Live from ICM 2026: What Is Math For in the Age of AI?
Mathematicians gathered in Philadelphia this July faced a question that would have sounded strange a decade ago: what is their field for, now that machines can do some of the work? The answer, according to three leading researchers, is not about speed or medals. It is about what humans value in the act of thinking.
The discussion took place at the International Congress of Mathematicians, recorded live for the podcast The Joy of Why. Hosts Janna Levin and Steven Strogatz led the conversation with Akshay Venkatesh of the Institute for Advanced Study, Ravi Vakil of Stanford University, and Alex Kontorovich of Rutgers University. The panel addressed recent AI systems that have solved competition problems and produced proofs, and what those results actually mean for the future of the discipline.
The Olympiad Moment
The conversation opened with a look at recent milestones in machine mathematics. In the 2024 International Mathematical Olympiads, a system called AlphaProof achieved a silver medal. A year later, in 2025, a more advanced model with DeepThink took gold.
Levin asked the panel who had competed in the Olympiads themselves. Vakil admitted he had, and Strogatz noted that Jordan Ellenberg had spoken about Vakil’s performance there. Vakil met Venkatesh at the event, though Venkatesh did not remember the encounter.
Vakil framed the competition as one of many paths into mathematics. “There’s no royal road to mathematics,” he said, “but this is one of the many ways by which we attract people into mathematics, and it’s also a great way of advertising mathematics, and it helps to develop a certain way of mathematical thinking.”
He stressed that the value of the Olympiads lies not in the six problems or the handful of winners, but in how the event encourages many young people to practice thinking. “The important thing about the competition isn’t the six people or the problems, it’s how it encourages millions and millions of kids to hone their minds.”
What a Medal Really Proves
When the AI models performed well, Vakil said he was pleased but not alarmed. He called the results “a proof of concept” and “an amazing milestone reached,” while cautioning that some people may have read too much into them.
He drew a distinction between a machine answering a question and a student answering one. “The first time a model answers a question, it’s exciting. A milestone is reached. The first time a student answers a question, it’s exciting for a different reason, because they’ve learned how to think.”
The seventh time a model answers the same question, he said, is far less interesting. The seventh time a student does so is also less interesting, but for similar reasons. The excitement, for humans, comes from the development of the mind, not the mere production of a correct answer.
Levin noted that the AI system did not even achieve the highest score in the year it appeared. Vakil responded that the next year it did, and the year after that it likely would again. “I’m happy about that, and I’m absolutely not alarmed,” he said.
“It can both be an amazing milestone reached, while also I think perhaps people might have misinterpreted it.”
A Concern About Competition
Venkatesh agreed with much of Vakil’s assessment but raised a separate worry. He said the attention on AI competition results has contributed to a view of mathematics as a contest, which is not how he sees the field.
“One unfortunate thing about this is it has contributed to the image, even among mathematicians, of mathematics as a competition,” Venkatesh said. He called this image “particularly unhelpful at the moment.”
He acknowledged that competition can drive young people, noting that validation from others feels good when you are young. But he expressed mixed feelings about how healthy that drive is. “There’s some competitive drive. You know, when you’re young, you get validation if people think you’re good at something,” he said. “I have mixed feelings about how healthy this thing is.”
Vakil agreed that competition carries risk. “As Akshay said, it could be a danger. Everything’s a double-edged sword,” he said. He added that some people are driven out of mathematics because they believe they are not good at it, often because they did not perform well in competitive settings.
Storytelling and Understanding
The panel then turned to a deeper question: what do mathematicians actually value about doing mathematics? The answer, according to the speakers, involves proof, understanding, and the surprising role of storytelling.
The conversation moved toward these themes without settling on a single conclusion. The speakers raised the question of what proof and understanding really mean, and how storytelling fits into the practice of mathematics. The discussion did not report a final position from the panel on these matters.
| Comparison | AlphaProof (2024) | DeepThink (2025) |
|---|---|---|
| Result at the Olympiads | Silver medal | Gold medal |
| Year of achievement | 2024 | 2025 |
| Panel reaction | Milestone, not superhuman | Expected further progress |
The Road Ahead
The full scope of the panel’s predictions was not established in the discussion that was presented. What was clear was a view of the field’s values.
Vakil said the AI results were exciting and a good thing, but did not represent anything like superhuman intelligence. He said he was happy about continued progress and not alarmed by it. Venkatesh warned against framing mathematics as a competition, especially at a moment when the field is changing.
The discussion made clear that the arrival of AI in mathematics raises practical questions about tools and methods. It also raises a more personal question for every working mathematician: why do this at all?
The episode is available on Apple Podcasts, Spotify, TuneIn, and other podcasting apps, and it can be streamed from Quanta. The live recording at the ICM in Philadelphia on July 26, 2026, captured a field in transition, still sure of its purpose, still figuring out its tools.
Source: quantamagazine.org
Get the Notebook.
The day's best stories and every fresh verdict, in plain English, in your inbox by seven. One email a day, no more.