Terence Tao argued that AI is depleting the supply of fruitful open math problems faster than mathematicians can identify new ones.
His warning follows a real precedent of AI labs solving historically hard problems.
Tao wants mathematicians to label certain problems “analysis-required,” so a bare AI-generated answer without explained reasoning counts for little.
Terence Tao, the UCLA professor widely considered the best living pure mathematician, has sounded the alarm over the accelerating AI race in math happening right now.
Tao, who was awarded the Fields Medal in 2006, posted a warning on the math-centric Mastodon instance Mathstodon yesterday in which he argued AI is draining the field’s supply of good open problems, the unsolved questions that actually push math forward. Not proofs. Not papers. Good questions.
Anyone can invent infinite new math questions; the googol-th digit of pi is technically an open problem nobody has calculated. Almost none of them matter, because most teach nothing about the wider field. What actually matters, Tao wrote, is to know what is actually worth the effort.
“In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained,” Tao wrote.
With the release of reasoning models and the latest generation of frontier AI systems, labs have begun throwing enormous amounts of computation at mathematical and scientific problems. Anthropic and OpenAI have put their models to the test on problems that have resisted human mathematicians for years, sometimes decades.
The results have ranged from quantum physics to applied mathematics and medicine. But mathematics is different: genuinely difficult problems are relatively scarce, and researchers often choose carefully which ones to spend months or even years pursuing.
Working that out used to depend on a field’s “difficulty landscape”—which questions are trivial, which take real effort, which are hopeless with current tools. New methods have always flattened parts of that landscape, but they also opened fresh frontiers past their own limits. AI breaks the pattern, Tao argues, because nobody can say exactly where a model’s ability stops.
From rumor to race
Tao isn’t describing a hypothetical. In May, an OpenAI model disproved the Erdős unit-distance conjecture, an 80-year-old question about how many pairs of points on a plane can sit exactly one unit apart. Outside mathematicians, including Fields medalist Tim Gowers, verified it.
Within the same week, Anthropic researcher Levent Alpöge ran the identical problem through Claude Mythos, the company’s unreleased top-tier model, working offline so it couldn’t copy OpenAI’s published solution. Anthropic engineer Sholto Douglas called the result a “cute, simple proof,” shorter than OpenAI’s. Mathematician Daniel Litt called it “a bit worse” than OpenAI’s version, though Mythos found OpenAI’s own solution too.
Huge credit to the OAI team for solving the unit distance problem with 5.5 – it is now my go to example that models can in fact pull together disparate ideas into new discoveries.
As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute,… https://t.co/NFymE8P8lu
Just this week, Anthropic formalized a centuries-old proof of Fermat’s last theorem and a few days later OpenAI cracked a 90-years old problem, hours after a researcher published his own proof, coauthoring a paper with an Anthropic researcher.
That race is exactly what worries Tao. “We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential,” he wrote.
Tao argues this ends up reversing centuries of open science.
Judge the process, not just the answer
Tao’s proposed fix is to mark certain problems “analysis-required,” meaning a correct raw answer counts for little unless it comes with reasoning that reveals something about nearby problems. He compared it to food banks that stopped accepting any donation that was merely edible.
It’s either this or banning AI in math, a solution, Tao says is “technically infeasible.”
The proposal hasn’t turned into policy anywhere yet, and based on how the big AI labs are behaving, even this may be technically infeasible right now.
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