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. As the authors note, AI threatens the values of the discipline.

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, which I’ve paraphrased from the declaration. I’ve also expanded them slightly.

1. The autonomy of mathematics is at peril. We should prioritise research questions articulated by experts, rather than results admitting proofs tractable with AI tools. The research agenda shouldn’t be governed by AI hype.
2. Restricted access to the most capable models creates an uneven playing field. If your instution doesn’t offer a premium AI subscription and you cannot afford it yourself, you’re at a disadvantage relative to your peers – there’s usually a significant difference between the free and paid models.
3. The announcements of novel results via press releases or blog posts endangers their proper evaluation. The underlying issue is that current mathematical infrastructure cannot accommodate AI-generated content – arXiv is cracking down on AI slop – so AI companies are forced to communicate findings via other channels².

Two questions #

The declaration is open-ended, inviting to reflection. Here are two questions 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 Price³, 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 wonderful initiative. 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.