Is it fish love?

Tancredi Schettini Gherardini, postdoctoral researcher based both at the University and at the Max Planck Institute in Bonn.

This reflection starts with a parable I learnt from a recording of Rabbi Dr Abraham Twerski. He came across a young man who was clearly enjoying a fish that he was eating, and asked: ‘Young man, why are you eating that fish?’. And the young man answered ‘because I love fish!’. The Rabbi said: ‘Oh you love the fish, that’s why you took it out of the water and killed it and boiled it? Don’t tell me you love the fish; you love yourself, and because the fish tastes good to you, therefore you took it out of the water and killed it and boiled it.’

The message is that so much of what is usually called love is actually fish-love, i.e. we don’t love the object/person per se but how it/they make us feel. My intuition is that the nature of one’s love for mathematics is intimately related with their views on AI.¹

What is it that drives a mathematician to persevere through pain and frustration until a conjecture is proven or disproven? Is it to establish that they are better than others? Is it the satisfaction which comes from reaching a goal that has required so much of their time and energy? Is it the pleasure of knowing the answer to a question they find really interesting? Supposedly, in practice, it will be a mixture of the three. But is there one which overweighs the other two? Is there one which should outweigh the other two?

The answer is deeply personal, and I shall not argue here whether one is better than another. My message is that to understand our own views on AI for mathematics, the most appropriate starting point is an introspective analysis of why we – not as a community, but we-ourselves – love mathematics. This might be a complicated and even disturbing process; but, as Aristotle said, “knowing yourself is the beginning of all wisdom”.

Let me articulate my argument in a way that is agnostic to the notion of what is a correct motivation for doing mathematics. If mathematicians are most concerned with (possibly interesting) answers to interesting questions, then it is quite hard to argue against the benefits of AI in the subject. One can argue about the negative consequences in the general picture that is wider than mathematics (like environmental damage, privacy issues, monopoly, increase of inequality and unemployment, not to mention the risk of extinction); these are all very serious and well-founded worries which would need many essays, and I shall not deal with them here.²

When restricting to the features that are more specific to our discipline, one can argue about the potential risks in mathematics, which I think mainly boil down to two aspects.

Firstly, losing some important habits and routines essential in the practice of doing good mathematics – mostly those which ensure a deep understanding of the material, such as insightful human interaction, long-term projects and frequent productive struggle, for instance. But, regarding this concern, we have all the tools to deal with it effectively. In fact, we can act upon it by following these good habits ourselves, adapting them in a meaningful way when needed, and transmitting them to the newer generations. To ensure that they keep being part of a mathematician’s workflow, we might require some adjustments on a few fronts, such as the publishing process (where it is desirable to cut out or at least flag AI slop), the hiring process, and many general criteria for judging the quality of a mathematician. This is not just completely in our hands, there is also (almost) complete unanimity: I have never heard any mathematician, optimistic or pessimistic about AI, ever saying that we should give up understanding as a fundamental part of the discipline. To summarise, the temptation of these tools might pull us unwillingly away from understanding, but this risk has already been identified and acknowledged by our community and we have the power to make practical changes discouraging and preventing misuse of AI; in fact a few of these changes have already been implemented and many are currently being discussed.³

The second risk, which I personally consider to be scarier, is that of mathematics losing appeal for young bright minds; once more, it is up to us to not let this happen, illustrating how AI can be embraced in a constructive way, without disrupting the essential features of our field and the understanding-related practices mentioned above. Maybe even more importantly, it is hard to believe that the conservative choice of refusing any use of AI could attract more smart kids to join our community.

As of today, I do not see bigger problems than these two, which are only potential. And so, what are the benefits?

Since a few months ago, most of us have had our own version of Namagiri Thayar. It does not reveal formulas in our dreams, like the Hindu goddess used to do with Ramanujan, but it does so while we are awake and sitting in front of our laptop.⁴
Our reaction to this fact seems a bit different from the one people had one hundred years ago: I did not find any references of mathematicians from that time complaining about these revelations, nor signing petitions for banning Namagiri Thayar from Ramanujan’s dreams. But now that we all have something equivalent, a different chord was struck in the collective consciousness of our community. A purely emotional one, I argue; because if one’s priority is really the progress of mathematics, then why not embrace this new reality, made of Ramanujan-like moments, driven by AI suggestions, constructions, and results, and Hardy-like moments, trying to make sense of these results, with rigour, clarity and sharp understanding. If one’s love for mathematics is a genuine strive for advancement, and not simply the fish-love of Twerski, then it is impossible to not see the incredible chance we have to push our explorations in this beautiful subject.

The opposite is true if one’s love for mathematics mainly comes from the way that mathematics makes them feel. The feelings of finding a new clever way around a seemingly insurmountable obstruction, constructing a special interesting object that no one had thought of, or proving an important theorem for the first time, are all very much at risk. Because that new argument, example, or proof, could be generated by an LLM operated by someone who may or may not, in many instances, be an expert in the subject; in that case, the emotions which usually come with the mathematical discovery/invention are just gone.

The truth is that inside everyone’s passion for mathematics, and inside everyone’s love for someone or something, there is often a component of genuine and unselfish love, inevitably mixed with some fish-love. We are humans, after all. But if the former prevails, and we are driven by the sincere admiration of the exquisitely intellectual activity that has led humans from a few primitive logical observations to the immense and sophisticated body of knowledge that we have today, we might live the advent of AI with more optimism.

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Received 24 September 2026.

1. Throughout this essay, I will use ‘mathematics’ to mean ‘pure mathematics’ and ‘mathematicians’ to mean ‘pure mathematicians’. Many of the considerations below apply in general, but not all of them. ↩︎
2. Let me spend a few words on those global consequences which impact mathematicians as a part of society. The first one is the possible shortage of funding; as of today, theorems in mathematics are a perfectly inelastic good, and there is no good evidence to suggest they should change to be so. Concerning inequality, that is a real issue which should be dealt with; it might be mitigated by the improvement of open-weights models, but there is no guarantee. In any case, this social aspect is somewhat orthogonal to the one I would like to focus on, i.e. the development of mathematics itself. Regarding privacy and intellectual property, they are also real concerns, but it seems possible to deal with them. One can use incognito sessions for sensitive material and do a much more detailed literature search than just quoting the LLM’s output, respectively. ↩︎
3. One might argue that a foreseeable future scenario is that in which we delegate all of our thinking to the machines. Once more, that is ultimately up to us, and not a very likely prediction under mildly optimistic assumptions. Finally, if that will really be the case, we will have bigger problems than worrying about mathematics… ↩︎
4. With all the obvious caveats, of course, such as hallucinations (although very rare nowadays) and the abundance of AI slop. ↩︎