A group of 25 Fields Medal recipients has voiced their concerns regarding the rush by AI companies to solve complex mathematical problems. In a joint statement, they cautioned that utilizing such results to showcase the capabilities of models could harm the scientific community and the training of future researchers.

Among the signatories are renowned mathematicians Terence Tao, Peter Scholze, Marina Vyazovskaya, and Maxim Kontsevich.

Tao explained that the document was drafted following discussions over the past week. The authors deemed the situation urgent enough to release a statement without broader consultations, and they are continuing to gather signatures.

Reasons Behind the Criticism

The authors believe that the objectives of developers and the mathematical community are misaligned. They argue that in science, the process is as important as the final answer; new methods that enhance understanding of problems and facilitate ongoing research are crucial.

"The increasingly rapid mass production of 'true/false' claims could destroy fertile ground rather than breathe life into new ideas," the letter states.

Once a proof is obtained, it must be analyzed, connected to previous work, and explained to colleagues and students. However, the rush to announce results leaves little time for this critical work and proper attribution, the signatories noted.

They also pointed out that the risk extends to education: the ability to independently seek solutions fosters the capacity to ask new questions. The authors recognized a similar issue in other scientific and creative fields.

Despite their concerns, mathematicians acknowledged the benefits of AI in research, emphasizing that the implications of AI applications largely depend on the choices made by those in charge of the technology.

Context of the Statement

This statement comes shortly after OpenAI announced results related to the Navier-Stokes equation, one of the "Millennium Prize Problems." The statement itself does not mention the company.

On September 8, OpenAI reported that its internal AI system had provided a proof for variants C and D of the problem, which allows for external forces acting on the fluid.

According to OpenAI, a team of about 10,000 agents took 88 hours to find the solution. An additional 17 hours were spent on formalizing and verifying it in the Lean system.

The company published the proof and code, stating that it does not intend to claim the Clay Institute prize.

The announcement sparked controversy regarding the potential use of unpublished work by mathematicians Tristan Buckmaster and Levent Alpoge.

OpenAI claimed to have conducted an internal review, concluding that Buckmaster's queries to Codex could not have influenced the system, including through training.

Buckmaster described the sentiments within the scientific community in a comment to The Guardian:

"The main issue in mathematics right now is that no one wants to share anything anymore."

It’s worth noting that in September, Anthropic presented a formalization of the proof of Fermat's Last Theorem prepared by Claude. In just 11 days, agents translated previously known mathematical arguments into code for computational verification.