Even if AI completely surpasses humans at theorem-proving, mathematics' value will barely change
Math funding comes mainly from teaching, not from proofs; once AI turns theorem-proving into raw data, the scarce skills become building theory, practicing oral presentation, and deciding who deserves academic credit.
The argument · tap a timestamp to hear it
Math funding comes mainly from teaching, not research
He makes a counterintuitive observation: the largest revenue source for math departments is not NSF grants or private foundations like the Simons Foundation, but teaching—because math departments teach far more than just math majors; the department brings in revenue through course enrollments and tuition. This means value at the individual level (training in problem-solving ability, the aesthetic pleasure of doing math) is primarily monetized through the teaching channel, not directly through research output. This premise becomes crucial for understanding AI's later impact.
— KarpathyProgress speed deserves more attention than current capability
He argues with several examples that the pace of AI's mathematical ability improvement is underestimated, not that its current level is overestimated: DeepMind's olympiad geometry model in 2023 relied on hand-designed techniques that felt clunky; later general-purpose language models can now solve IMO-level problems by any reasonable standard; the first Erdős problem proof was questioned as lucky, but nobody says that anymore. The conclusion: four years ago these models couldn't reliably do addition; now they're producing proofs for serious research-level questions.
— KarpathyProving ability is not the core of math's value
Even if AI completely surpasses humans at theorem-proving, he argues this has almost no impact on math's funding or value because real application value never comes from individual proofs, but from the theoretical systems that grow from them—it's not the truth or falsehood of Fermat's Last Theorem itself that matters, but the entire framework of algebraic geometry and elliptic curve theory developed to prove it, which later spawned cryptography. To public and private funders, mathematicians will only become more leveraged, not redundant.
— KarpathyTwo reactions from mathematicians when AI generates proofs
Online discourse is mostly negative: if a mathematician is working toward a problem and OpenAI suddenly dumps hundreds of proofs out, it drains motivation. But in face-to-face conversations he sees more excitement. He shares the experience of Konstantin Kogler at Princeton's Institute for Advanced Study—who brought one of the most important open questions in their field to a model, saw the key insight Thursday, and had the problem solved by Sunday, that state of being excited and unable to sleep, which is how Kogler described it personally.
— Karpathy / Konstantin KoglerProofs are becoming a kind of raw data
He proposes a redefinition: proofs should be treated as raw data like numerical computation, not as an endpoint. For years mathematics treated producing a proof as equivalent to understanding, but he thinks that standard is failing—for instance, he doesn't care about the proof of the Navier-Stokes equation itself; what matters is whether someone organizes the ideas behind these proofs into a coherent theory, who does that, and who should get the Millennium Prize, not the model that generated the proof.
— KarpathyFunding may not flow to the most capable AI systems
Picture an extreme scenario: AI not only proves theorems but proposes conjectures, builds theory, and applies theory to science and engineering all better than humans. By pure efficiency logic, that's when pouring public and private money into a large pile of compute dedicated to mathematics research becomes rational. But he doesn't believe policymakers will literally switch public funding directly to machines; more likely, AI-enriched individuals will set up private foundations to pour into compute for math research, while public funding shifts toward emphasizing math training as externality, or redefines human mathematics as a funded art form.
— KarpathyTeaching is the hardest math work for AI to replace
He argues teaching is one of the safest jobs in the face of AI pressure, not because AI can't explain clearly—even if AI can teach any concept more clearly than any human, the bottleneck to learning was never clarity of explanation, but motivation: does someone want to learn? The biggest driver of motivation is often seeing another person who genuinely cares about the thing, something deeply dependent on human connection that a screen cannot replace.
— KarpathyNewcomers can reshape how mathematics distributes academic credit
His advice to 2026 math PhD students is not to use AI to unlock new mathematics, but seize the moment: the entire math community knows its credit system must change and is searching for models, meaning newcomers have a genuine chance to shape how mathematics awards credit in the future. He uses himself as an example—ten years ago, proposing math visualization as a dissertation would likely get you dismissed from the department, but this is precisely when such ideas might gain acceptance. He also urges that whether you use proof machines for unprecedented theory-building or stay true to math done for human audiences, practice talks and oral presentation more, because that will increasingly define what it means to be a mathematician.
— KarpathyIn their own words · checked verbatim
there has never been a better time to go into math, that there's never been a better time to fund math, and that maybe the most radical change that we'll see in this moment is a reframing of how we assign academic credit
Karpathy1:00
you know, did DeepMind just crush Olympiad-level geometry?
Karpathy11:09
four years ago, these things couldn't even add numbers. They came to be able to do contest level math much faster than anyone anticipated.
Karpathy14:10
First I felt incredible excitement because about the math, about the power, about the truth I would learn, about the power of ideas I saw.
Konstantin Kogler18:12
The proof is just data, it's like giving me more digits of π.
Karpathy23:14
Let's call this the anything you can do I can do better future.
Karpathy31:18
Teaching in general just feels to me like one of the most safe positions from a standpoint of AI job displacing because it's so relational, because it depends so much on a human-to-human interaction.
Karpathy34:22
The reason I think it's one of the best times to go in is because the community as a whole knows that it needs to change, and so many people are leaning back looking for guidance and examples on what that change should be.
Karpathy37:25
Figures
| Number of math proofs released by OpenAI | Hundreds of problems | 13:09 |
| Start time of Karpathy's mathematician interview project | Mid-2025 | 11:09 |
Glossary
- Erdős problems
- A large collection of open problems posed by mathematician Paul Erdős, commonly used by AI companies as a benchmark for theorem-proving ability.
- rising sea
- Grothendieck's metaphor for theory-building: rather than directly solving hard problems, raise the level of overall understanding so problems dissolve naturally.
- anything you can do I can do better future
- An extreme scenario in which AI surpasses humans in proving theorems, proposing conjectures, building theory, and applying theory to science and engineering.
- spiky frontier
- AI's mathematical ability varies wildly across different domains and individuals, with no uniform level.
How to listen
Current or prospective PhD students in math or theory, math professors advising students on careers, and anyone worried that AI will devalue this path.
Familiar with academic funding structures? You can skip the 5–8 minute explanation of where math research money comes from.