What Happens to Math When AI Is Better at It?
The Problem Isn't Whether AI Can Do Math
Terence Tao is not worried about whether AI can solve mathematical problems. It can, and it is getting better at it every month. What worries him is something stranger: the possibility that the field of mathematics itself might not survive the encounter intact.
In a new essay written for the 2026 International Congress of Mathematicians, the Fields Medalist argues that AI could push mathematics into a crisis on par with the foundational upheaval around 1900 -- the "Godel crisis" that forced mathematicians to spell out assumptions they had always left implicit. That crisis produced a rigorous framework that held up for a century.
This time, the stress test is different. It is not about mathematical truth but about what Tao calls "the largely implicit framework of mathematical values and practices": what counts as a contribution, what gets rewarded, what it means to understand something, and whether a machine can be said to have done the work at all.
Proof Abundance Is the Problem
Tao's working hypothesis is blunt: "AI tools will, reasonably soon, become capable of performing a reasonable fraction of research-level mathematical tasks, with reasonable levels of success, quality, supervision, and cost."
That is not speculation. In a controlled test, ten never-published research problems were tested against four AI systems. Seven of the ten received at least one passing grade from at least one system -- a solution judged essentially flawless or needing only minor revisions. The cost ranged from tens to hundreds of dollars per problem.
If the hypothesis holds, Tao warns, the field could shift from proof scarcity to proof abundance. AI-generated proofs would pile up faster than anyone can check, read, or absorb. The arXiv preprint server already contains dozens of AI-generated submissions that no human expert has volunteered to verify.
The Many Goals of Mathematics
The Decoder, which first reported on Tao's essay, notes that the mathematician sees the problem as structural. The many goals of mathematics -- solving problems, building theories, fostering community, and training the next generation -- have always been tightly linked. AI threatens to pull them apart.
When AI can produce results on demand, the incentive to build shared understanding collapses. Why spend months developing a theory when a model can generate a proof in minutes? Why train the next generation when the machine already knows the answer?
Tao draws on Goodhart's law: "When a measure becomes a target, it ceases to be a good measure." Generative AI is especially prone to this because it chases the appearance of a good output rather than the real thing. The financial incentives of the AI industry make things worse by rewarding exactly the kind of quotable, benchmarkable wins that mathematicians have long used as stand-ins for deeper goals.
AI Proofs Are Easy to Read and Hard to Learn From
One of Tao's most striking observations concerns the texture of AI-generated mathematics. In human-written proofs, the hard parts tend to retain natural friction: a careful lemma, a change of notation, a paragraph that has clearly been rewritten several times. These "mistakes" in human exposition, Tao writes, "can be genuinely helpful to the reader."
An AI-polished proof strips away both the clutter and those useful signals, producing text that is "easy to read and hard to learn from." The result is a paradox: the better the AI gets at writing clean proofs, the less useful those proofs are for building human understanding.
New Scientist, which covered Tao's essay in a piece titled "Why mathematician Terence Tao thinks AI must spark a rapid revolution," notes that Tao himself uses AI for literature search, diagram creation, text completion, and converting his slides into paper format. He is not anti-AI. He is trying to figure out what happens when the field's implicit contract -- that a proof is something a human can understand and explain -- breaks down.
The Test That Matters
Tao proposes a single test for AI-assisted mathematics: if the authors cannot convincingly demonstrate that they can give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
Training young mathematicians needs special care, Tao argues, because the field needs to protect the "irreducibly human aspect" of their work. AI tool use should be tightly restricted in training, not because the tools are dangerous, but because the goal of training a mathematician is not achieved by having a machine do the work.
A Crisis for Every Field, Not Just Math
Tao's essay arrives at a moment when the broader implications are becoming visible. The Malaysian Reserve ran a piece titled "Math's AI crisis has a lesson for the rest of us," arguing that the same tensions Tao identifies in mathematics -- what counts as a contribution, how to train the next generation, what happens when the machine is better than the expert -- are playing out in every profession that AI touches.
The question Tao poses is not whether AI can do mathematics. It can, and it will get better. The question is whether the field can redefine what it values before the machine redefines it for them.
Sources
- The Decoder: Terence Tao says AI could trigger maths biggest crisis since Godel
- New Scientist: Why mathematician Terence Tao thinks AI must spark a rapid revolution
- The Malaysian Reserve: Math's AI crisis has a lesson for the rest of us