Request for Immediate Release of Yang–Mills AI Output

We call on OpenAI to make public without delay the natural-language and Lean outputs behind its announced existence proofs for Yang–Mills theory, quantum chromodynamics, and a completion of the Standard Model.

While these are central questions in physics, they are also important questions in mathematics. The existence of quantum Yang–Mills theory is part of a Millennium Prize problem and the construction of interacting quantum field theories in four dimensions has been a goal of mathematical physics for decades.

Giving all mathematicians access to this material will accelerate both the understanding of these proofs and the wider application of any new ideas they contain.

We have great respect for the scientists asked by OpenAI to lead this work. But as we explained in our recent statement, understanding should develop in the open, with everyone given the same access. OpenAI have said they delayed release until the Lean formalization was complete. By their own account this is now complete, so there is no scientific reason for delaying the release any further.

In our September 29 recommendations, we outlined an approach to the release of AI-generated mathematical output by AI labs. Since then, we have been asked by people from multiple labs and by several mathematicians about a specific aspect of the recommendations — that the development of human understanding following a release must remain organic and community led — and what it says about the question of the labs choosing specific mathematicians to participate in various ways in the release of their output. The purpose of this document is to clarify this point and to explain the reasoning behind our position on it. We welcome further feedback from the community and engagement with these arguments.

In some past releases an AI company has designated mathematicians to receive the output on a problem, often before anyone else. Those mathematicians then worked to uncover the ideas in the output, check them, develop them, and present them to the wider community. The appeal of this release model is easy to see: it puts expert eyes on the output early, can lead to a better initial public writeup, and gives each result a knowledgeable point of contact.

After consideration of many negative effects that this release plan has, however, we have come to the conclusion that on balance the disadvantages outweigh the advantages. This should in no way be construed as criticism of the mathematicians who have taken on such a role: they have acted in good faith and done valuable work. Nonetheless, we recommend that AI companies do not adopt this practice for future releases, for the reasons below.

Delayed or unequal access. In cases where designated mathematicians see material before everyone else, they get a head start on problems others may have worked on for years. Other mathematicians may have valuable contributions to make based on the material but may not have access to it, and may be dissuaded from working on it.

The remaining reasons apply even if all the material is released publicly at once.

Denied agency. The choice of who works to understand, check, and write up an important AI-generated result is consequential, both for those chosen and for the field, especially in the current period of transition when norms around credit for mathematical activities are in flux. If an AI company designates a particular mathematician to undertake or lead this task, it is to an extent making this decision for the community and denying it agency over its field of study. Further, this choice may discourage other mathematicians from contributing to the understanding of the results.

Biased selection. Any choice of designated mathematicians by the AI companies reflects their networks and priorities, which are different from those of the mathematical community. However carefully the choice is made, it is opaque and unaccountable. Moreover, this practice could incentivize mathematicians to align with whatever they perceive the AI companies’ priorities to be.

Borrowed reputation. In practice, designated mathematicians’ names end up vouching for the release and shielding the AI company from criticism. Given the wide range of views on the release of results by companies in the mathematical community, that puts the designated mathematicians in a difficult position that could compromise their role of helping with understanding.

It is unnecessary. Recent experience has shown that human understanding can develop organically and efficiently when AI-generated material is made available. In many cases recently, mathematicians have independently read released AI output, worked to understand it, and written useful papers providing clear arguments that solve the problems. We are also aware of several reading groups, workshops and websites being organized to understand AI-generated results, and there are new funding opportunities for such activities.

We recommend that any lab releasing AI-generated mathematical output follow either pathway 2A of our recommendations (for scholarly articles produced by AI lab employees, adhering to standards set by the mathematical community) or pathway 2B (for unfinished products that the employees do not intend to write up as scholarly articles). A brief summary of pathway 2B is:

Full details are provided in our September 29 recommendations. We recall that our recommendations are intended for mathematics, and not necessarily for other areas of science.

As announced a few weeks ago, OpenAI has released a large collection of mathematical results generated by an internal model, reporting solutions to hundreds of open questions. This is an important event for mathematics, with consequences both for mathematics and for the mathematical community that extend far beyond the individual results.

AGMAI’s advisory role should not be interpreted as a judgment of the impact of these results or an endorsement of the process by which OpenAI obtained them. We do not speak on behalf of the entire mathematical community, and only the mathematical community can undertake the assessment that is needed.

Making this work public is a first step. This release is the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge. At the same time, the future of mathematical research cannot consist only of understanding results produced by AI labs. Mathematicians must be able to formulate their own questions, develop their own approaches, and explore directions that have not been selected as examples of an AI system’s capabilities. Equitable access to powerful research tools and adequate computational resources are essential to that freedom.

We reaffirm our published recommendations on responsible release. We have discussed them with OpenAI and appreciate the company’s willingness to engage. While we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest. We remain committed to engaging with any frontier AI lab on these questions and have already been in contact with several of them.

Here are our general guidelines for the responsible release of AI-generated mathematics by AI labs, informed by over six hundred survey responses.

The rapid advances in artificial intelligence (AI) present both opportunities and challenges for mathematical research. We believe that we are at a historic moment for our discipline. Recent events raise urgent questions about how to support the long-term prospects for deep human understanding of mathematics.

The purpose of this group is to advise AI companies on their interactions with mathematical research and with the mathematical community, including the responsible presentation and release of mathematical results. We seek to work for the best interest of mathematics and the mathematical community, and to serve as one possible channel of communication between mathematicians and the AI industry.

This group operates independently of any AI company and members do not accept payment for this work. We will publish our recommendations to AI companies on this website. We are willing to offer such recommendations to any AI company whose models are likely to have a significant impact on mathematics. Although we will give advice, we do not have decision making power at any AI company, and the responsibility for the decisions made by any company will rest with that company.

• François Charles (ENS-PSL) • Camillo De Lellis (IAS, GSSI) • Timothy Gowers (Collège de France, Cambridge) • Martin Hairer (EPFL, Imperial College London) • Nikhil Srivastava (Berkeley, Simons Institute) • Ulrike Tillmann (Oxford)

• Ravi Vakil (Stanford) • Edward Witten (IAS) • Melanie Matchett Wood (Harvard)

This group came together after OpenAI approached some of its members about establishing an external advisory board. In agreement with OpenAI, they decided to instead create an independent group and invite the others to join.