Slow Maths

Isabelle Gallagher, head of the French Mathematical Society

For a long time, I had the ideal job. As a teacher, I passed on not just mathematics, but also the taste for critical thinking, for confrontation, and the joy of discovery. As a researcher, I contributed my small part to the greater endeavour, alongside the wider mathematical community. I was part of this collective adventure, which I believed would never end. Slowly, insidiously, however, some flaws began to appear. We elevated colleagues to the status of heroes and heroines for their technical prowess and for the number of their publications in so called prestigious journals. We awarded an ever-increasing number of prizes, with ever-larger sums, to a small number of individuals, organisations or institutions, often focusing more on their productivity and reputation than on the substance of their work, or its inherently collective nature. We watched, amused or even flattered, as a Foundation placed a prize in dollars on a small list of mathematical problems to be solved within the millennium. And we used international competition and the lack of institutional funds as excuses to embark on a frantic race for publication, without taking the time to reflect on the fundamental purpose of our work. Over the past few months, doping has become a major issue in our profession. You can obtain it by yourself, or sometimes the institution provides unlimited access to it. At first, it was simply a matter of asking ChatGPT to check a bibliography, rephrase a paragraph, proofread a calculation or improve it. Then it became possible to ask directly to perform the calculation, or even to work out the correct calculation to perform. Now we can act as ‘super-prompters’, putting hundreds or thousands of agents to work to explore as many avenues as possible, having them correct each other’s work, letting them come up with ideas, and thus ‘crack’ one after the other doctoral subjects, problems that colleagues are working on, or those that the Clay Foundation has considered to be the most important. The ecological cost of this new way of practicing
mathematics is not addressed. What price is the mathematical community prepared to make humanity pay to answer its questions? Soon, the AI industries will have grown tired of testing and refining their models on our questions, using our very work we make available to them. In the meantime, we will have turned our profession into an ultra-doped race. In the face of this transformation, it is both urgent and essential that we return to the original purpose of our work and rethink the way we assess it. I dream of a new way of practicing mathematics, one that does not require us to resort to ‘doping’ just to stay in the race. It would be ‘slow maths’, just as there is ‘slow food’ or ‘slow tourism’. A form of maths where we have a firm control of its structure and objectives. Maths that allows us to stray down side paths which sometimes turn out to be more beautiful and more interesting than the one we originally set out to explore. Maths where we take the time to reflect, to write, to explain, and to share. This practice of ‘slow-math’ is essential because it is not the final result that matters and enables us to go further, but rather the process itself, the detours, and the collective endeavour. I am convinced that it is ‘slow-math’ that will help society progress collectively and soundly, and enable young people to continue wanting to learn, to question and to understand. This practice is now only possible if we collectively decide to put an end to the race to publish, and if we agree to value the idea that can lead to a result just as much as the techniques that finalize the proof, and just as much as proofreading, rewriting, and the sharing of ideas and methods. Only then will we be able to leave the race behind, take the time to understand things in depth, and once again practice the ideal profession.


Received 29 September 2026.

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6 responses to “Slow Maths”

  1. billjr Avatar
    billjr

    Doping makes it sounds like mathematics is some sort of athletic competition, like marathon running, which for most people is a hobby. I’m not sure this is going to be a helpful comparison for maintaining funding levels. If we preserve the slow nature of mathematics, but government agencies lose interest because there is less connection with other areas of science and less progress, then there will be even less money for young people. (There are big differences in the way that science is funded between Europe, the United States and China; maybe in Europe it is more feasible to argue for ai-free mathematics funding as an essential part of the human endeavor, but in the United States it is not.) If funding levels drop dramatically, in what sense have we preserved the field? For decades the community has promoted the idea that mathematical progress has applications and advances science in general. The rest of science is “very” excited about artificial intelligence. It’s hypocritical to change our tune now. The part about valuing ideas and sharing methods I agree with.

    1. N Avatar
      N

      In what sense does paper-prompting “preserve the field”?

      1. billjr Avatar
        billjr

        We are going to have to get more creative about allocating resources, and not reward paper-prompting as the OP says. But that doesn’t mean we should turn off agentic AI.

  2. M Avatar
    M

    I agree fully with the above comment by billjr, but also with the post itself. I think the situation is simply very complex and there are many layers.

    There is one layer, clearly, at which we have to understand math (and many other things) the slow way (due to our biological limitations), as otherwise humans will lose control and we will make way for some new species or entities to dominate the world and us, potentially in a way very bad for us, though it could also be otherwise. Also, math and other sciences, likewise literacy, arts, and so many subjects, are an immense heritage that we must treasure and develop further.

    There is another layer, which is about the fact that we need to make a good living if we put in 40-80 hour work weeks or more. The importance of our survival as intellectual species alone can lead to enough funding, e.g. to make sure future generations become smarter and can use their inherent abilities to keep stronger and stronger tools in check, while using them in responsible ways. The point is that most of us need to put in a lot of work to rethink how we can add visible value and how we implement the suggestions made in the post. This might not only be along the seemingly obvious ways, I think we really need to come up with creative ways to demonstrate the importance of having agency over our knowledge.

    For a third layer, I think we need to clearly map out the limitations of AI in math, even though these limitations change daily and mapping them out influences them. Math is infinite, AI is finite, maybe I am wrong with this, but I think it may be an idea worth considering to push back against AI firms by posing meaningful problems, endless of them, not just the few famous known ones, all kinds of new problems (on which nobody worked on so far) which they should be able to solve if they solved math, as claimed. So difficult and potentially interesting ones that they need much more compute than they can afford. So well-communicated ones that it will be noticed by the public that we are able to deliver well-motivated problems which we expect to be answered by AI within a month if AI would have solved math, and if AI solves some to respond with deeper and more difficult questions. Similar challenges can be posed for other aspects of research, like exposition and presentation. Certainly, this may help AI to get better, but I think in any case it will get better, especially if companies receive public funding that would be better invested in mathematicians and other scientists that are crucial to our collective ability to steer the ship. I think our public response should be a convincing ‘no, math is not solved’.

  3. postdoc Avatar
    postdoc

    “Soon, the AI industries will have grown tired of testing and refining their models on our questions, using our very work we make available to them”.

    I am sorry, but saying this means you don’t get what is going on at those labs at all. Why do you even think that they will be ever tired of what they are doing? The only reason they will ever be tired is when they run out of money, which is not happening anytime soon in the next 5-6 years (assuming “soon” means 1-2 year).

  4. classycloudfe751e4564 Avatar
    classycloudfe751e4564

    The title “slow maths,” with a European “s” rather than just “slow math,” reminds me fondly of “slow food” that is briefly mentioned in this essay. “Slow food” was a movement in Italy when I lived there, on weekends driving in my Fiat Tipo to all those slow food restaurant in Tuscany and collecting plates. “Slow food” was started around 1989 by a group of dedicated people who opposed the opening of a McDonald hamburger joint near the Spanish Steps in Rome. The aim was to promote locally grown food and traditional gastronomy, including taking time to enjoy meals and good company. It is this idea, I believe, that Dr. Gallagher is applying, mutatis mutandis, to mathematics. I also want to support her opinion, “Soon, the AI industries will have grown tired of testing and refining their models on our questions,” by giving some reasons for this.

    For several reasons AI companies will withdraw from an all-out conflict with math. Firstly, a long-term engagement with the truly difficult problems, such as the Millennium Prize Problems, may simply be too expensive, counting the company’s human resources (e.g., in-house mathematicians) and computing resources. Rumor has it, that the proof of the Quasi-Rieman-Hypothesis was very expensive, not “only” a three-hour run. Secondly, an AI company’s use of its spectacular math results for marketing or as a demonstration of competitive power will show a diminishing return. Instead, it may sell additional higher-priced models to universities and science institutions and turn its attention to more lucrative ventures (that are likely less innocent than proving theorems). Rich individuals may, similar to art collectors, still buy from AI a proof of, say, the irrationality of a certain value of the zeta-function, and hang it on the wall like a minor Picasso. Thirdly, in spite of the hype in the media, AI companies have received some bad press related to safety, transparency, intellectual property, number of data centers, and general rude behavior. AI’s ubiquitous presence has raised the specter of Big Brother, leading to angry public responses and calls for more regulation, for instance by democratic governments.

    OK. This may sound like a naïve claim, like wishful thinking. True, it doesn’t contradict the undeniable fact that AI can do certain things that traditional math, Math 1.0, cannot do, or will ever do. Attacking 4000 math problems at once, publishing 722 papers on one day, and spending billions of dollars to impress the world, that’s not what creative humans do. Virgil spent eleven years of his life to write “The Aeneid,” a grand national epic poem that would link Rome’s origins to the gods. Michelangelo perched high on rickety scaffolding for four years paining the ceiling of the Sistine Chapel. Andrew Wiles hid for seven years proving Fermat’s Last Theorem. With the right prompts, ChatGPT could possibly have done any one of these three works in about three hours. Does this mean that the era of “heroes” like Virgil, Michelangelo, Euler, Gauss, Hilbert, Ramanujan, Wiles, and Fields-Medalists is over? I don’t think so. I hope for more heroines.

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