Terence Tao was still working with AI on a mathematical proof in the final minute before going on stage.
Backstage at the 2026 Frontiers and Pioneers symposium, host Ken Ono glanced at Tao's screen and asked whether he was still doing math. Tao, without looking up, replied that he had just asked his agent to generate a 19-page proof.
The proof concerned the Sendov conjecture, a decades-old problem about how far apart the zeros and critical points of a complex polynomial can be.
For Ono, the striking part was not the 19 pages themselves. He said that, in the past, Tao would usually be waiting with a yellow legal pad, scribbling notes before a talk. This time, Tao had an open laptop in front of him, with an AI-generated answer on the screen.
"This is a world-famous mathematician. To me, that represents a paradigm shift," Ono said.
The exchange captured a broader point from the conversation: AI has entered the workflow of elite mathematicians, and not only as a tool for searching references or writing code. It is starting to participate in proof work on research-level problems.
Recent cases highlighted in the discussion
Ono and Tao pointed to several examples. In January, GPT-5.2 Pro and the formal mathematics system Aristotle solved Erdős Problem #728, and the final proof was verified by Lean.
In May, an OpenAI model overturned a long-standing conjecture in the planar unit distance problem, a classic hard problem in combinatorial geometry first posed by Paul Erdős in 1946.
The latest example mentioned in the conversation was Lech Mazur's AI-assisted solution to the decades-old Sendov conjecture, again with Lean used for verification. Tao later helped reorganize that proof into a version more readable for humans.
Ono said he has been working in a similar direction himself. Trained in integer partitions and number theory, he now serves as founding mathematician at Axiom Math, where AI and mathematics is one of the main areas of focus.
A 2023 forecast revisited in 2026
Tao had publicly predicted in 2023 that by 2026, AI might become reliable enough to serve as a co-author on technical papers.
Asked again whether that forecast had held up, he joked that he should have specified the month as well.
His view was that in January this year, the claim could still be debated. By August, he said, the answer had become fairly clear.
Tao's main view of what AI changes in mathematics
AI explores in a way that is almost orthogonal to human thinking
Tao said AI is not simply moving faster along established human routes. In his view, it is exploring in a way that is almost orthogonal to how mathematicians usually think.
He described a thought experiment: imagine a mathematician who knows every technique that has appeared in the literature and can intelligently try hundreds of combinations of those techniques. That kind of search could solve some problems that human researchers would only crack in rare moments of insight.
Not every problem fits that mode. Still, mathematics contains thousands, even tens of thousands, of open problems. Tao said no one yet knows the success rate for these tools. If it were 10%—a number he explicitly presented only as an offhand example—that would still imply that hundreds of problems might be solvable and that many new links could come into view.
He said he believes the field is getting close to that state.
"AI is a helicopter that gets you near the answer"
Ono brought up one of Tao's earlier metaphors: doing mathematics with AI today is like trying to reach a distant place on foot, except AI acts as a helicopter that drops you near the answer.
Tao's response was that the mathematical community needs to explain more clearly what mathematics is actually for.
He said that as a child he vaguely imagined a committee of mathematicians handing out problems for others to solve. Even now, some people seem to picture mathematics as a kind of giant egg hunt, with problems sitting out there like a list of tasks waiting to be checked off. Tao said that is not really what the field is.
He compared mathematics to exploring a landscape. Researchers are trying to draw a map of terrain whose structure they do not yet understand, though they can see certain landmarks. There may be a mountain here or a waterfall there. If they can reach those points, they gain a better view. The real value lies in building roads, drawing the map, and sharing what is learned along the way. Reaching the summit is only one milestone.
Sometimes, he said, what looks like a distant mountain turns out to be just across a bridge. The full structure is not known in advance.
In that sense, he said, the recent headline-grabbing breakthroughs fit the same pattern. There are many shortcuts in the mathematical landscape that people did not realize were there. That is useful, because it reveals more of the terrain itself.
For a long time, humans explored using only human intelligence. Now there is another mode of exploration that is close to orthogonal. Over time, Tao said, that should produce a richer understanding of mathematics. In the short run, though, it can create an odd impression: some problems long considered difficult may turn out to be easy for AI, leading people to think AI has surpassed humans. Tao said "orthogonal" is probably more accurate than "superhuman."
A correct proof is not yet human knowledge if nobody can explain it
Tao returned several times to the idea that mathematics is not valuable only because it reaches the endpoint.
The roads built on the way, the maps that get drawn, the connections that are found, and the structures that let later researchers keep moving forward matter more. Even if a proof has been verified as correct, he said, it has not really become part of human mathematical knowledge if no one can explain what is going on in it.
That leads to one of his central claims about AI and research: as proof generation becomes more automated, the scarcest part of mathematical work may shift from finding the answer to understanding the answer.
Why mathematics now has to explain itself again
During the conversation, Ono referred to a talk Tao gave at this year's International Congress of Mathematicians, where he said the field is going through a crisis that touches both values and practice.
Tao answered that a crisis can also be an opportunity.
For more than a century, he said, mathematics was relatively stable. There was a broad consensus that the field solved problems, built theories, and built communities. Those goals generally aligned, so the community could pursue them together.
Now, he said, they are starting to split apart. AI can advance some of those goals while cutting against others.
That is why the field now has to say more explicitly what it wants to do and what mathematics is for. In the past, he said, there was no pressing need to debate that question because there was no outside force pushing mathematics in a particular direction. Now there is. The discussion is no longer only about technical matters such as how to prove a theorem, but also about values.
Tao said he thinks mathematics will ultimately come out stronger.
He compared the present moment to the foundational crisis of roughly a century ago, when inconsistencies appeared in the axioms people were using. That crisis was resolved, and mathematics became stronger afterward. He said he expects the same this time.
Asked whether mathematics remains, at its core, a human enterprise that can be enhanced by AI, Tao said a large part of mathematics is about helping people understand the world better.
Because of his mathematical experience, he said, the world feels less frightening to him. People live with technologies they may not fully understand: why a phone can connect them to someone on the other side of the world, why the internet works, why AI works. Mathematics can explain those things, and Tao said that kind of explanation is reassuring.
When AI can produce something that looks like a PhD thesis
Ono also asked what advice Tao would give to a doctoral student who began in 2022 expecting a stable profession, only to find that the ground had shifted dramatically.
Tao said people are living in a time of rapid change and deep uncertainty.
He added that no one's future is fully under personal control. Economic conditions, research funding, and changes in AI capability all matter. A person may make every correct decision and still fail to get the hoped-for outcome. That does not make good decisions any less important.
He said graduate education in mathematics still offers substantial value, but the traditional visible markers of value—such as a dissertation or a strong research paper—may now be reproducible at the surface level.
In his words, the field is close to a point where AI can generate something that looks like a PhD thesis, and it may be hard to distinguish that from a dissertation a graduate student spent four years producing.
But the purpose of doctoral education is not to manufacture a paper, he said. It is to train a person to acquire valuable abilities: absorbing complex material, synthesizing information, and asking questions. Education also carries other forms of value that were not always stated openly because the field had visible credentials such as papers to stand in for them.
If those values are made clearer—if people understand that universities are not training someone who only writes prompts, presses buttons, and produces papers, but someone who can actually think—then that person will remain valuable, Tao said.
Lean and formal verification
Ono asked Tao to explain the formalization and verification work he has strongly supported.
Tao said mathematics, in principle, has a full set of logical rules that permit only certain forms of reasoning. In practice, however, mathematicians often cut corners a little. They write informal proofs, say that something is obvious, skip details, or wave through a step with a gesture.
That is a very human way to argue, he said. Some level of omission makes sense, but mistakes do happen.
In recent years, he said, researchers have developed computer languages that can check a mathematical argument in full, provided it is written in a strict enough format. Learning to do that is difficult.
His first experiences with Lean felt, he said, like having an extremely picky teacher standing behind him. A tiny mistake would trigger a blunt response: no, that is not correct. The screen would fill with red marks that had to be fixed one by one.
Even so, he said, the process is valuable training. And when a proof finally compiles, the result comes with a strong dopamine reward.
He added that if AI is used in education, business, or science, it can still make many mistakes. The error rate has fallen, but it is not zero, which puts a limit on how much trust people can place in these systems. Combining AI with formal verification, he said, may be a way to force strict rule-following and make the technology genuinely useful.
What remains for humans after proof generation gets automated
In the audience Q&A, an undergraduate from the University of California, Berkeley asked about the skills younger mathematicians should develop if AI can now produce genuinely novel proofs. The student referred to a recent case in which an OpenAI model overturned Erdős's long-standing conjecture on the planar unit distance problem, and to Tao's later writing that explained and digested the construction.
Tao's answer was direct: more attention now has to go to work beyond the production of proofs.
In the past, creating the proof was the hardest part. Now that part is beginning to automate. The more important skills, he said, will be understanding proofs, explaining them to other people, and recognizing similarities between different arguments across the literature.
Put differently, if AI gets better at dropping researchers near the answer, the scarce work may become explaining how that route works and what it means within the wider map of mathematics.
The reference link provided for the conversation is a YouTube video at https://www.youtube.com/watch?v=TtOMM8HrT64. The article says the original material came from the WeChat public account Quantum Position, written by Tingyu, and was published by MarsBit.