Salvaging that which is dearest

David Cimasoni, senior lecturer at University of Geneva

AI use: none. See the last footnote of this post.

My emotional state during the past months may best be described as passing through the five stages of grief – every single week. However, it was also heartening to discover the numerous beautiful and inspiring essays written by fellow mathematicians. I frequently experience positive emotions reading them, including a sense of community belonging which is stronger than ever. It seems that dealing collectively with grief provides many of us with a genuine bonding experience.

I also find it poignant to see how, in the midst of such turmoil, we attempt to make sense of it all by trying to salvage what is dearest to us. High profile mathematicians often eloquently advocate preserving the “artisanal way” of research which played such an important role in making them who they are, while passionate instructors primarily focus on how best to reform curriculums in order to address the challenges of the new era. As for junior mathematicians, they frequently embrace the new tools to keep alive their dream of a successful career in academia – and understandably so.

This post¹ is about what, to my own surprise, I instinctively rushed to salvage, what appears to be dearest to me as a mathematician. Its aim is not so much to contribute to a debate, but rather to elicit the same kind of emotion I experienced myself while reading other contributions to this remarkable platform.

Disclaimer

I am blessed with an academic position among the least impacted by the AI revolution: high enough not to worry about my professional future (aka tenured), and low enough to experience neither dramatic loss of status nor constant fear of being scooped.² From this advantageous situation, it is not too difficult for me to adopt a relatively positive tone for this note. This does not mean that I am unaware of the dire situations faced by many colleagues (especially junior ones), and that I do not deeply care about them.

Societal impact of the AI revolution

Like many others, my first reaction in trying to make sense of the rapid societal changes is to reach for historical parallels and analogies.

Similarly to the industrial and agricultural revolutions which gave us access to unimaginable amounts of physical power and nutrients, generative AI tools provide us with direct access to “answers” that were beforehand only available via (at least some minimal amount of) personal reflexion. Just as it is now widely accepted that regularly using one’s physical power is a good idea and binging on food is not,
it seems crucial to understand the importance of following a balanced “AI diet”³. Those who fail to do so face the danger of a rapid loss of cognitive well-being, a deskilling incomparably more rapid and brutal than those induced by the industrial and agricultural revolutions.⁴

Reaching for another analogy, I tend to think that AI tools are to intelligence what social media are to socialization. While Facebook and Instagram made us globally more connected, it is doubtful that many of us actually became more social in the process. Similarly, while ChatGPT and Claude might well allow for spectacular collective progress with respect to specific goals, I do not believe that it is making any of us smarter – rather the opposite.

There is a real risk that new generations will fail to put in the hard graft necessary to develop their cognitive abilities, reaching adulthood with their pockets full of answers but with little intellectual rigor, critical thinking, etc. In this new era where answers are available at our fingertips, it is crucial to insist on the fundamental right to make mistakes. Quoting Grothendieck:

To fear the error and to fear the truth are one and the same.
One who fears to be wrong is powerless to discover.⁵

Delivering these messages is most probably one of the greatest contemporary challenges faced by parents and teachers. Hopefully, this will allow us to refocus education on its primary goal: teaching how to think independently without taking answers at face value, whether it comes from a friend, a parent, a professor, a politician seeking reelection, or an LLM. The stakes for our democratic societies are difficult to overestimate.

Even more fundamentally, the emergence of these tools brings to the forefront the philosophical question of the intrinsic value of an activity, since AI can more often than not carry it out on our behalf. Nowadays, it is certainly possible to ask ChatGPT to chose the birthday gift of one’s child and to write the card – this does not mean that it is a good idea. Similarly, immediately asking Claude for the answer to a given question will often defeat the purpose (which is to think about the question rather than to obtain the answer), just like taking a helicopter defeats the purpose of a mountain hike.

Societal role of mathematicians in the AI revolution

How can I, as a mathematician, be useful in trying to address the challenges of the ongoing revolution?

Since “hallucinations” can be filtered out more efficiently in our field than in any other, it has been argued that mathematics could be used to supply “theoretical upper bound for what the maximal safe level of AI use can be”. I disagree: this bound is extremely high, and therefore of no practical value whatsoever. Mathematics could once again⁶ provide a false impression of rigour and security regarding the application of these tools to the fields they will inevitably tackle in the future.

On the other hand, I see three reasons why mathematics constitutes the ideal discipline to help us all face the societal impact of the AI revolution.

The first reason is obvious: mathematics is par excellence a human activity which strengthens cognitive reflexion. Here is the second: formal mathematical language upholds the highest standards of clarity, rigour, and precision – the ideal framework for conducting a healthy debate. Thurston formulates this beautifully in his famous essay:

Because we have a high standard for clear and convincing thinking and because we place a high value on listening to and trying to understand each other, we don’t engage in interminable arguments and endless redoing of our mathematics. We are prepared to be convinced by others.

Research in cognitive psychology conducted during the onset of the COVID-19 pandemic precisely identified these two criteria (scoring high at cognitive reflexion and low at socio-cognitive polarisation) as the most heavily correlated with the ability to discern real or fake news. In times of uncertainty, mathematics therefore constitutes a field of the utmost importance to help us become enlightened citizens.⁷

The third reason why I believe that mathematics forms a crucial part of the solution to the societal challenges of AI lies in the true goal of our discipline. As passionately explained by many, the product of mathematics is neither proofs nor theorems, but human understanding, which will always remain the prerogative of human beings.⁸ For an honest description of our raison d’être, we absolutely need to articulate the neuroplastic value of intelligibility. And once again, it is on Thurston’s shoulders that I like to stand to do so, via his famous post⁹ on MathOverflow:

It’s not mathematics that you need to contribute to. It’s deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? ($…$) The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat’s Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that
increased our understanding. The world does not suffer from an oversupply of clarity and understanding (to put it mildly).

Afterword

In 1994, I had proudly announced to my neighbour that I was about to undertake studies in mathematics. His reply had amused me quite a bit: “But mathematics is useless nowadays, with computers!” It was easy to laugh about it thirty years ago – less so today.

As late as March 2026, I was still claiming that while translators and programmers would rapidly become obsolete, the activity of mathematical research still had a bright future ahead and would certainly be the last one impacted$…$ Yes, I lingered in the first stage of grief for longer than I would like to admit. I now realise that this delusion was rooted in an inappropriate feeling of superiority: the AI revolution has forced upon me a lesson in humility that was probably long overdue.

I feel extremely fortunate to have secured a stable professional position before the advent of these new tools. This allows me to make a free choice about their use¹⁰ without fear for my own future. But I do fear for the future of my children.

Given the revolution unfolding before our eyes and the threats it poses to our democratic societies, it is legitimate to ask how our skills might best be put to use. As a mathematician, how should I devote my efforts to the “well-being of the world“? Should the priority be to broaden our individual and collective understanding of the world through research? Or should it rather be to help the next generations choose the path of cognitive independence, of intellectual rigour, and of questioning their own beliefs? Of course, the two are not mutually exclusive, and the abilities required are not interchangeable. Yet, in light of my personal competences and values, I find myself tempted to redirect a substantial portion of my energy from the former to the latter.

Only time will tell if this is just me dwelling in the third stage of grief.

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Received 30 September 2026.

1. It is loosely based on a more comprehensive essay (in French). ↩︎
2. Anyone at an AI company trying to run its frontier model on the kind of questions I am currently pondering would probably get fired on the spot. ↩︎
3. An expression coined by Tao for university students, but which applies to everybody. ↩︎
4. Incidentally, the first (neolithic) agricultural revolution did not lead to a reduction in famines and malnutrition, and historians argue that it is not Homo sapiens that domesticated wheat but rather the other way around; this makes the analogy with the AI revolution all the more interesting. ↩︎
5. Craindre l’erreur et craindre la vérité est une seule et même chose. Celui qui craint de se tromper est impuissant à découvrir. (English translation from this source.) ↩︎
6. I am old enough to remember the role played by mathematics in the 2007 subprime mortgage crisis. ↩︎
7. Plato has understood this fact, as mathematics and dialectic formed the core disciplines of his Academy. ↩︎
8. A tautology that I find soothing. ↩︎
9. A post written on the day of his 64th birthday, less than two years before his death. ↩︎
10. In my research, but also elsewhere: no LLM was used in the production of this text (though thanks are due to Paul Turner for reviewing the language). ↩︎