Summary
- Terence Tao cautioned that AI is solving significant mathematical problems faster than new ones can be identified by mathematicians.
- This concern is grounded in real instances of AI tackling historically challenging problems.
- Tao advocates for labeling specific problems as "analysis-required," emphasizing the need for AI-generated solutions to be accompanied by reasoning.
Renowned mathematician Terence Tao, a professor at UCLA and regarded as one of the leading pure mathematicians today, has raised concerns regarding the rapid advancements of AI in the field of mathematics.
Tao, who received the Fields Medal in 2006, expressed his concerns on the math-focused social platform Mastodon, arguing that AI is rapidly diminishing the pool of valuable open mathematical problems that genuinely drive the discipline forward. He emphasized that it is not about solving proofs or publishing papers, but rather about identifying significant questions.
Myriad: Predict Nvidia's September trading high. Make your prediction here.While anyone can create an endless array of mathematical queries—such as calculating the googol-th digit of pi—most of these questions lack importance as they do not contribute meaningfully to the broader field. Tao emphasizes that it is crucial to discern which problems are worth pursuing.
He stated, “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.”
With the advent of advanced reasoning models and cutting-edge AI systems, research labs have been applying significant computational resources to tackle both mathematical and scientific challenges. Organizations like Anthropic and OpenAI have tested their models on problems that have confounded human mathematicians for extensive periods, sometimes decades.
The outcomes have included advancements in areas like quantum physics and applied mathematics. However, Tao points out that mathematics is unique in that genuinely challenging problems are rare, and researchers must be selective about which ones they choose to investigate for long durations.
Traditionally, determining which problems to tackle depended on the field's "difficulty landscape"—identifying which questions are straightforward, which require substantial effort, and which are currently insurmountable with existing tools. Although new methods have historically expanded this landscape, they have also unveiled new challenges. Tao argues that AI disrupts this pattern, as it is unclear where a model's limitations lie.
The Current Landscape
Tao's concerns are not unfounded. In May, an OpenAI model disproved the Erdős unit-distance conjecture, a question that has remained unresolved for 80 years regarding the maximum number of pairs of points that can exist one unit apart on a plane. This was verified by mathematicians outside the organization, including Fields medalist Tim Gowers.
In the same week, Anthropic researcher Levent Alpöge used the company’s unreleased Claude Mythos model to solve the same problem, generating a proof that Anthropic engineer Sholto Douglas described as a "cute, simple proof," which was shorter than OpenAI's version. Mathematician Daniel Litt noted it was "a bit worse" than OpenAI's proof, although Mythos also managed to find OpenAI's solution.
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
— Sholto Douglas (@_sholtodouglas) May 26, 2026
This week, Anthropic formalized the proof of Fermat's Last Theorem, a problem that had remained unsolved for centuries. Shortly thereafter, OpenAI solved a 90-year-old problem just hours after a researcher published his own proof, leading to a co-authored paper with an Anthropic researcher.
This competitive environment is exactly what concerns Tao. He remarked, “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.”
Tao believes this trend threatens to undermine centuries of progress in open science.
Evaluating the Process
Tao suggests a potential solution: marking certain problems as "analysis-required," meaning that a correct answer should be accompanied by reasoning that provides insight into related issues. He likened this to food banks that ceased accepting merely edible donations.
According to Tao, the alternative would be to ban AI in mathematics, a measure he deems “technically infeasible.”
As of now, his proposal has not been adopted as policy, and given the current behavior of major AI labs, even implementing it may not be feasible at this time.