Twenty-five Fields Medal recipients have voiced opposition to the race among AI companies to solve complex mathematical problems. In a joint statement, they warned that using such results to showcase model capabilities could harm science and researcher training.
Signatories include Terence Tao, Peter Scholze, Maryna Viazovska, and Maxim Kontsevich.
Tao explained that the document was prepared following discussions over the past week. The authors deemed the situation urgent enough to publish the appeal without broader consultations. The collection of signatures is ongoing.
Why Scientists Criticize the Race
According to the authors, the goals of developers and the mathematical community diverge. Science values not only the answer but also new methods that help understand the problem and continue research.
“The increasingly rapid mass production of ‘true/false’ statements can destroy fertile ground instead of breathing life into new ideas,” the letter states.
The obtained proof needs to be analyzed, connected with previous work, and explained to colleagues and students. However, the rush to make announcements leaves no time for this work and proper attribution, the signatories noted.
They believe the risk also affects education: independently finding solutions develops the ability to ask new questions. The authors saw a similar problem in other scientific and creative professions.
At the same time, the mathematicians acknowledged the benefits of AI for research. They emphasized that the consequences of its application largely depend on the decisions of those managing the technology.
Context Behind the Letter
The appeal was released shortly after OpenAI’s announcement regarding a result on the Navier-Stokes equation, one of the “Millennium Prize Problems.” The company is not mentioned in the declaration itself.
On September 8, the firm reported that its internal AI system had obtained a proof for cases C and D of the problem, which allow for external influence on the fluid.
According to OpenAI, a group of about 10,000 agents found the solution in 88 hours. An additional 17 hours were spent on formalization and verification in the Lean system.
The company published the proof and code, stating that it does not intend to claim the Clay Institute prize.
The result was accompanied by controversy over the possible use of unpublished work by mathematicians Tristan Buckmaster and Levent Alpoge.
OpenAI stated that it conducted an internal review, concluding that Buckmaster’s queries to Codex could not have influenced the system, including through training.
Buckmaster described the sentiment in the scientific community in a comment to The Guardian:
“The main thing in mathematics now is that no one wants to share anything anymore.”
In September, Anthropic introduced a Claude-prepared formalization of the proof of Fermat’s Last Theorem. Over 11 days, agents translated already known mathematical reasoning into code for computer verification.
