Leading Mathematicians Warn AI Labs Threaten Mathematical Integrity and Open Research

Twenty-five leading mathematicians signed an open letter arguing that AI labs are threatening their intellectual work as they seek to one-up each other with solutions to famous math problems. Each signatory has been awarded the Fields Medal, considered the most prestigious prize in mathematics.

This week, NYU professor Tristan Buckmaster accused OpenAI of pressuring him not to credit a collaborator who works for Anthropic for solving an important math problem, and wondered if the company had used their work with Codex to produce its own ground-breaking proof over a marathon weekend of inference.

On Thursday, OpenAI withdrew its sponsorship of a math event at CalTech after the company was criticized by researchers at the university.

While the ability of AI models to solve the world’s outstanding mathematical challenges could be a boon to humanity, the signatories of the new letter argue that will only be the case if those solutions can be understood and communicated by the math community, and ultimately, the rest of the world.

“Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others,” they wrote — and OpenAI’s proof remains unverified. “As in all creative professions, this raises severe attribution and plagiarism questions. Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.”

With other mathematicians growing paranoid and wondering if their Codex use was in turn fed into OpenAI’s new models, there is real fear that the culture of open research will be threatened. Today, if frontier labs see a useful path to a discovery, they can spend tens of millions of dollars using LLMs to beat the original researchers to a proof — a dynamic that will incentivize secrecy.

This letter follows the Leiden Declaration, released by a working group of mathematicians in June. That document also grapples with the ways that LLM proofs will change their work, and offers a set of recommendations for mathematicians, institutions, and policymakers.

As with software engineering and other areas where AI tools are changing workflows, mathematicians find a justification in the work around the work: The value in math isn’t just the proofs and who gets credit, but the intellectual super-structure that nourishes students, finds new questions and ideas, and integrates them into broader human civilization.

And If you don’t particularly care about the cutthroat world of high-stakes mathematical proofs, don’t forget: Your field of interest is next.

“The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place,” they wrote.