He feels within him the obscure joy of the abyss; He endures, overwhelmed by suns and skies,
The inexpressible horror of prodigious places. He gazes, at a loss, at the truth—this precipice.
The Titan’s Discovery (Victor Hugo, The Legend of the Ages)
The Titan Phos longs to break free from his prison. He digs downward, moves a rock, and, blinded, discovers the other side of the Earth: the infinite, the cosmic truth, the abyss. He is terrifed to see what no one ever witnesses…
What Titan Phos experienced in Victor Hugo’s poem, almost all mathematicians experienced last month, to varying degrees of stupefaction, and I, first among them.
The indications of the superiority of the large reasoning models (LRMs) appeared in spring, with the resolution of a few conjectures that one might carelessly call secondary; then in summer, serious conjectures were solved every day, until the announcement of a solution to the Navier–Stokes problem. The polemical disaster surrounding this announcement delayed the follow-ups, postponing the climax by roughly a month. OpenAI ultimately committed the irreparable on October 6, unveiling proposals to solve more than 350 conjectures. The demonstrations are spread across more than 700 articles.
There is nothing exaggerated in saying that October 6, 2026 is the most significant date in the history of our discipline. There will be no turning back. The humble pedestrian of mathematics that I am did not hesitate to admire the spectacle: in a very short span of time, the frontier of knowledge leaped several decades into the future, and we have not yet touched down. A colleague predicts that, in a few years, we will ask one another: “And you, do you remember what you were doing on October 6?” In a few decades, we will reminisce by the fireside about the 300 conjectures of 2026: for now, let us savor the moment, strike while the iron is hot, and prepare our memories. What was the first sensation that followed the shock? I think I know my answer. It is unspeakable, but I know it is shared far beyond myself.
For me, the moment of astonishment arrived earlier, at the moment of the Unit Distance Problem’s solution in May. But almost immediately afterwards, I felt a genuine relief, and a sense of freedom recovered. I hope this account will make the confession less indecent to those who are currently roiled by gloom.
Let us speak a little of the astonishment—the astonishment of discovering among us non-human systems that excel in every domain of mathematics. The question of whether my field is “touched” is frequently posed; some leading researchers have spoken with emotion of the annihilation of all their avenues of research, while others seem “spared.” But the question is not pertinent: it is wiser to presume that, in the future, all current conjectures will be resolved by LRMs, rather than assuming the contrary.
That is why some researchers carry the sorrow of heavy losses. In laboratory corridors, the atmosphere can be terribly dark, whereas mathematicians are usually jovial and lighthearted around the coffee machine. Part of the anxiety lies in the fact that no one can say exactly what has died. A certain way of doing mathematics is dead and will have to be buried with honors. And after? What becomes of a discipline when the production of its results, the pillar of its value system, is no longer constrained by scarcity? The whole community is now turning its gaze to these questions. For a discipline united by a love of solving hard problems, I think we are quite fortunate.
Ending the Humanslop
Many share secretly, and for a long time, a faint disgust with a way of doing mathematics to which they have resigned themselves: I speak of the dogged production of extremely long, almost unreadable, and highly technical papers. What is the scientific value of a result when its sole demonstration runs to hundreds of pages, read (or claimed to be read) by only a handful of mathematicians, and that no one will ever return to read it?
The resolution of a problem does not exhaust its value. The difficulty of the solved problem should never have been the dominant criterion for judging a piece of work.
One solution to the conjectures of October 6 runs across thirteen articles, totaling several hundred pages that are evidently poorly written. This is absurd. But is this situation really unique? It is an old state of affairs, a crisis we had learned to tolerate without solving. The system pushed us to produce texts that exhausted everyone—the author and the readers—for the sake of a vast waste of time and talent. We spent hours performing tedious tasks, writing the proofs of technical lemmas that were uninteresting yet necessary, rechecking calculations, composing opaque details that no one would ever read. We should never have become accustomed to this: I propose to call this production a “humanslop.”
That some of these texts do resolve conjectures deemed significant I can understand; some long and difficult demonstrations are masterpieces… But only some. Logic has its limits, and OpenAI’s papers demonstrate this. From my point of view, there is no difference between some aislop papers and old humanslop papers.
The paradox is that LRMs will be both the poison and the antidote: on the one hand, they produce a caricature of this science at the very end of its tether, spewing pages and pages of opaque mathematics merely to prove a prestigious result.
And on the other hand, LRMs are capable of finding the right shortcuts and the proofs that are truly efficient and elegant, enabling a bypass of existing demonstrations that no one would read. I was struck by an example given by Hugo Duminil‑Copin: in a 2020 article published in a prestigious journal, he and co-authors presented a partial solution to a conjecture. It already ran to several tens of pages: in May, an LRM produced a demonstration of the general case, of great elegance, contained in two airy and complete pages. The method was a “long-distance analogy,” that is, a link between two theories that no one had seen—a domain in which AI excels.
In these conditions, how can one not be enthusiastic? How not to laud such progress? How not to hope that we can finally rid ourselves of a portion of the fifty-year-old humanslop papers—these papers important because they establish significant results, but long, badly written, incomprehensible, and which ultimately repel when they should be akin to poems?
These past months may seem to contradict me, as the dismal picture of ArXiv demonstrates. ArXiv is a site where researchers publish their articles in open access, before submitting them to journals. ArXiv is a pillar of open knowledge exchange, and an indispensable tool for our community. At the start of my PhD in 2016, my supervisors advised me to monitor the probability section daily, as one would check the morning headlines. There were about a dozen articles per day at the time, which was already a lot. The pace gradually accelerated, then exploded in 2025. Last week, there were between fifty and a hundred publications per day. It’s the gold rush: many researchers have finally obtained, via an LRMs, the solution to a conjecture dear to them. Many have made the effort to produce beautiful papers useful to the community; others did not exercise such courtesy and haphazardly dumped unreadable scrolls onto the world, though probably correct (no one will read them), foreshadowing the events of October 6.
I see in this only a transient frenzy, where new technologies coexist with the old hierarchy of values, the one that gave a disproportionate premium to the first discoverer of a conjecture. But where will the hierarchy of values move? And what will remain to do, concretely?
Freedom at Last
My relief comes first from a sense of regained freedom. A few years ago, well before October 6, a colleague confided that he was fed up with doing the same mathematics again and again. He would have liked to switch subfields, to engage with other sciences perhaps, but for most of us, modest laborers of mathematics, the cost is high: several months of work, a possible dry spell of publications, a real intellectual risk, great difficulty learning how to speak to researchers in that other field.
This resignation is more widespread than one might think. It is one of the causes of the hyperspecialization that had weakened our discipline. This hyperspecialization carried risks, and one of them is that many of us are wholly dispossessed of what they had devoted their energy to. Some use this to vilify “bad researchers” incapable of retooling outside their turf: beyond the stupidity of such talk, it is false. There are researchers at all levels with highly specialized skills and others with an enormous breadth of knowledge, whether Fields medalists or not.
Today, there is hope that, collectively, we can remove these barriers to movement within mathematics and beyond. Some specialization is probably necessary, but it had become a problem. LRMs help us break these barriers. They streamline access to knowledge. They know the references in my field and in others, they know the sticking points and good analogies, they respond swiftly to questions. The experience of recent months shows that they do not replace scientific discussions among colleagues, but they enrich them. And there is no need for very costly “cutting-edge” models to do this.
There is also the hope of another benefit, perhaps more anecdotal but certainly not less controversial: a weakening of hyperspecialization—the end of implicit hierarchies between disciplines. I have always been struck by the hauteur of some colleagues toward what they take to be “sub-mathematics” (for instance, numerical analysis or logic) as opposed to “noble,” “high,” “real” mathematics, etc. Our elder colleagues recall a time when grand names of the French School guarded the doors of the Temple of Mathematics. It must be admitted that this hauteur had steadily receded in recent years; it must now disappear. By engaging probability, theoretical computer science, statistics or numerical analysis as much as arithmetic, group theory or differential geometry, LRMs may bring a certain egalitarian virtue that harms no one.
But another hierarchy is at stake: that which separates research and teaching.
Navier and Stokes Stand with High School Protests
The hierarchy of academic prestige does not value teaching tasks. For instance, “pure” research positions without teaching duties are more competitive and prestigious. Yet we can take pleasure in the fact that eminent figures in the field, such as Fields Medalists or CNRS Gold Medallists, highlight the importance of teaching and the transmission of knowledge. Mathematics is a fundamental knowledge and forms the language of other sciences, including machine learning that gave rise to LRMs: teaching needs are constant at all levels of schooling and university education, including at the highest level, for doctoral students.
That said, chaotic times invite wild predictions: it is not forbidden to think that AI could become, in the long run, much better pedagogues than humans, especially in mathematics. Should we conclude that, in the long term, teachers will be replaced by “a video in a live stream of an impeccable and engaging young professor, equipped with the best pedagogical talents, and broadcast simultaneously to all students in France,” as one colleague sarcastically predicted?
Nothing could be further from certain: because even if that were true, students themselves would not want to replace their teachers with machines. Without wanting to hand out laurels, it seems to me that in many universities and grandes écoles, students bond with their professors, and vice versa: the human adventure is part of mathematics and its teaching. Michael I. Jordan, a computer science researcher, summed it up well: “People will decide in which areas they accept the use of LLMs and in which they don’t. They will decide when they want to interact with an LLM and when they prefer a human.” Many high school students publicly express their dismay: listening to their demands, one quickly becomes convinced that they crave humanity, empathy, and consideration (which are the foundations without which one does not teach anything lasting) and certainly not more generative AI.
Moreover, the question also arises in the opposite direction: I would not want to replace my students with AIs to whom I would have to teach mathematics, which would, however, have certain advantages.
I Lost Pascal’s Bet
One question remains: will there still be enough reasons to become a mathematician? Will we become a factory of professors who seek nothing more? The defense that there will always be research tasks that machines cannot accomplish is extremely risky. Nothing prevents the thought that LRMs may be better than we humans, including at producing human understanding.
We increasingly hear a counterargument in the form of a Pascalian wager. This is a claim often found among techno‑boists, who have an interest in appearing louder and more triumphant than they truly are.
The argument runs as follows. We may stand at the dawn of a golden age for mathematics, an explosion of knowledge without precedent. If so, for someone already in the profession, the arithmetic is simple: if mathematical research goes dormant, staying put yields nothing and costs little; but if a true revolution occurs, what a pity to have left the ship. The expected value calculation commands us to stay. Yet the Pascalian wager has never converted anyone. That is precisely why Pascal mentions it, after all. I can hardly imagine this reasoning convincing a single colleague currently weighed down by uncertainty. It did not convince me either.
I chose a career in mathematics because I love mathematics, and because I am fortunate that this personal taste coincides with work considered highly useful to society, which in turn offers career prospects. My choice is not that different from that of a cook who loves to cook and who finds people to feed. It should be remembered that, well before LRMs, the mathematical vocation was already somewhat irrational: many of my colleagues would have accepted considerable sacrifices to stay in the profession. Discoveries, medals, prestige added to a passion that already preceded them. I seriously doubt that Pascal’s wager could convince anyone to stay in mathematics, just as I doubt that the secret motivations we all had for entering this path have disappeared.
Alas, our freedom does not depend only on our motivations.
The Leviathan of Silicon and the Behemoth of Knowledge
At this point, one fear cannot be ignored: who will produce the machines that produce mathematical knowledge, and who will determine the conditions of their access?
Everyone knows that OpenAI and Anthropic do not pursue mathematics for the love of mathematics, and that their interests do not align with those of our community. Fields Medalists have expressed this distrust in a widely discussed letter, speaking of fundamental misalignment.
The construction of LRMs, this Behemoth of Knowledge, is the most important, original, and surprising technological achievement humanity has accomplished to date. It was also the most costly. When a project demands astronomical capital, on unprecedented scales, there are inevitably many misalignments. This time, my scientific community bears the brunt directly, and there is a good chance we will not be the last. If successful, the misalignment with our internal goals and practices was inevitable. Is realignment possible?
I feel very distant from these questions, and more generally from the concerns raised by our dependency, as mathematicians, on these enterprises. I pay around twenty euros a month to access LRMs. These models accessible to all, and other fully open models, already possess prodigious capabilities. The fact that we do not have access to OpenAI’s internal Behemoth does not worry me. At the speed of progress, I would be astonished if the feats today reserved for private, expensive infrastructures do not become accessible to all in the near future.
That does not solve the political question: who will guarantee durable access? Should Europe build its own models? If we must invest heavily to avoid depending on the Silicon Leviathan (as they call the American AI‑industrial complex) in the long term, we must do so now. But this urgency goes beyond mathematics: it concerns society as a whole and carries socio‑economic risks that are truly worrying. And in this respect, the choices and especially the non‑choices that we Europeans are making worry me far more than, for example, an unexpected appearance of zeros of the Zeta function off the critical line.
Do Not Forget Euclid
Euclid of Alexandria would have lived around 300 BCE. The writing of his Elements is one of the founding acts of mathematics. Yet a large portion of the results he contains were not new: most were already known to Eudoxus or Pythagoras.
The central contribution of Euclid lay in selecting problems and giving meaning to the word “prove.” For this, he organized the existing knowledge by presenting it in a logical structure that clarified reasoning: postulates, definitions, theorems, and proofs. Through this method, Euclid produced proofs that were easily verifiable for results that were believed true, but had been only “vaguely proven by his predecessors,” as a later commentator, Proclus, tells us. The method and structure of the Elements are the fabric on which the mathematics of the following two millennia were woven. The reason for this longevity is that the method used by Euclid is the most effective way to understand why things are true and to present it, which is the work of mathematicians.
Today there are alternatives to the human brain for verifying that things are true; not yet for understanding. For example, LRMs have almost made free access to formal languages like Rocq or Lean, which allow, albeit with a dense syntax, to rigorously verify whether a deduction is valid. These languages, with their structure of stripped-down postulates and deduction chains, seem to be the ultimate evolution of the method introduced in the Elements, but they are still hard to interpret. Their democratization (notably thanks to LRMs) is a considerable and necessary advance. However, I am deeply convinced that Euclid would never have been satisfied with a collection of truly true facts that are entirely independent of the understanding we humans have of them.
From a personal (psychological) standpoint, I prepare for the possibility of facing a post‑mathematical science, an immense non‑human construct produced autonomously by machines, existing outside of me and existing mathematics.
Were the ancient Greek masters also in this attitude? Yes, indeed: they were permeated by the intuition that numbers, geometric figures, or planets were autonomous objects obeying coherent laws that they sought to understand, albeit awkwardly. What Euclid did with the knowledge of his time, mathematicians have never stopped doing. He created the conditions that made this science develop, he made mathematics habitable, he made possible a structured and universal understanding of things, for the use of all other sciences.
We have never ceased to be in this posture, even if we sometimes forgot it.