathematics. I think it’s the most exciting part for me. People was something that guided me a lot in this choice [to do mathematics for a living].

The host, Maria Yakerson, smiles and remarks that many mathematicians chose mathematics because they appreciate mathematicians.

Indeed, the mathematical community is remarkable. For this reason, I was pleased to learn about the Leiden Declaration on Artificial Intelligence and Mathematics, which calls for action to address the challenges posed by AI within mathematics research.

To me, the declaration seems extremely well thought through. At the same time, it feels like an impassioned plea to safeguard the mathematical community – in some ways, it reads like a love letter. In this post, I wanted to comment on the passages that particularly resonated with me.

By humans, for humans #

What I like the most about the Leiden Declaration is that it stresses that mathematics is a distinctly human activity. They put it as follows:

Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions.

In other words, mathematics is largely about training mathematicians. A paper isn’t merely a certificate that a result is true; it’s also a piece of exposition. Therefore, an AI-generated proof which only AIs understand, even if correct, is of limited value. There is a sense in which only human mathematicians can do mathematics.

Three risks #

Out of the risks associated with AI in mathematics, I particularly agree with the following three.

The first threat concerns academic freedom.

These developments [recent developments in AI] put the autonomy of mathematics under threat. The increasing involvement of technology companies in mathematical research raises the risk that research questions may come to be prioritized because of their amenability to automated mathematics, rather than expert judgment of their deeper significance.

Yes – the research agenda shouldn’t be governed by AI hype, but by the experts who put in the effort to understand a proof properly. Interesting mathematics is, almost by definition, the mathematics humans care about.

The second risk concerns unequal access to AI – a problem not restricted to mathematics within AI, of course.

Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives. The use of artificial intelligence — and thus also the sort of problems which it can address — may become incentivized for its own sake, disrupting our mechanisms for hiring, funding, and recognition. This disadvantages researchers who do not have access to the technologies or decision-making related to them, or who are unwilling to use technologies controlled by organizations whose values they do not share.

I agree on this point: there’s a marked difference between the free and paid models. If you can vibe code an autonomous research agent – with subagents web scraping open questions from arXiv, solving them, formalising them and crosschecking each other’s solutions – you would likely solve some open problems (e.g. conjectures about points on a plane). Presumably the labs are doing this right now; individual researchers with deep pockets could do the same.

Finally, there’s the risk of science degenerating into marketing.

Proper evaluation is endangered if results are communicated through informal channels such as press releases or blog posts, often without any research paper or other disclosure of information necessary for scientific evaluation. This practice seeks publicity for new results on market timelines before the accepted processes of community evaluation in mathematics can take place.

For sure. As Terence Tao has pointed out, there’s a need for new mathematical infrastructure, to complement traditional infrastructure: current publishing outlets cannot accommodate AI-generated content. Because the arXiv has a strict policy against AI slop, AI companies are forced to communicate their findings via other channels. I also imagine this policy misfiring, with authors reluctant to disclose AI use. Anyway, this third problem seems easier to solve than the first two.

Two questions #

The declaration is open-ended, inviting reflection. Here are two questions that came to mind.

The declaration asserts that results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness. However, the notion of authorship is becoming increasingly ambiguous. For example, Erdős problem #1196 was solved by GPT-5.4 Pro, prompted by Liam Price², and the result was then verified by various experts. Who is the author here? Only citing the experts as authors seems misleading.

With regards to the autonomy of mathematical research, it’s worth imagining a future where most research takes place within research labs in industry. I’m not saying this is plausible nor desirable – this is just a thought experiment – but the situation is worth pondering.

The research university is a relatively recent invention: before the 19th century, cutting-edge research took place in scientific institutions. If research becomes extremely capital-intensive – because it requires state-of-the-art AI – more of it might take place in research labs in industry. What will then be the role of universities? Universities might become more like the teaching institutions they used to be in ancient times (not just October 2025, but in the 1800s).

Conclusion #

Overall, the Leiden Declaration is a very thoughtful report. Mathematics has a unique stature among academic subjects: it is the softest hard science – the most human-oriented. As such, it is particularly vulnerable to challenges introduced by powerful AI.

AI is undoubtedly changing mathematics, and will continue doing so; the discipline could lose its distinctive character or it could flourish. I view the Leiden Declaration as a crucial step in making the adoption of AI go well.