Can Math as We Know It Survive AI?

Can Math As We Know It Survive AI?

Aventine

Jul 16, 2026

Image Credit: Ian Lyman/Midjourney

Can Math As We Know It Survive AI?

While many of us have watched with a mixture of panic and awe as AI gobbles up fundamental parts of our jobs, mathematicians are seeing the very rationale for their existence threatened as machines topple one mathematical challenge after another.

Progress has been swift. This time last year, artificial intelligence models joined the ranks of International High School Math Olympiads. In the months since, they have solved math problems that had stood unsolved for decades, using reasoning that their human peers consider worthy of publication.

For some who have devoted their lives to advancing the frontier of mathematical understanding by developing proofs and theorems, it’s a world-rattling experience. “The field is going to change, and these tools are going to change the field, whether people are on board with it or not,” said Bryna Kra, a math professor at Northwestern University and former president of the American Mathematical Society.

What to do? The question is the basis of the recently published Leiden Declaration on Artificial Intelligence and Mathematics. Signed by over 3,000 people, including math heavyweights such as Terence Tao from UCLA and Peter Scholze, director of the Max Planck Institute for Mathematics, the document is a stark warning about how AI could undermine the field of mathematics, and a 23-point plan aimed at mathematicians, math institutions and policymakers for preserving math as a human-first endeavor.

In presenting mathematicians as a united front, the document belies a profession struggling with disruption in real time. Behind the scenes, some mathematicians are embracing new AI tools, eager to advance mathematics in any way possible while others are uneasy about handing tasks to systems that can’t be fully understood. Questions about how the field will adapt — or be forced to adapt — to accommodate AI, how human accomplishment can be preserved, where a line should be drawn in trusting what an AI produces and how to work productively with the AI labs are all up for grabs. And while the field of math is in some ways uniquely exposed to AI, some mathematicians believe it is a bellwether for the impact AI will have on other disciplines and that their response will help shape the way other sciences adapt to the technology.

AI vs. mathematicians

Achievements of AI in mathematics have been gradually stacking up for months. In the summer of 2025, models from Google DeepMind and OpenAI achieved gold medal status at the International Mathematical Olympiad, a contest for the world’s most mathematically gifted high school students. Then last winter, models started biting off low-hanging research problems, notably some of those formulated by Paul Erdős, a prolific Hungarian mathematician who died in 1996, leaving behind more than a thousand deceptively simple yet unsolved questions, many of which remain so.

In recent months, AI models began solving problems many mathematicians say constitute PhD-level research. Google DeepMind’s Aletheia model solved a problem in arithmetic geometry that had eluded human researchers. More recently, a general-purpose AI system built by OpenAI disproved a conjecture (a mathematical theory that hasn’t been proven right or wrong) with reasoning that some mathematicians considered worthy of publication in a major journal. The way the OpenAI model approached the problem, combining ideas from disparate mathematical disciplines, was seen by some as a paradigm shift, illustrating how language models can become experts in “everything all at once,” said Kevin Buzzard, a math professor at Imperial College London.

“You can basically solve conjectures within a day that were lying low for months or years,” said Bartosz Naskręcki, a math professor at Adam Mickiewicz University in Poland and a co-author of the Leiden Declaration who also collaborates with OpenAI. He described the overall rate of progress as “ridiculous.”

But AI is not good at everything when it comes to math, and recent results don’t impress all mathematicians. Ravi Vakil, a math professor at Stanford University and the current president of the American Mathematical Society who has worked with Google DeepMind, said that “[AI] can prove interesting things, but every single time it’s being pointed in that direction by people.” Aimed at long, complicated problems, he added, it quickly starts to get things wrong. Naskręcki, meanwhile, pointed out that the recent OpenAI result was an example of “cherry picking,” a single success from hundreds of attempts. He also downplayed the complexity of the work, saying that “it wasn’t some kind of rocket science.”

There are fault lines running through the community about what happens next. One is whether, in the future, mathematicians need to be able to understand the work that AI creates. Proponents of AI argue that we should embrace the expansion of the mathematical frontier regardless of whether a human comprehends it; critics contend that if a human cannot understand an AI-generated proof, we may never truly know if it is correct. “If you don’t know why it’s true, you don’t know what the next interesting question is,” said Vakil. Buzzard imagines a future in which an AI produces a giant proof of the long-unproved Riemann Hypothesis and an automated system verifies it — at which point “some people think ‘This is great,’ some people think ‘This is a disaster.’” It is possible that the field will bifurcate into camps that are comfortable with AI making advances they don’t understand, and those that aren’t.

The Leiden Declaration tries to thread the needle, articulating the concerns about AI that mathematicians largely share, arguing that researchers should be transparent about their use of AI, take responsibility for correctness and choose their tools carefully. Other recommendations are, for now, more aspirational: that policymakers regulate the AI industry, and invest in public computational infrastructure.

What do AI labs want from math?

The relationship between mathematicians and AI labs has been one of the more difficult areas on which to reach consensus. Across many conversations for this story, there was unease about the power the AI companies wield, alongside a desire to experiment with what they create. “We need to be the ones making decisions about what’s happening,” said Kra. “If we aren’t proactive about that, we will just be reactive, and we will not perhaps be happy with the outcome.”

A common concern is that the AI labs’ models are proprietary: Nobody outside the labs understands exactly how and on what data models are being trained, and ongoing access to the models can’t be guaranteed. There is also concern that the labs will increasingly dictate the direction of research, using their tools for a narrow set of problems and ignoring others, reshaping the field in terms of where both attention and money go. For some, the stakes run beyond mathematics. Naskręcki, who tests models for OpenAI, described unease at realizing that the same reasoning capabilities he helps benchmark on abstract algebra can be used for purposes he wants no part of. “I was actually very scared one day when I realized that, you know, if you help develop reasoning models, that can be easily used on the battlefield to just kill more efficiently,” he said, comparing the position to that of the physicists on the Manhattan Project.

To some extent, insulation from these pressures is a luxury pure mathematicians have enjoyed for centuries — the ability to pursue esoteric work without significant outside funding. “In pure mathematics, it’s kind of shocking that your research might be guided by where your funding is coming from,” said Vakil — a comfort long abandoned in the physical sciences, where expensive infrastructure has made industrial collaboration a fact of life.

Yet many researchers feel an imperative to work closely with the labs to understand what’s coming. “We have to know what’s there,” said Vakil. “To not experiment, [to] not engage, seems not the right choice.” Kra conditionally agreed. “One has to engage, but that doesn’t mean one has to agree,” she said.

Longer term, said Michael Harris, a math professor at Columbia University and another co-author, there is hope that public computational infrastructure might emerge — a sort of CERN for AI, providing computing power to academics across disciplines so they do not have to rely on AI companies.

A model for others

In some ways mathematics is distinct from other sciences: The majority of its results can be shown with certainty to be right or wrong, which is what makes it such an attractive target for labs looking to test their models and generate publicity. As a result, “the conversation in math is happening probably a couple of years before it happens in a lot of other areas,” said Daniel Litt, a mathematician at the University of Toronto.

But AI will come for other academic disciplines as well. “Maybe in other fields they have substantially different methods, so they probably are going to use AI in a different way,” said Naskręcki, “but I think the same kind of issues arise.”

As that happens, the Leiden Declaration could be a template for how to respond. “It’s the start of a conversation,” said Kra. “But I’m hoping that it will lead to concrete policies.”