Acknowledgement: This essay was edited with the help of AI.
The day mathematics felt different to me was sometime in July. Until the beginning of this year, I had mostly avoided AI, hoping the hype would blow over. Anyway, the models hallucinated too much to be very useful. Then something changed. They got better, very very quickly.
By July, I had to admit that these models were better than me at doing mathematics. Unsettling as this was, it was not an entirely unfamiliar feeling. After all, there are plenty of people with far greater mathematical abilities than me. So I told myself: here is another better mathematician, one who just happens to have no body.
Then came Navier–Stokes.
It is hard to describe what the Navier–Stokes announcements did to our community. We need time and distance to take full stock of the shock, anger, grief, and the profound sense of disorientation, anxiety, and vulnerability that has ensued. But time is precisely the luxury we do not have. We must therefore press ahead.
Of course, mathematics was not the first victim. Earlier in the year, coding had already gone through its own version of this upheaval. But this did not produce quite the same shock waves in the society: for better or worse, nothing embodies intelligence in the popular imagination quite like mathematics. For programmers themselves, however, the shock was profound, as recounted vividly by Bill Gates in a recent interview.
As mathematicians, we might treat one instance of a phenomenon as a curiosity. Give us two, however, and we start looking for a new general principle, one that explains both phenomena and extends beyond them. So let me state explicitly a conjecture which appears to be widely believed within the mathematical community:
Conjecture. AI will far surpass humanity in all intellectual domains.
It is, of course, impossible to know whether this conjecture is true. Nonetheless, the implications are so vast, and the indications already so strong, that we must treat it as a serious possibility. Granting this, what then is our responsibility as mathematicians? To have seen and felt what AI can do to mathematics, to have some sense, however vague, of what it might do to humanity at large, and then retreat into our own little corner of life could be, I believe, a kind of abdication.
One of our key responsibilities is to find a language adequate to what AI is doing on its own, to us, and to the world. This is, after all, something we have trained for all our lives: when the language we inherit is insufficient to the task, we invent new vocabulary, notation, and conventions which allow us to contemplate something that was previously difficult even to formulate.
The need begins with those closest to the technology. Mathematicians and scientists working inside AI labs see things that those of us on the outside do not. The vast majority of people use only a tiny fraction of what current AI systems can do. Inside the AI labs, researchers encounter capabilities and behaviours long before they reach the rest of us, and what they see increasingly strains our inherited vocabulary. The AI researchers (many of them mathematicians) have a responsibility not merely to measure these phenomena, but to find ways to show the rest of us what they are seeing: through equations, words, pictures, movies, whatever it takes.
The problem of language is also present when discussing AI at the societal level. Here, mathematics can be unexpectedly useful. Think of the exponential curve. Before COVID, “exponential growth” was mathematical jargon that most people were happily ignorant of. Afterwards, millions learned, rather painfully, that you cannot outrun the exponential. Wait too long, and suddenly there is no room left to act. AI capabilities may not follow a literal exponential curve, but that is beside the point: we are confronting a technology whose capabilities are increasing at extraordinary speed. We in mathematics, who felt this like a punch in the gut, need to find ways of making it palpable to the public now.
What might such a new language look like? There is a story a close friend and colleague told me recently that I cannot get out of my head. On his deathbed, John von Neumann was asked if we can build an intelligent machine. After thinking for a long time, he replied: “We have to grow it, not build it.”
We are used to talking about “building” AI. But perhaps this is the wrong word. Yes, we build the chips. We build the data centres. We write the algorithms. But the intelligence itself is not assembled piece by piece according to a predetermined blueprint. We are creating conditions in which a new intelligence is emerging.
We are growing a new intelligence.
In this analogy, the data centres are intelligence farms. And is it not fascinating that, just like carbon-based intelligence, silicon-based intelligence also depends, ultimately, on water and energy, much of it drawn from the sun? (And as mathematicians, isn’t it tantalising to contemplate unifying these two intelligences?)
Is dwelling on words like “building” and “growing” a mere hairsplitting? I think not. “Building” carries with it an aura of control. “Growing,” however, carries the possibility of the unknown within it. The metaphor is necessarily imperfect. But imperfect metaphors may be all that we have time to develop.
Of course, finding the right language is only part of our responsibility. AI is confronting us with questions that reach far beyond mathematics: What is intelligence? What happens when it can be reproduced at scale? What becomes of human agency, work, and purpose? Can silicon-based intelligence be conscious? Does humanity have a chance of survival?
It is tempting to say that these are questions for AI researchers, or philosophers, or economists, or politicians, or tech bosses. But a quick perusal of what has been said and written about AI makes clear that no single discipline, profession, or group of people has anything approaching an adequate answer to these questions.
This is the context in which the recent letter by Royal Society mathematicians should be understood. These are mathematicians at the highest levels of our subject who do not ordinarily issue warnings about the fate of humanity. Yet what they have witnessed is serious enough to compel them to step outside the usual confines of mathematical life and express their extreme concern about the pace of AI development and its implications for humanity and civilisation. There comes a point when what one has seen no longer permits silence. The letter suggests that this point has been reached.
If the central challenge confronting us is not merely capability but the speed at which it is arriving, then the first thing humanity needs is time. A slowing down of AI is required to provide us with time to breathe; to catch up; to devise a strategy. Of course, “Slowing down” is borderline heretical in a world obsessed with growth as a value. Thus, such a serious, dare I say revolutionary, change of direction will require a mobilisation of the public. Governments will only impose meaningful constraints on the development of AI when large numbers of citizens are actively demanding it. And mathematicians can, nay must, play their part in giving voice and direction to this popular demand.
For generations, mathematics has rewarded an extraordinary narrowing of attention. We choose a problem, then a subproblem, then a tiny corner of that subproblem, and we give it years of our lives. There is something beautiful in this. Something sublime. To converse across the centuries and millennia with the likes of Euclid, Euler or Gauss is transcendental. It is spiritual. I want my children to have the possibility of participating in this ancient human endeavour.
So yes, some mathematicians should continue to practise mathematics as if AI had never arrived. They should continue to spend years thinking about obscure and beautiful problems, following mathematics wherever it leads, without having to adjust their work to immediate concerns. Indeed, preserving this way of life is itself part of what is at stake. But if all of us were to carry on in this way, then we would be failing to fulfil our collective responsibility to society.
There are moments in history when looking deeply is not enough. Moments when it becomes our inescapable responsibility to look wider, to the implications for humanity at large. Navier–Stokes was the warning shot for us. The moment of reckoning has arrived.
Received 7 October 2026.
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