As the stewards of a body of work dating back thousands of years, mathematicians are rarely in a hurry. Problems can lie open for decades or even centuries before they are cracked, and individual mathematicians think nothing of spending years devoted to a single question. But now , arguably the world鈥檚 greatest living mathematician, says that he and his colleagues have mere months to react to a crisis driven by the rise of AI. He warns that, for the first time in more than a century, mathematicians are facing a peril so severe that they ought to come together and reimagine what it means to be a mathematician.
鈥淲e don鈥檛 have to passively accept changes by external forces. [We] can鈥檛 just passively prove our theorems; we have to organise, become activists, get a little political,鈥 Tao tells me when we sit down to talk at the International Congress of Mathematicians in Philadelphia. In his estimation, mathematics needs a huge overhaul of its culture and practices, and it needs it very soon 鈥 by the end of this year. 鈥淚 wish we had more time to do this slowly,鈥 he says.
His sense of urgency is based on the stunning progress that AI models have made in mathematics this year alone. Throughout 2026, mathematical conundrums that had gone unanswered for decades are seemingly falling at the hands of AI at a pace of a few each week. Remarkably, some of these efforts have been helmed by amateurs and hobbyists who have simply asked models for solutions. Tao says it is likely that humans are about to lose their monopoly on problem solving.
Advertisement
In the face of this upheaval, Tao is perhaps uniquely placed to lead a rethink of what it means to be a mathematician. Growing up, he struggled to answer that question. He loved mathematics 鈥 in fact, he was a veritable child prodigy 鈥 but he had no idea what a mathematician does all day. Does some shadowy council just hand open problems to each mathematician like homework? Maybe, Tao reasoned, he should instead just be a shopkeeper 鈥 his love of mathematics would make him good at balancing accounts and taking inventory.
But it quickly became apparent that Tao was destined for a mathematical life. In one oft-cited anecdote, he was teaching other children to count at age 2. In another, a 7-year-old Tao is recounted reading a calculus textbook. At age 10, he became the youngest winner of a medal at the International Mathematical Olympiad. In 2006, he won the Fields medal, often called the Nobel prize of mathematics, and the award citation listed four different branches of mathematics he had influenced profoundly, having only just entered his 30s.
Now, aged 51, Tao has made the sort of singular mark on mathematics that would take most in the field several lifetimes to achieve. He has tackled a centuries-old question about patterns within prime numbers. He also chipped away at the Kakeya conjecture, which asks about the path taken by a needle as it rotates through space. Solving a version of this problem just earned Hong Wang at New York University the Fields medal. Tao has also settled seven problems set by legendary mathematician Paul Erd艖s, whom he met at age 10 (pictured below), and contributed to some of the biggest unsolved problems in mathematics, like the Collatz conjecture and the Riemann hypothesis.
Then there is his work related to physics, such as wave maps, which are linked to Albert Einstein鈥檚 theory of general relativity, or the nonlinear Schr枚dinger equation, which describes light that interacts with itself within fibre optics. He even developed an algorithm to make MRI scanners more efficient.
As this list demonstrates, Tao is both prolific and versatile, and he is frequently at the cutting edge of new ways of doing mathematics. For example, he helped lead the Polymath Project, an experimental enterprise in massively parallelised mathematics where large teams of volunteers tackled an open problem by splitting it into many mini problems. He isn鈥檛 against AI, saying he uses it regularly 鈥 but he is still remarkably worried about what the rapid pace of advancement means.
To outsiders, this ongoing shift from proof scarcity to proof abundance, as Tao describes it, might seem like a good thing. But Tao says it is as if mathematicians have been driving their cars along outdated roads built for pedestrians and horses, but now AI has joined in while driving larger, faster cars. Traffic jams and accidents are all but inevitable, and the whole infrastructure is proving to be unstable 鈥 AI is revealing and magnifying all its potholes, bumps and cracks. For example, it used to be that generating proofs was hard, but now that we have massively accelerated that part of the process with AI, the normal channels of peer review and mathematical acceptance are becoming clogged. 鈥淰alidation is in short supply,鈥 warns Tao.
There are some solutions already. Traditionally, mathematicians write up their proofs in a combination of mathematical symbols and natural language, and their colleagues read these papers to follow the argument and verify its logical truth. More recently, some mathematicians, including Tao, have turned to formalisation, in which the mathematical argument is encoded using a programming language called Lean, allowing a computer to verify each step. This has now been turbocharged by AI with autoformalisation, which hands the task of writing a proof in Lean over to AI.
But Tao worries that allowing AI to both produce and formalise a proof could easily lead us into territory dangerously close to meaninglessness. We might end up with something that a computer says is correct, but if a human can鈥檛 understand the proof, what is the point? Is it even really a proof? In Tao鈥檚 view, it would be bad for mathematics if all that the future held was just more and more AI-generated proofs. 鈥淭here is a danger that if all science becomes automated, the next generation of highly curated knowledge will be lost,鈥 he says.
The last time mathematics was in serious crisis was the early 1900s, when a variety of paradoxical results threatened to break the very foundations of the field. Mathematicians and philosophers had to come together and rebuild on firmer logical ground. 鈥淭hat was traumatic,鈥 Tao says candidly. This AI crisis is different 鈥 not one of mathematical arguments, but rather values and practices. Until now, mathematicians have mostly been able to put philosophy back in its box after the crisis of the 1900s, but AI is opening wounds old and new.
It all goes back to Tao鈥檚 question of what exactly a mathematician does. During their training, mathematicians become extremely proficient in technical skills, he says, but how mathematics works, and why it works, is something that they only learn implicitly from talking to their mentors and peers.
As they progress, young mathematicians tacitly pick up on how best to present their work, how to teach their technique to others, when to trust someone else鈥檚 work and what it means to have good taste and discernment when deciding which problems and research topics to work on. With a wry smile, Tao jokes that he wishes AI models could spend some time in graduate school and learn all of this before being unleashed onto some open problem. 鈥淎 lot of people that are picking up AI are treating maths as a sport where you just collect tick marks,鈥 he says.
This competitive spirit may be impressively productive on the surface, but it doesn鈥檛 necessarily advance mathematics. In a well-attended lecture at the conference, Tao laid out what he sees as the real work of mathematicians. He focused on problem solving. In his framework, the first step is posing a problem, followed by resolving it with a proof. The solution then needs to be verified, but it doesn鈥檛 become meaningful unless it is also well written, he argued. Such proofs must be easy to understand (for an expert, at least), engaging to read and clearly lay out the innovative parts of the argument and its connections to existing literature.
But this isn鈥檛 the last step, said Tao. The process ends only once the well-written, verified solution has been digested and accepted by a community of experts and becomes integrated into how the next generation of experts is trained. 鈥淚n order to actually influence the future development of mathematics, it needs to be accepted and valued by [the] community. Other mathematicians need to actually want to read it and digest it and put it into their own work,鈥 he said to a captivated audience. Heads nodded across the room.
AI models are very good at generating proofs and proficient at verifying them, but AI mathematics is really frustrating to read, Tao continued. Sometimes, an AI model will spend pages proving something that is obvious to a human mathematician, but then compresses the hardest part of the proof into just a few sentences, glossing over the most meaningful parts. Worse yet, the way AI models arrive at solutions is often opaque, hidden by both the privately run nature of software, like ChatGPT and Claude, and the fact that we still don鈥檛 fully understand their underlying technology.
Finally, community acceptance is simply not something that can be optimised with AI tools alone, he said. If being a mathematician simply means producing proofs, then AI models stand a chance of being good mathematicians, but Tao鈥檚 analysis, in part based on his own experience as a remarkably flexible and prolific mathematician, clearly made the case that a mathematician is something much more.
One area that will need careful consideration is the education of new mathematicians, with Tao saying in his lecture that students will need to be restricted in their use of AI, allowing them to develop their own intuition through old-fashioned elbow grease. Tao tells me that he has already heard stories of students whose otherwise commendable skill really declined after they started overly relying on AI. 鈥淎t some point, it becomes irreversible,鈥 he says. To avoid this, he can already offer some recommendations. 鈥淵ou can use AI if you can present your work to your advisors and answer questions intelligently without looking at your phone.鈥
I ask him whether he expects resistance from mathematicians when it comes to implementing such changes, as well as doing analytical and self-reflective work about their profession that they aren鈥檛 used to. They will simply have to, he tells me without hesitation. Then, a small concession to just how difficult cultural change can be: 鈥淒enial is such a strong force, especially if you have to change everything.鈥 But the alternative is also clear to him 鈥 not only will mathematics stop advancing, but mathematicians will lose the authority over what their profession is, and the figure of the mathematician will instead be defined by technology companies.
In fact, Tao thinks this is already happening. 鈥淯ntil recently, only mathematicians cared about mathematics. We had full control,鈥 he says. 鈥淣ow, for the first time, mathematicians have temporarily lost the narrative.鈥 In one striking example, Jacob Tsimerman at the University of Toronto in Canada, who was another winner of the 2026 Fields medal, is going on hiatus from mathematics to join OpenAI as a researcher.
And while it is undeniable that AI models are solving mathematical problems, we are far from having a scientific understanding of what it takes to achieve these results, or even something as simple as how many attempts it takes a model to spit out a proof 鈥 something that companies like OpenAI or Anthropic don鈥檛 necessarily have an interest in clarifying. 鈥淲e have sort of selectively disclosed results, which look impressive, but we don鈥檛 know exactly what the prompts were. We don鈥檛 know the failure rate. And many of the companies that are disclosing these have their own incentives to maybe present the results in as favourable [a] light as possible,鈥 Tao said in his lecture.
He wishes that mathematicians leveraged their authority more and spoke up more often. The public already doesn鈥檛 understand what mathematicians do, and now there is all this noise about it coming from a very different crop of researchers and technologists. In Tao鈥檚 view, tech companies may be able to shift the focus to simply generating as many proofs as possible, but mathematicians ought to get louder about all the parts of the process of doing mathematics where those firms鈥 AI tools can鈥檛 compete. 鈥淭hey tried to redefine what our profession is,鈥 he says. 鈥淸But] mathematicians have more influence than they think.鈥
Furthermore, Tao is actively involved in efforts to evaluate the mathematical prowess of AI in a more scientific way. He is part of the , which aims to test AI on unpublished problems in mathematics, meaning the models can鈥檛 rely on answers found elsewhere. Earlier this year, after posing 10 problems, the project鈥檚 reviewers found seven solutions generated by AI models to be of a high-enough quality to be published in mathematics journals. 鈥淲e need to identify the problems that really are best suited for AI,鈥 says Tao.
Even once AI models鈥 competency has been thoroughly evaluated through efforts like First Proof, questions will remain about the best way to leverage them. It might be that, instead of solving a few very hard problems in opaque ways, AI tools could tackle thousands of slightly less hard problems and advance mathematics through a more cumulative effect, Tao suggests, echoing some of his past community projects that had a similar aim. This could usher in an era of more experimental mathematics, maybe even mirroring how big international collaborations, for instance surrounding particle colliders, have advanced physics. 鈥淚f we get away from our obsession with solving [famous] open problems and chasing prestige, these tools can be useful,鈥 says Tao.
He is chipping away at the culture issue, too. The shape of a mathematical paper hasn鈥檛 really changed for decades, but Tao has just launched a video-based journal where mathematicians鈥 contributions will be evaluated not just on correctness of proofs, but how well they can explain them to their peers.
But if one of the lessons of the crisis in the foundations of mathematics a century ago was that mathematicians must come together, that is also happening now. Tao points me to the , a community initiative that produced a series of recommendations that were then endorsed by the International Mathematical Union and, at the time of writing, has more than 3000 signatories across all levels of mathematical research.
鈥淢athematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them,鈥 the authors of the declaration state in its introduction. 鈥淭his has been the result of months of community input about the fundamental values and goals of the mathematical community. In retrospect, these were questions we should have been systematically discussing years ago,鈥 Tao commented when adding his signature.聽聽
Mathematics, then, stands at a hugely significant moment, one where it must deal with a century鈥檚 worth of history as it is quickly barrelling into the future 鈥 a future that, without action, could be decided by technology companies rather than mathematicians. For Tao, this struggle for the heart of mathematics is as simple as it is personal. 鈥淚 love my profession,鈥 he says. 鈥淚 think this is worth fighting for.鈥
