A Beginning for Mathematics

Recorded: Sept. 14, 2026, 9 p.m.

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Sep 14, 2026
A beginning for mathematics

Daniel Litt, professor at the University of Toronto
Three years ago, AI systems could not reliably add two numbers. A year ago, internal models at OpenAI and DeepMind received the equivalent of a gold-medal score on the IMO. Now, these systems are autonomously resolving major open questions. It’s hard to imagine this trend continuing for another year, but I expect it will. It is clear that this will require a radical rethinking of our profession.
A few weeks ago, I gave a talk titled The End of Mathematics. If you only read the title1, you might guess that this talk was about how, soon, AI will “solve” math. That’s not what it was about. The talk instead laid out a gloomy vision of the future, in which, despite the possibility of AI systems that are robustly superhuman at mathematics, the design of our institutions causes human understanding of mathematics, and possibly even mathematical progress in the abstract, to stall. I think we will avoid this future, but I also think it is plausibly the default if academic mathematics does not adapt. Despite my relative enthusiasm for the use of AI to do mathematics, I share this view with many of its detractors.
Here I want to lay out, instead, a positive vision of the future of mathematics, and the human practice of mathematics. I claim we can deepen human understanding even as the production of interesting mathematics becomes less dependent on it.
This essay will take as a premise that AI systems that are robustly superhuman at most or all aspects of mathematics will be here soon. But the concrete changes to our institutions I propose only require accepting the weaker premise that the production of mathematical text is becoming increasingly disconnected from mathematical understanding.
What are we even trying to do here?
I think it has now become clear that there is no consensus in the mathematical community as to what our goals are. Some of us want to solve problems; some of us think of mathematics as play or as poetry. For some: “Wir müssen wissen –\text{\textendash} wir werden wissen.”2 Some of us think we are penetrating the mysteries of the platonic realm. Some of us think the goal is to embody love of and understanding of mathematics,3 and to transmit that love and understanding to the next generation.
My personal, if self-referential, answers are:

We’re trying to produce and understand high quality mathematics.
We’re trying to produce high quality mathematicians.

These goals should be construed broadly. What high quality mathematics consists of has changed quite dramatically over time; we come to its definition as a community. We are not just training PhD students to do research in mathematics. A substantial part of our job, though perhaps an underemphasized one, is to educate the general public about high quality mathematics and mathematical thinking.4
Whatever our goals are, we’ve operationalized them primarily through proving theorems. Almost all papers or PhD theses have a main theorem, and ostensibly a proof of it. But it should be clear that the goal of mathematics is not to prove theorems; if it was, it would be trivial to automate. A computer or monkey could easily start at the axioms of ZFC and iteratively apply deduction rules to them, with no attention whatsoever paid to their meaning. It has had particular significance when a theorem resolves an open problem, especially one that has resisted substantial effort. Again this is easily automated; our computer or monkey can simply conjecture all mathematical propositions in alphabetical order.
The general attitude of our community towards a technology that can prove theorems and solve open problems suggests that these operationalizations of our values are at best incomplete.
The prospect of automating mathematics by enumerating all conjectures, and all proofs of ZFC, is probably not so disturbing to you. But let us for a moment assume the computer or monkey is very smart; perhaps it understands the results it is proving, and writes beautiful expositions thereof. Perhaps it has a good sense of what we find interesting, and is primarily focusing on those questions. Perhaps it has, in the course of enumerating theorems of ZFC, answered many of our most pressing open questions, and is asking many more fundamental open questions. Is there still a need for human mathematicians?
I think so. This machine might produce answers we value, but it would not, in itself, produce human understanding of those answers. In fact I think we are at the beginning of an incredible, wonderful explosion of mathematics, and if we value human understanding, there will be more need for human mathematicians than ever before. But the profession will have to change.
In the course of this change, we will have to decide what to hold on to and what to throw away. Some things I would like to preserve: learning seminars; serendipitous conversations that spark an idea; students knocking on a professor’s door to chat about math. A robust community learning exciting new mathematics. Thousands of people that, together, slowly start to resolve their confusion.
I worry that much of what has been written on this topic, including some of my own past writing, focuses too much on trying to preserve the precise shape of the institutions of academic mathematics, rather than our values. How can we preserve the journal and peer review system?5 How can we protect the arXiv? How can we keep our role as gatekeepers? If you have internalized the fact that existing AI systems can produce relatively high quality results for the marginal cost of a few dollars, the idea that any semblance of the current equilibrium can survive what’s coming is absurd.
As we try to find a new equilibrium, we could try to chase the edge of model capabilities. Right now AI systems arguably underperform us at theory-building, asking questions, exposition, …\ldots so we could prioritize and reward those skills. I think this is unwise: compare the speed at which the academy adapts to the speed at which model capabilities improve. We need to consider the endgame. If the models remain incapable in some domain, we can adjust later.
Before I propose some relatively concrete steps we can take, let me remark on what we’re trying to protect mathematics from. There is a lot of anger at AI labs, and certain individuals at those labs. But whatever our judgment of the labs, we need a plan that does not depend on AI capabilities disappearing. The basic issue is not the labs’ behavior, ethical or not.6 It’s the technology itself. I think there is some belief that the labs will “move on” from math next year, be nationalized or broken up, or that a financial bubble will pop, somehow returning things to normal, or…\ldots But there is no way our institutions can survive unchanged when anyone with a laptop and a few hundred dollars can generate what would have been an Annals paper last year. AI does not care if you are anti-AI.
Producing high-quality mathematicians
The most urgent question our profession needs to answer right now is: what should our students be doing? It’s now possible to produce a PhD thesis one hasn’t even read; in terms of demonstrating understanding, mathematical text is worth the paper it is printed on.7 The text no longer reliably conveys a signal about the person who produced it.
In my view we should welcome interesting mathematical results regardless of provenance. But our institutions have historically relied on the same signal to indicate both mathematical progress and mathematical expertise. These now must be distinguished.
I propose the following reconceptualization of the goal of a mathematics PhD: to become a world expert on some interesting, deep topic, and to be able to convey that interest and understanding to others. Part of operationalizing this might be a thesis, but the degree would be awarded primarily on the basis of a rigorous defense, in which the student explains the topic to their examiners until they are satisfied. While we might require the topic to be original, its provenance—\text{\textemdash}AI or not—\text{\textemdash}is irrelevant.8
How different would this look from current PhDs? I think students would still meet with an advisor, who might suggest a topic. That topic could be explored with AI assistance, or not, but the student would be responsible for understanding it; it might be much more open-ended and larger than the typical PhD is currently. The student would be trained to ask interesting questions and try to resolve them, by whatever means. To keep students on track, there might be regular meetings in which the student is asked to independently work through an unfamiliar example, apply a technique in a new case, etc.
The allocative aspects of our job (hiring, graduate admissions, etc.) are in dire need of reform if we want to retain human mathematical expertise. Broadly speaking I think we should focus on rewarding skill in the parts of our jobs that cannot be automated: the internal (e.g. understanding mathematics) and social-relational parts, and operationalizations that hew as closely to those aspects of the profession as possible. For example, talks and sustained mathematical discussion now demonstrate understanding much better than papers. Once AI systems improve at exposition and “digestion,” this will be even more the case. We already interview faculty hires; we must now do the same for graduate admissions.
I think we should try to foster a robust seminar culture in which speakers are expected to explain their topic to the audience’s satisfaction. Much has been written recently (by myself among others) about the fact that we are primarily interested in understanding, not merely the truth value of mathematical statements. If that is the case, let us make sure we actually understand each other.
Right now the use of AI systems to do mathematics above some minimum bar relies on the fact that our community has produced many open conjectures, whose interest is evidenced by the existence of human mathematicians who care about them.9 The recent importance of this fact suggests to me our community plays a very important function that we have, arguably, underrated: namely, figuring out what is interesting. It is not entirely clear to me how to operationalize this, but one possibility might be to reward the construction of research programs (either with help from AI systems or otherwise) that persuade others of their worthiness.
To be clear, I am not saying that AI systems will not be able to ask interesting questions, make interesting conjectures, pursue interesting programs, and so on. I think they most likely will, resulting in the production of an abundance of PDFs. The contents of some of those PDFs may even have important applications. But others will primarily be of interest because they tell us something fundamental about basic mathematical objects, and accrue value only if we can and do engage with them. It seems to me that it will be up to us to build a community of researchers to do so, and we should reward mathematicians who do. And even if the AI is asking excellent questions, there is no reason to think it will ask the same questions we would.
All of these changes are oriented towards increasing the amount we talk to each other about mathematics. It seems to me that this would be positive even in a world with no AI.
I think there is room in this world both for mathematicians who, like me, are enthusiastic about AI, and for those who do not use it. But as the models begin to produce huge quantities of mathematics, it will not be possible to avoid their outputs entirely.
Producing high-quality mathematics
As we think about how to reshape our profession, it’s important to understand that, whether one likes it or not,10 it’s impossible to stop people, amateur or professional, from pushing a button to produce mathematics. The idea that we will persuade people not to play around with math, or that we will be able to “reserve” problems for graduate students, is just not realistic.11 And we shouldn’t want to do this!
There is now more interest in math than at any other time in history. We should be ecstatic for mathematics’s sake, even as we are concerned about mathematicians and mathematical expertise. And by and large, the value of this button-pressing comes from the mathematical community. If a conjecture falls in the woods and no one is around to hear it, who cares?12 For the abundance of new mathematics to have value outside application, we will need an abundance of new mathematicians. And for results with applications, we will want people to be capable of understanding their assumptions and consequences.
I wrote above that solving problems and resolving open conjectures is an incomplete operationalization of our values. But nonetheless it is important to solve problems and resolve conjectures! The provenance of such solutions only matters insofar as it intersects with the existing structure of the profession (incentives, prestige, and so on). It is obvious that structure needs to change in any case.
Mathematics used to be the cheapest of the sciences. I think the biggest change we are facing is that now, some portion of our questions will be answerable via a cash injection. I know some of my colleagues find this distressing. Previously those questions might have brought together a research community, led to interesting auxiliary developments, and so on. This contingent progress may now no longer occur.
But don’t you believe in mathematics!? There will always be more to learn. If a basic question can be resolved for the cost13 of a nice dinner, we should be delighted. But that’s only the beginning. We will ask what the answer explains, and what it helps us understand. It will lead to many more new questions, some of which can in turn be resolved for the cost of a nice dinner, and others which renew our confusion and lead to the development of a research community.
Our industrious new helpers will be churning out an unbelievable amount of math, pursuing our interests or perhaps their own. We will have our own questions, and confusions; sometimes they will be resolved by the models, and sometimes they won’t. Sometimes the answers will be complicated, and we’ll devote a learning seminar to them. Sometimes progress will be minimal, but the question itself will be so motivating it gives rise to a research community.
A student will be confused. They will knock on their professor’s door. Maybe the two of them will ask a model for help, or maybe not, but first they might spend some time at the blackboard thinking through the question. And the model might give them a beautiful explanation, but we all know that’s not enough; no one can understand mathematics for us. We have got to do the work.
There is so much more to learn—\text{\textemdash}an infinite amount. We’ve always been at the beginning, and we always will be.
Acknowledgments
I am grateful for comments from Mohammed Abouzaid, alz, Boaz Barak, Frank Calegari, Ben Church, Jennifer Cutler, doomslide, Elden Elmanto, Francesco Fournier-Facio, Tony Feng, Dan Freed, Peli Grietzer, Michael Groechenig, Stephanie Koh, Joshua Lam, Mark Sellke, Ravi Vakil, and Amal Vayalinkal.
I regret choosing this title. ↩︎Hilbert’s full opinion is as relevant today as ever: ‘We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be Wir müssen wissen – wir werden wissen (“We must know –\text{\textendash} we will know”).’ ↩︎I owe this phrasing to Peli Grietzer. ↩︎Note that this list consists mostly of internal and social-relational functions (understanding, coming to a determination of what’s interesting, training, and so on). This is in contrast to our operationalizations (proving theorems, solving problems, etc.). ↩︎This system was already close to breaking before AI; it is overdue for radical reform. ↩︎Obviously some of it has not been ethical. But even if every lab had behaved perfectly, the capabilities of AI systems would still force us to radically adapt our institutions. ↩︎Which is not to say the text is necessarily uninteresting. ↩︎This is a practical necessity. There is no way to enforce restrictions on provenance, and attempting to do so will only create incentives to conceal use of AI. But I find it unlikely that someone whose only contribution was to push a button, and who did not engage deeply with the material, would be able to pass a rigorous defense. ↩︎To be clear, many open conjectures are less interesting than one might have hoped, post hoc, and are generally not an end in themselves. They are often meant to measure our failure to understand some object, but they are sometimes resolved without improving that understanding. ↩︎On balance, I think I like it, though I am sometimes annoyed to find slop PDFs in my inbox. It took me some time to understand that these PDFs expressed a need for understanding; a person elicited them, often without being able to meaningfully engage with their contents, and needed to know that someone could engage, and that someone cared. ↩︎That we cannot reserve a problem for a graduate student does not mean we can’t give them the opportunity to work on it. This is compatible with the reconceptualization of a PhD outlined previously. ↩︎Some have suggested that interest in using AI to answer mathematical questions may soon fade. It is hard for me to see how this will happen as long as questions we care about remain unanswered. ↩︎ By this I mean marginal cost. Michael Groechenig points out to me that it is unclear that we should directly compare the cost of a machine proving a theorem to the cost of a human doing so, as the products of this work are arguably different. Only one of them produces understanding and expertise in a human being, which I think we might value independent of the result itself. ↩︎

Received 9 September 2026.
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32 responses to “A beginning for mathematics”

JS
September 14, 2026

I feel like when I read people excited about AI I get way more cynical about math compared to when I read people who are pessimistic about AI. I think this was well written and completely reasonable but weirdly it makes me not want to do math.

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Anonymous
September 14, 2026

I agree the text is reasonable and yet I can’t say I feel delighted about the fact that the money for a nice dinner could produce a solution to an interesting math problem. I would rather just go have a nice dinner and ponder the problem the next morning.

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JS
September 14, 2026

Yeah, I think one of the frustrating things about reading a lot of these pro ai people is they say things like “people derive joy from math for a lot different reasons!” and then present a “hopeful” view of math that precludes the joy for the majority of people who don’t hold their view. They aren’t wrong but it’s just very depressing.

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Sukessh Velusamy
September 14, 2026

I don’t think that Litt’s point is that everybody will think his suggested way of doing math is ‘better’ than the current way, just that there is no possible way to maintain the current way of doing math, and his new system does have some improvements over the current system. One day, the mathematicians of the future might not even be able to imagine a world without superhuman math AI, the way many chess players today can’t imagine a world without chess engines.

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Pádraig Daly
September 14, 2026

Inspiring and credible vision!
One worry is that it sounds a bit like mathematicians becoming akin to poets and critics of poetry. Which there’s nothing wrong with but how much funding would there be? Before we could claim there is some use for pure research as it leads to unexpected applications in computer science, cryptography, physics, engineering etc. With an AI that solves any problem they can just go straight to application without funding the “useless” mathematics. Especially with the AI solutions costing a fair bit of money this is an issue.
I suppose this is an different issue than the one the post discusses as it’s more about how our society and economy is organised, and what we deem to be worthwhile activities.

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MS
September 14, 2026

This is a very important point (perhaps THE most important point), and I think most of the commentary regarding the impact of AI on mathematics has failed to address it. All of the discussion regarding how to train and assess mathematicians is pointless if the public decides not to fund mathematics. We have to do a much better job advocating for the continued existence of professional human mathematicians. A large proportion of the general public already thought academics should not be publicly funded, and it is surely becoming a much larger proportion every hour of every day.

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a
September 14, 2026

Presenting mathematics as “beauty, joy, etc.” will only make people more cynical. Instead, its prospects (if any?) for applications (e.g. AI safety?) could/should be emphasized as it always has been.

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Sukessh Velusamy
September 14, 2026

I think mathematicians should emphasize there is no way advancements in math from a chatbot could ever be applied unless there is a community of people who can understand the math (unless the chatbot itself can do the application, but that would probably be AGI anyway).

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a
September 14, 2026

Indeed, if there is no prospects for applications, one should expect less funding. Then this beginning for math will be to end up as some kind of poetry.

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Sash
September 14, 2026

> it’s impossible to stop people, amateur or professional from pushing a button to produce mathematics.
This is not true, you can just ask the frontier model companies to refuse answering research mathematical questions. They already do that for cyber security, bioweapons, copy righted music and art, I don’t see why we can’t add some areas of maths to it if we want to.
This is not like invention of calculator or even a chess engine. It costs millions to even acquire hardware to run a frontier model if you had their weights and it costs billions to train said frontier model. These costs are still going up, I reckon we won’t see GPT 3 (a model from 5 years ago) running on our smart phones in my lifetime. It still can’t run on my beefy 5k Desktop PC.
In the present we live in, it is totally an option to prevent AI from destroying some areas of mathematics if there is political will, a move I strongly support.
If anything this will create a great randomized control trial. Let’s have some areas of mathematics with AI allowed and some with no AI and then 5 years later we can compare both the fields and judge what’s better for the health of mathematics and its mathematicians.

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Benjamin Andersson
September 14, 2026

Seems to me that nothing prevents people from downloading a local verison of the model on their computer that does not contain these guardrails. Compare with banning pirated material online, or drugs.

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Irreverant
September 14, 2026

Qwen 3.8 is 5 times smaller than GPT-3, orders of magnitude smarter, and can definitely run on your PC, unless you mean 5K from 10 years ago ….

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Sukessh Velusamy
September 14, 2026

Two problems with your argument:
1. No government is going to ban chatbots from doing math:
Even for cybersecurity and bioweapons AFAIK there is no law forcing these companies to avoid answering those questions, and answers in these areas could lead to a lot of real world harm! How, then, is anyone going to convince Congress of the grave harms of chatbots solving math problems? And even if you managed, mathematics and AI are global. I really don’t think it’d be possible to convince even America to prevent their models from answering math problems, let alone every nation on Earth.
2. This is very much like the invention of the chess engine:
According to Deep Blue project manager C. J. Tan, the system’s hardware cost at least $2.5M dollars in 1997, or $5.2M today. 30 years later, it would be crushed by Stockfish running on an iPhone. You may not be able to run GPT-3 on your PC, but you can run (highly quantized) GLM 5.3 Flash on the most expensive Macbook Pro, which is WAY better. In fact, Qwen 3.8-27B is better than GPT-3, and much smaller. Considering all of this happened in ~6 years, do you really think local models will remain behind for long?

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Marcin Kotowski
September 14, 2026

“anyone with a laptop and a few hundred dollars can generate what would have been an Annals paper last year. ” – isn’t this a hyperbole? I mean, no idea what capabilities will be available a year from now, but today a laptop and a Pro subscription are not enough to churn out Annals-level papers.

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Sukessh Velusamy
September 14, 2026

Maybe he means GPT 6 Astra is at the level of capability where it could have generated the Unit Distance Conjecture paper, which Timothy Gowers said he “would have recommended acceptance [to the Annals] without any hesitation.”

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Vincent again
September 14, 2026

What if not only proving the conjectures, but deciding what is interesting, what is a deep notion, a fruitful point of view or theory is better done by the push of a button?
What if it becomes a common experience for a mathematician that she think about a question, and then, when prompting an AI model succintly about said question, she find a wiser, deeper and better formulated prose than hers?
I understand this may sound too naive to actually happen. Yet this is what the current trend suggests for the near future if you open your eyes a bit. At least it should be treated as a plausible development, something to consider.
And while this hypothetical situation still leaves room for math to be done for the beauty and pleasure of it (maybe for more people and in more quantity than before,who knows?), and AI math to be read by humans in order to understand it, it would drastically change what math is by removing a lot of initiative from the activity.
If you prefer, imagine that all serious mathematics is like what physics (or whatever) is to you currently. You can follow some discoveries made by real physicists (powerful AI in this analogy) and enjoy them, but there is little sense in you contributing to them, and your activity as a “physicist” can be at most that of a science journalist.

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Marcin Kotowski
September 14, 2026

How the hell did suddenly an AI model become “she”?

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Vincent again
September 14, 2026

I meant “she find[s]” as in “the mathematician finds on her screen” ^^

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taken_aback
September 14, 2026

Hi Daniel,
It is no secret that many people are not happy with your so called ‘AI-realist’ views on twitter/X, including me.
I think you are a bit too confident in ignoring various aspects of human agency, in particular, mathematicians agency in controlling their future. However, that is not what concerns me most (to each their own opinion).
What concerns me is why you attended a secret summit at OAI in early August to discuss the ‘future’ of mathematics.
I have seen you compare that summit with Oberwolfach for example, but note that Oberwolfach is a summit *for* mathematicians and it is **strictly** not a summit on the so called ‘future of mathematics’, a topic in which no one person can comment on.
What exactly made you think that you were qualified to represent all of us (your twitter/X micro-celebrity status notwithstanding)? If you knew this was a secret summit, why not work to invite people with opposing views and of equal or more academic reputation as you?

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Jake Levinson
September 14, 2026

I think this accusatory comment is totally inappropriate, darkly insinuating that “many people” aren’t happy with his “so-called” views. At the moment, the mathematics community does not have a unified view, so it is no secret that *anyone* with clearly articulated views is in disagreement with some fraction of our community.
As for accusing him of some kind of secret conspiracy: Daniel posted his “secret” talk on the internet, the same day he gave it!
Yes, Litt is indeed not “qualified” to “represent” all mathematicians — what would it would even mean, to be qualified in that way? Neither is Terry Tao, who despite his obvious stature is in no way the spokesperson, President or Pope of mathematics. Nor are any number of other mathematicians qualified to speak for all of us. But we are all entitled to comment on the future of AI in mathematics, with all our viewpoints.
Litt is simply a mathematician who has thought and written about AI in math, and has done so in the public sphere. That seems like a fine justification to invite him (along with dozens of other people) to an event about the future of AI in math, and for him to accept the invitation.

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anon
September 14, 2026

If in fact AI systems become more capable than human mathematicians at the majority of their cognitive work, isn’t this whole discussion just of minuscule importance compared to the broader implications for society / knowledge workers?

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just different
September 14, 2026

> A substantial part of our job, though perhaps an underemphasized one, is to educate the general public about high quality mathematics and mathematical thinking.
Here’s where the money is, literally. All of the high-minded pronouncements about mathematical understanding sound like navel-gazing copium to an awful lot of people. It won’t matter if the field sorts itself out and adapts to AI if the general public assumes it’s all pointless bullshit anyway and that we’re just among the many who are getting displaced.
BTW, I wish we had a less off-putting term than “digestion” (although I understand the metaphor Tao was getting at). Is the coinage “synegesis” (by analogy with “exegesis”) any better?

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Jules Verne
September 14, 2026

I would rather quit math than subscribe to this utterly dystopic vision of mathematics that you launder as a utopia just to secure funding. Screw this.

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BlaineTheMono
September 14, 2026

>> “it’s important to understand that, whether one likes it or not, it’s impossible to stop people, amateur or professional, from pushing a button to produce mathematics. The idea that we will persuade people not to play around with math, or that we will be able to “reserve” problems for graduate students, is just not realistic. And we shouldn’t want to do this!”
Hi Daniel! I need to push back on this. Under the current status quo in AI use in mathematics, not being able to stop people from pushing the button means that the days of speaking on work in progress at a conference are over. How could one feel safe announcing unpublished results in the abstract of a talk, knowing that there *will* be people, whether colleagues or strangers on the internet, prompting the hell out of it possibly before the talk even takes place?
I don’t have an answer to this problem, but I do think it’s a serious issue. Wanting to prevent the morons to push the button is not just reasonable. It’s a necessary consition for trust and free communication within our specialized mathematical subcommunities.

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Sukessh Velusamy
September 14, 2026

I think Daniel explains the solution well enough, stop assigning prestige to being the first person to prove something, and to slop proofs which leave you more confused after reading than before. Instead, assign prestige to people who have demonstrated a deep understanding of the mathematics and the capability to explain it well. This is much more feasible than banning the entire population of the world from using chatbots.

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Jonathan Noel
September 14, 2026

I agree. Our existing systems of training, credit, and assessment in math will require serious changes. They were flawed and we should not mourn their loss. We should redesign them both to address the new issues posed by AI and to reduce existing bias, unfairness, and other shortcomings. It will be a heck of a lot of work and we will make mistakes, but the biggest mistake would be try to keep everything the same.

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Novum Organum
September 14, 2026

This is the first essay I’ve read from inside the profession that takes robustly superhuman AI as a premise and then asks what mathematics should become, rather than what should be defended. That’s why the title is right: a beginning, not an end.
And the golden era is going to be much bigger than mathematics. Math is the canary: it’s the cheapest, most closed-loop discipline, and its bottleneck was pure human-years. Once that bottleneck is priced in dollars and tokens instead of decades, the same dynamic extends to every pure and theoretical science and to engineering. There will be more math done than at any point in history — especially applied math: whole classes of problems that used to be cost-prohibitive, including the systems problems sovereign programs actually care about (rigorous verification of the software and hardware we build, the math of AI models themselves, control, logistics, materials). The “cash injection” line is the key sentence in the post. It used to be that a question either had a research community attached to it or it never got answered; now any question worth a datacenter afternoon can be attacked. And when AI starts running experiments — with humanoid labor close behind — the same cash-injection logic reaches all of empirical science. Math is the preview.
Which is exactly why there’s no reason to fear a stall in mathematical progress. The supply of open problems is effectively infinite — by your own closing words, there is “so much more to learn — an infinite amount” — and solving problems generates the next questions. The worry that the labs are “mining non-renewable problems” treats the map as if it were the territory. The engine is just finally fast enough to explore it.
What changes is the profession — the same way software engineering has already changed. In SWE, the shallow work — boilerplate, routine features, straightforward implementation — has simply disappeared, and the bar for being a competent hire went up, not down: you now have to understand more, faster, in order to steer and verify what the machine produces. The same is coming to math. Shallow math (routine lemmas, bookkeeping, standard formalization, literature navigation) goes to the machines; deep math (conjecturing, framing, understanding, synthesis, teaching) survives and becomes worth more. Mathematicians will always be needed — you’re right that an abundance of new mathematics requires an abundance of new mathematicians to digest it — but the skill level required to be a competent research mathematician is going sky-high. People who can’t make that jump won’t be “replaced”; they just won’t be in the profession. That’s fine.
So the institutions must change, and the shape of the change you sketch is the right one: the rigorous defense that actually signals understanding, provenance irrelevant; seminars where the speaker has to teach the audience; research programs rewarded, because deciding what is interesting is now the scarce skill; interviews for admissions. Versions of the university that can’t do this will be disbanded — or bypassed by registries, labs, national programs, and events like the Mathathon that do. The 2027 “slot machine” is a real risk, but it’s an incentive problem with exactly this kind of fix, not a capability problem. One more thing worth naming: the duplication we’re seeing right now (three groups proving Feige’s conjecture independently) looks like waste, but it’s just transition noise — like bitcoin mining. The marginal value of the first solution collapses, while the information it produces (which problem classes are solvable, at what cost) is precisely what re-prices the field and points human effort at what matters.
To the trad-math apologists, including the very good ones: you will be bulldozed by the advance, and most of you will know it was right the moment it happens. That is not the end of mathematics. It’s the beginning.

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just different
September 14, 2026

> research programs rewarded, because deciding what is interesting is now the scarce skill
The missing link here is that at present, someone’s credibility about what is interesting is proportional to how many “interesting” theorems they’ve already proven. It’s not at all clear how that sort of status will be reorganized.

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Yemon Choi
September 14, 2026

Was it really necessary to get an LLM to write this for you? At the very least, you could ask your machine to trim it down and remove the attempted rhetorical flourishes that just make those of us with English as a first language think of people like Boris Johnson.

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Marcin Kotowski
September 14, 2026

The problem of all such optimistic future visions is they assume that young people will want to enter the profession in its new incarnation. I’m not so sure they will. Imagine you’re a bright and curious 20-year old – would you rather join a profession that in a couple of years may decline or be reduced to exegesis of machine content, or do something else? The prestige of mathematics has already suffered a serious blow. When young people choose alternative, a field dwindles and dies.

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MS
September 14, 2026

I fear the same. It all seems so hopeless. The only question that remains is what will kill mathematics first: (1) a complete collapse of bright young people who wish to become mathematicians, or (2) the government and general public deciding that there is no longer any need to fund professional mathematicians. Both seem inevitable. When (2) happens, mathematics will all but die out — it cannot survive as a hobby for people in their spare time, and there will be nobody left interested in prompting the machine and understanding its output.

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sukessh velusamy
September 14, 2026

I don’t really see any other option. Would the average person really hold mathematicians in high regard if they tried to ignore/avoid all proofs written with the help of AI, and if all the conjectures they are working on could easily be solved by the chatbot on his phone?

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Timeline of events

September 14, 2026
A beginning for mathematics

September 14, 2026
Nothing changed

September 13, 2026
The Platonist view

September 12, 2026
The Association for Human Mathematics

September 12, 2026
On the impact of AI on the mathematical practice

September 11, 2026
Protesting the protests

September 11, 2026
We Need a Stockfish for Math

September 10, 2026
A somewhat optimistic view of AI in mathematics

September 10, 2026
A response from Mathathon

September 10, 2026
Open Letter about the Mathathon

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Daniel Litt posits that the rapid advancement of artificial intelligence in mathematics necessitates a radical rethinking of the profession, moving beyond concerns about simply automating theorem proving to focusing on human understanding and the structure of mathematical practice. He suggests that while AI systems may soon be superhuman at mathematical computation, the focus must shift to deepening human understanding, asserting that this is achievable even as the production of interesting mathematics becomes less reliant on individual human effort.

Litt notes a lack of consensus within the mathematical community regarding its goals, highlighting divergent views ranging from solving problems to viewing mathematics as an embodiment of love and transmitting understanding. He argues that the traditional operationalization of mathematical goals, primarily through proving theorems, is flawed because these tasks are easily automated, suggesting that focusing solely on these outputs is incomplete. He contends that while machines can produce results, they do not generate human understanding of those results, underscoring the enduring necessity of human mathematicians.

To address this shift, Litt proposes preserving human-centric elements of the profession, such as learning seminars, serendipitous conversations, and student-professor interactions, rather than focusing solely on maintaining institutional structures like the peer review system or the arXiv. He argues that the future equilibrium must prioritize rewarding skills that are difficult to automate, specifically the internal understanding of mathematics and the social-relational aspects of the profession.

He outlines a reconceptualization of the mathematics PhD, suggesting that the goal should evolve into becoming a world expert on a deep topic and mastering the ability to convey that interest and understanding to others, with the degree awarded based on a rigorous defense where the student demonstrates mastery of the subject matter, regardless of whether the source of the work was human or artificial. This requires students to be trained to ask interesting questions and pursue them, with faculty roles focused on fostering robust seminar cultures where speakers must educate the audience.

Litt emphasizes that the community’s crucial function is figuring out what is mathematically interesting, a necessity supported by the existence of open conjectures that motivate human inquiry. He suggests rewarding the construction of research programs that persuade others of their worthiness, allowing mathematicians to focus on deep understanding rather than mere procedural output.

Regarding the impact of AI, Litt addresses the fear that AI will erode human activity by noting that the possibility of pushing a button to produce mathematics is inevitable. However, he counters that this inevitability should prompt a focus on mathematics’s potential applications and its inherent value. He suggests that the economic dynamic is already shifting; mathematical problems are becoming accessible through "cash injection," which accelerates mathematical progress exponentially, meaning the bottleneck shifts from human time to computational power. This acceleration will lead to more mathematical output, but it simultaneously increases the demand for mathematicians capable of deep synthesis and teaching.

Ultimately, the new focus should be on fostering communication and engagement. Any answers produced by AI must be subjected to human scrutiny and interpretation to yield novel insights. Litt suggests that this change will be positive, as it encourages mathematicians to engage more deeply with the material, rather than merely focusing on the truth value of statements. The future of mathematics lies in an expanded scope where the pursuit of knowledge is driven by curiosity and the continuous interplay between human insight and increasingly powerful computational tools.