On the great hypocrisy behind « human understanding»

Anonymous, Postdoc

« J’ai comme une impression que ces dispositions grossières de compétition, des dispositions “sportives” si on peut dire, sur lesquelles je viens de mettre le doigt dans ma personne, devaient commencer à devenir courantes dans “mon” milieu mathématique, vers le moment où elles étaient courantes en moi. Je serais bien en peine de situer dans le temps le moment de leur apparition, ou celui où elles sont devenues comme une partie intime de l’air qu’on respirait dans ce milieu, ou celui que mes élèves respiraient au contact de ma personne. La seule chose que je crois pouvoir dire, c’est que cela doit se placer dans les années soixante, peut-être dès les débuts des années soixante, ou la fin des années cinquante. »

“I’m under the impression that these gross dispositions towards competition, these “sportive” dispositions if you will, which I have just uncovered within myself, had to be somewhat common in “my” mathematical milieu around the time they were common in me. I would have trouble recalling when they first arose, or when they became fully integrated in the spheres I or my students were in. The only thing I can assure is that it had to be around the 1960s, maybe at the beginning of that decade or at the end of the previous one.”

Alexandre Grothendieck, Récoltes et Semailles, 40. La mathématique sportive.

Disclosure: This was entirely written by a human, no LLMs were harmed in the process.

When Gregor Samsa woke up one morning from unsettling dreams, he found that mathematicians all around the world were suddenly obsessed with “human understanding”. “What had happened to them?” he thought. No one could provide a coherent answer.

Since the irruption of AI into mathematics, after the first major strike and the subsequent second wave¹, much has been said about what the true meaning of mathematics and life are, about what mathematics is or how it should evolve. However, almost all the discussion so far seems to be stuck at an abstract or moral level, systematically avoiding many of the hard questions that are pressing to address.

In my opinion, little of what has already been said is anchored in the reality of what academia² really was (or is), in what the material conditions of it were (and still are) and does not reflect the extent to which the previous (and current) system was utterly dysfunctional. This is why, at the risk of adding more noise to the chaos and antagonising some people, I decided to write this essay.

Big conjectures as a benchmark for humans in the worldwide math fitness competition.

It has been particularly charming to hear all these poetic descriptions of what mathematics really is about, of how, at its core, it is about producing “a human understanding” of the hidden structures of the universe, and of how collaboration and companionship are the basis of the so-called mathematical community. These solemn proclamations that the millennial endeavour of mathematics cannot be threatened by AI are certainly appealing but fundamentally misplaced.

Don’t get me wrong: I can agree with this. The problem is that, while this holds for Mathematics—I’m glad we all seem to agree now—this is certainly not what mathematical academia was all about. And this explains why all this sudden lyricism comes off as rather hypocritical now that the academic system is threatened by this new external force. Nobody seemed to give a damn about Thurston’s essay one year ago³, but since AI started nuking conjectures all over the place, all the major figures in each field have exhumed its corpse and fervently brandished it at the general public in the hopes of convincing it that “human understanding” was all they ever cared about.

The truth is that the main goal of the rat race called mathematical academia is to get first a tenured position, and then keep going until you are Herr/Frau Prof. Prof. Dr. and you can hire armies of slaves with your grants. The key factor to progress in this worldwide competition is not the quality of your exposition, the beauty of your craft or the profoundness of your understanding; the key factor is how many publications you have and how good are the journals you publish in. That’s it. In some sense, it is quite simple. Therefore, your whole future prospects are entirely dependent on the judgments and whims of a finite (and particularly small) number of editorial committees⁴.

Mathematics has grown a lot since the sixties. In particular, it is now very hard for an expert of any given subject to understand or assess the quality of a paper coming from another subfield of mathematics⁵. This, coupled with the productivist mindset that penetrated mathematics (and sciences) during the end of the century (reinforced more and more by external pressure, such as governments and grant agencies), created the need for a “standardised” measure of mathematical quality. Thus, conjectures became the main instrument to assess mathematical merit and shaped the reward system of the academia rat race.

Conjectures were and indeed are great lighthouses that can effectively drive genuine progress in mathematics. A great example of this are the Weil conjectures, which prompted Grothendieck to develop schemes, topoï and étale cohomology in the sixties. Their final resolution by Deligne is very impressive, but it is undoubtedly all the concepts and language introduced by Grothendieck when he tried to make sense of these conjectures that changed the course of mathematics. Unfortunately, like any metric, conjectures have been Goodharted⁶ to death. Solving a conjecture is no longer a means to further beauty, mathematical flourishing and understanding, but has become a goal in of itself. To further one’s career, get tenured or obtain grants. The system is so that you can submit a 100 pages obscure and badly-written nightmare to any top journal and, if the name of the conjecture is famous enough, get easily published, all the while any 20 pages long, beautifully enlightening conceptual simplification of an existing result would get desk-rejected under the pretence that “the paper provides no new applications”.

Before becoming a benchmark for AI, conjectures had already become a benchmark for humans. If today a subfield X can be nuked into extinction by solving all of its conjectures, it is not because of the inherent lack of beautiful mathematics to explore in that said field, but rather because, under the current system of credit, this subfield is no longer able to provide any effective benefit to its participants. Recall, this is not just about honour and glory. Having a top paper can be the difference between paying the rent or not. This is why they leave en masse, forced to seek new big conjectures elsewhere before some tech giant nukes them. Although it is far easier to only blame tech giants for their reckless attitude, much of the fault here also lies in senior mathematicians, who benefited from the previous status quo and refused to amend it to any degree.⁷

Pressure from underspending, nepotism and selecting against creativity.

“Was it so bad, though? In any competitive human system, there needs to be some metrics to assess people. Big conjectures are big for a reason. Why are you complaining so much about them?” some may retort. And I somewhat agree: problem-solving is still a respectable skill and if mathematics academia was only full of brilliant problem-solvers, I would not have written this essay in the first place.

The fact of the matter is that, until very recently, a big conjecture being solved was quite a rare event. Far scarcer than the number of mathematicians whose papers needed to be refereed and whose applications needed to be reviewed. Since assessments could not simply be based on “has it solved a big conjecture? Yes/no”, the conjectures-proxy devolved first into “has it solved any conjecture?”. And since, at the end of the day, conjectures are simply questions asked by mathematicians, the effective proxy of assessing the quality of a paper became “does it solve a question the referee cares about? Does it solve a question someone with power in this subfield cares about?”.

“Of course, any assessment is going to be subjective!” some may rush to reply. Yes, indeed, but asking “does it solve a question I care about?” is a qualitatively different question than “does this paper introduce new, fertile ideas?” or “to which extent this paper furthers my overall understanding of mathematics?”⁸. One of the reasons why these two sets of questions are substantially different is the following: answering the first can be done in 5 minutes, with a quick glance at the abstract and the introduction; answering the second requires carefully reading the paper and actively trying to understand its content.

The material conditions of academic research have substantially degraded in the last 30 years. Senior mathematicians often crawl under administrative tasks. Junior mathematicians need to compete harder and harder because tenured positions have become far fewer. This means that, while the system keeps producing more and more papers, many can no longer afford to spend more than 30 minutes looking at a paper for a quick review⁹. Only 30 minutes which, as stated before, can amount to a life-or-death sentence to a young mathematician’s career.

On top of all of this, as the system is more under pressure from the lack of funds, this small set of misplaced incentives ends up easily twisted for personal interests. Abuse of power and nepotism are in fact not uncommon at all in mathematical academia. People systematically reject papers of persons they dislike; they trade favours among the powerful, help junior mathematicians if that increases their prestige and discard original ideas that might threaten their status within the community. In my limited experience, I have seen quite my share of abhorrent and unjust behaviours so as not to think that it is the exception rather than the rule.¹⁰

In substance, the problem is that the optimal strategy for getting tenured was to walk in the shadows of powerful mathematicians, mass-produce very technically involved epsilon-variations of existing papers and try to please important figures. To be very quiet and astute, gain sympathies and show that one is technically strong but certainly not a threat in terms of originality. Very concretely, mathematical academia ended up with incentives that effectively penalise originality, creativity and theoretical exploration. Of course, not every mathematician is like this. In times of abundance, many other profiles were selected by the system which did not fit these criteria. However, as the resources of the system plummet, it is those who overfit the metrics who tend to be selected. Ironically, it is those profiles who have been strongly selected against that would have thriven the most in the AI era of mathematics.

The current state of the academia machine.

This was the status of mathematical academia: a walking corpse devoured from the inside by its contradictions. And then came the AI.¹¹ And, from all the public discourse produced so far, it would seem that very little “human understanding” of the problems that have led to this situation has been acquired. On the contrary, mathematicians seem to have divided into three silly caricatures of themselves.

1. The techno-optimists: usually tenured mathematicians, they see a bright future ahead simply because their favourite problem has now a 1000 pages AI-slop solution. It does not seem like they care about the continuity of mathematics as a human endeavour or about anything else for that matter.
2. The moralists: they completely refuse to use AI on political grounds, arguing about the ecological and economical costs of this technology. Some of them do not have the first clue about the capacities of the current models and remain stuck with a 2023 ChatGPT-era mental image of AI. Of course, most are also tenured, otherwise they could not afford such noble stances.¹²
3. The doomers: all hope is lost; mathematics is forever gone; even Archimedes has been secretly nuked in his grave. Doomers vehemently express their grief non-stop without offering any concrete solutions.

The most curious thing seems to be that while this internet-fuelled civil war keeps happening, out there in the real world of mathematical academia, most people keep on going “business as usual” like nothing at all occurred. This, perhaps, is the most incomprehensible attitude of them all.

All the while PhD. and postdocs remain trapped in the same precarity as always. Big journals keep accepting big conjectures and the same set of wrong incentives that has created this whole catastrophe¹³ keeps on going. Except now AI attacks every weak spot of the previous state of affairs. ArXiv is flooded with shitty papers written in one prompt and subsequently big journals are flooded with this slop up to implosion. In this context, the current meta¹⁴ is to keep on conjecture-maxxing, one-shotting as many big boy conjectures as possible with Opus 5.5 or Astra 6 on Ultramaxturbo-thinking mode¹⁵, burning tokens like there is no tomorrow, until some pdf pops-up. Then, hurry to clean it in one afternoon and post it on arXiv before the next OpenAI dump¹⁶. This has turned mathematics into a ridiculous lottery game and a mockery of its former self. It is impossible to find any sort of meaning in this type of subservient work and, if things are not quickly amended, tenured mathematicians will end up roaming around empty departments just in a couple of years.

The many futures that lie ahead.

Luckily, as I said, I do think there is some truth in all these exclamations about “human understanding” and all the lyricism that comes with it. Even in a future where AI is better than us at any given mathematical task, I do not think human beings will stop marvelling at the beauty of the universe. Trains and helicopters have not stopped us from wanting to hike the highest mountains and admiring their views. As Grothendieck put it most eloquently in his book, it is our inner child that drives us in our never-ending quest to explore and experience the unknowns of reality, to name them carefully with words and patiently build great mental cathedrals one word at a time.¹⁷ Maybe some will use construction engines to build these mind-temples and to craft new horizons —AI does not seem incompatible with this artistic vision of math from the get-go¹⁸— but mindlessly one-shotting conjectures simply because they are famous is really the opposite of whatever I was talking about before. If one’s purpose is really to play like a child and experience the inner beauty of this world of ideas, then “human understanding” comes by default, as the whole goal of the game is to develop and experience higher and higher forms of understanding. So, I’m not particularly worried about mathematics as a human endeavour.

Mathematical academia is another story. Its whole system is deeply flawed and seems unwilling to adapt. Application season has started and no type of guidelines are available anywhere. Journals keep pretending like nothing has happened. PhDs and postdocs, which are already in a very precarious situation, are left in the dark while tenured mathematicians with too much free time have byzantine debates online.

The goal of this essay was to lay bare what I believe is the underlying state of the world that has led to this catastrophe. To lend a mirror to the mathematical community, in the hopes that it might reflect upon its mistakes and change its ways. As some kind of final service for all good things that this mathematical community has also provided me.

Sadly, I do not think that senior mathematicians are really doing their part during this tempest. And I’m not willing to bet my livelihood on their ability to come to terms with reality and grasp current events. So, I am leaving academia, and I will nevertheless continue doing math in my spare time because I still find lots of beauty in it.¹⁹ I’m quite certain not to be alone in this disposition. Make of that what you will. As a final word—and warning—to prominent mathematicians who seem to be inclined to preserve the status quo, I would like to recall the title of Grothendieck’s memoires: Récoltes et Semailles—which in other words means—“you reap what you sow”.

Notes

1. Navier-Stokes and whatever this was. ↩
2. Perhaps, this is correlated with the fact that most of the discourse has been so far produced by either PhDs (which luckily are somewhat sheltered from the harsh realities of academia) or by tenured mathematicians (which appear to be mostly oblivious to what the system has become). ↩
3. Particularly, no one in the editorial committees of the main journals it would seem. ↩
4. For anyone outside of mathematical academia: a particularity of mathematics is that whether a paper is accepted in a journal or not is not primarily determined by the correctness of the said paper. The paper is assessed (in theory) for abstract metrics like interest, originality and depth and accepted or not on this basis. Evaluating the correctness of a paper is also done during the referee process, but it is not the main goal. ↩
5. Among many other problems, this inserts huge biases between different subfields. Having an editor from your subfield (who likes you) can catapult you to glory or—if he dislikes you—sink your career. More on all the flaws of the system later on. ↩
6. See Goodhart’s law. ↩
7. Many being perfectly aware of how dysfunctional the system was. ↩
8. Or, for that matter, different to “is this paper well-written? Interesting? Clear? Original?” etc. ↩
9. Quick reviews/opinions are the first stage of reviews in big journals, where the “quality” of the paper is assessed before any checking is done. ↩
10. I could provide a very long list of them if requested, but I do not think it is in the interest of this essay to do so. It is my conviction that many readers (if not blinded by their corporativism), have at the moment a similar list in their minds as well. Note that most of my list does not concern me personally. ↩
11. It seems quite important for key figures in the mathematical community to fully understand where things were and what led to the current mess if any meaningful change is to be implemented. Idealisation of the previous state of affairs is, in my opinion, very counterproductive. ↩
12. I do take seriously the postdocs and PhDs who hold some of these views, as they are the ones with something to lose. The moralist stance for tenured professors can also be interpreted as an attempt to keep the old power structure going (in which they were at the top) and thus can come off as insincere sometimes. ↩
13. Had big conjectures not been turned into the alpha and the omega of mathematics, AI companies would have far fewer incentives to nuke them. ↩
14. Meta as in “the optimal strategy in a videogame”, not in the usual sense of the word. ↩
15. Of course, the prompt is always: “Crack wide open that conjecture, bro. Deploy a billion agents. Believe in yourself <3”. ↩
16. Unlike many people say, I do not think the OpenAI dumps will simply fade away. My impression is that they will keep using big conjectures to train their internal models, hence it will keep producing novel results on its own as capacities increase. In fact, they might be joined in this by other AI labs or companies sometime soon. ↩
17. This phrase is simply a humble attempt to convey the splendid lyricism of Grothendieck’s description of mathematics and, for that matter, of any human creative activity. I highly recommend anyone to read the original text. Particularly, the sections corresponding to Promenade à travers une œuvre—ou l’enfant et la Mère in Récoltes et Semailles. ↩
18. In particular, I think there are interesting ways to use AI to this purpose. One of them is to use it in a kind of Socratic dialogue, where you ask it many many small questions that slowly ramify into a global kind of understanding of a given picture. I also think that more remain to be discovered. ↩
19. If one does math out of passion and not forced by messed up incentives, then one is truly free to do it thoroughly and to one’s heart’s content, pursuing true understanding and beauty, without being bullied into conjecture-maxxing on an AI overdose or being ostracised by anti-AI fanatics for wanting to pay the rent. ↩

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Received 23 October 2026.