Twenty‑five mathematicians who have each been awarded the Fields Medal signed an open letter arguing that competition among AI labs is threatening the intellectual practices of mathematics. The signatories say that labs racing to apply large language models (LLMs) to famous mathematical problems risk undermining the verification, attribution and scholarly processes that sustain the field.
Recent disputes and practical examples
This week Tristan Buckmaster, a professor at New York University (NYU), accused OpenAI of pressuring him not to credit a collaborator who works for Anthropic in relation to the solution of an important problem. Buckmaster also raised the question of whether OpenAI used their work with Codex to produce its own major proof during a marathon weekend of inference. OpenAI’s alleged proof remains unverified.
On Thursday, OpenAI withdrew its sponsorship of a mathematics event at the California Institute of Technology (CalTech) after researchers at the university criticized the company.
Core worries expressed in the letter
The letter’s signatories acknowledge that AI‑derived solutions could benefit humanity, but only if those solutions can be understood, validated and effectively communicated by the mathematics community. They warn that such results are often announced in haste, leaving insufficient time for full writeups, the isolation and explanation of new methods, and proper citation of prior relevant work. This, they write, raises serious questions about attribution and plagiarism.
They further argue that without willing mathematicians who take responsibility for developing and integrating AI‑originated ideas into the mathematical canon, those ideas would not become fully alive and the vital human transmission chain between mathematicians would be lost.
Risk of secrecy and impacts on research culture
Other mathematicians, the letter says, are increasingly paranoid that their use of tools like Codex could feed back into the training or development of new models at large labs. There is a real fear that if frontier labs see an LLM‑based path to a discovery, they can spend tens of millions of dollars running models to beat the original researchers to a proof — a dynamic that would incentivize secrecy and erode the culture of open research.
Relation to the Leiden Declaration and recommendations
The open letter follows the Leiden Declaration, published in June by a working group of mathematicians. That document also examined how LLM‑produced proofs might change mathematical work and offered recommendations for mathematicians, institutions and policymakers.
The signatories emphasize that the value in mathematics is not only in the proofs themselves or in credit assignment, but also in the intellectual superstructure around them: the teaching, question generation, idea‑shaping and integration processes that nourish students, identify new problems, and embed advances into broader human civilization.
"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.
Broader significance
While the debate currently centers on high‑stakes mathematical proofs, the concerns raised are relevant across scientific and creative fields. If competitive model development and rapid, secretive deployment undermine openness and collaborative verification in mathematics, similar pressures could soon affect other disciplines. The authors call for institutional and policy responses to preserve the mechanisms of scholarly transmission, verification and attribution.
All named people and organizations are cited as they appear in the public debate. The letter’s signatory count is 25, and each signer is a Fields Medal recipient.
