Can Math As We Know It Survive AI? - Aventine
Aventine
SubscribeSign in
The Big Idea<br>Can Math As We Know It Survive AI?
Aventine<br>Jul 16, 2026
Share
Image Credit: Ian Lyman/Midjourney<br>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.<br>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.<br>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.<br>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.<br>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.<br>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.<br>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.<br>“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.”<br>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.”<br>There are fault lines running through the community about what happens next. One is whether, in the future, mathematicians need to be able...