Abstract:
OpenAI recently announced the establishment of an independent advisory group composed of top mathematicians to provide advice to OpenAI and other AI companies on the relationship between artificial intelligence and mathematical research. The new organization, called the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), will focus on how mathematical results produced by AI should be reviewed, published and disseminated, and how AI companies should follow long-standing academic and professional norms in the field of mathematical research.
This move occurred after OpenAI recently announced a number of major mathematical results. In the past few months, OpenAI's AI models have made a series of eye-catching developments in the field of mathematics. However, the way in which relevant results are published and the issues of citation and attribution of existing mathematical research have also triggered widespread controversy in the mathematics community. Some mathematicians question whether OpenAI fully understands how mathematical research works, and whether AI companies respect the long-established norms of attribution, priority, and academic communication in the mathematics community.
AGMAI has a total of nine members, who come from Stanford University, Harvard University, Oxford University, Cambridge University and other institutions, including many top scholars in the field of mathematics and winners of the Fields Medal and MacArthur "genius grant". The organization will be hosted by the Institute for Advanced Study in Princeton, New Jersey, USA. It was once the research site of famous scientists such as Albert Einstein, John von Neumann and J. Robert Oppenheimer. It is also one of the most influential academic institutions in the field of modern mathematics research.
OpenAI stated that this organization will remain independent and has the power to proactively provide suggestions to OpenAI, even if the relevant suggestions are not proactively proposed by OpenAI. The advisory group can also openly discuss the impact of AI on the field of mathematics and decide at its own discretion whether to make its recommendations public. OpenAI stated that members of the advisory group will not receive compensation from OpenAI and can adjust the membership composition themselves.
According to OpenAI, the advisory group will help the company determine how significant the new mathematical results generated by AI are, and provide opinions on how to coordinate the release of these results and how to comply with academic and professional norms for mathematical research. Additionally, the group will discuss how OpenAI’s AI tools can better support mathematics research and mathematics education.
OpenAI emphasizes that the real value of this organization depends on whether members can make independent judgments and question the company. In other words, the advisory group does not simply provide endorsement for OpenAI’s research results, but hopes to provide independent opinions from the mathematics community before the results are released.
However, after the announcement of this arrangement, there are still many questions in the mathematics community. The first is how exactly these nine members were selected. Simon Machado, a researcher at the Swiss Federal Institute of Technology in Zurich, believes that there are still many opaque aspects in the entire process. According to the introduction on the AGMAI official website, OpenAI initially contacted some mathematicians in the hope of establishing an external advisory committee; after discussions with OpenAI, these mathematicians finally decided to establish an independent organization and invited other members to join. But who was initially contacted by OpenAI, and how the remaining members were identified, has not been fully disclosed.
Martin Hairer, a member of the advisory group, later published an article to explain the large number of doubts surrounding the formation process of this organization. He said that artificial intelligence has had a profound impact on mathematical research and has brought about a series of issues such as attribution of results, research priorities, and whether humans truly understand the mathematical ideas generated by AI. Therefore, it would be unrealistic for the mathematics community to take a completely non-contact approach with AI laboratories and simply ignore these companies.
Hairer particularly emphasized that although the establishment of the advisory group did stem from contact with OpenAI, not all nine members had been directly contacted by OpenAI, and the organization ultimately established was independent of OpenAI and other cutting-edge AI companies. Beyond normal confidentiality requirements, members do not sign agreements that restrict their public expression of opinions and receive no financial compensation from OpenAI. The organization relies primarily on the Institute for Advanced Study in Princeton for technical and organizational support.
Hairer said that the most important goal of the advisory group is to represent the interests of the entire mathematics community as much as possible. He also acknowledged that it is obviously impossible for nine mathematicians to be a complete representative of the entire mathematical community, but he believed that all members took this responsibility very seriously and would participate with good faith and independent judgment.
The small size of the advisory panel also raises another level of concern. Modern mathematics has become highly specialized, and there are often very obvious knowledge barriers between different fields. Even the world's top mathematicians may not be able to judge AI results in another highly specialized field. Therefore, some mathematicians are worried about whether only nine top scholars can cover the entire mathematical research field that AI may involve.
Francesco Fournier-Facio, an incoming professor of mathematics at Heriot-Watt University in Scotland, said he has a mixed attitude towards the advisory group. On the one hand, he believes that allowing AI companies to communicate more with mathematicians will obviously help improve the status quo; on the other hand, he also questions whether this organization composed of a small number of top scholars can truly represent the vast number of mathematics researchers who are being affected by the rapid development of AI. He believes that the organization currently looks more like an "ivory tower" composed of top academic figures.
Whether the advisory group can gain the trust of the mathematical community in the future depends largely on how much actual impact it can have on OpenAI. It is particularly worth noting that when OpenAI announced the establishment of an advisory group, it also revealed an astonishing news: a new model that the company is developing that has not yet been officially released, which was previously claimed to have solved the Navier-Stokes Millennium Prize problem, has now solved more than 100 long-term unsolved mathematical problems, and these problems are distributed in a large number of different fields of mathematics.
OpenAI has previously announced that the model is challenging another Millennium Prize problem. As AI models continue to produce new mathematical results, how to review, verify, organize and publish a large number of research results in a short period of time has become a real problem. AGMAI stated on its official website that one of the first tasks currently facing it is to help OpenAI coordinate the release of a large number of major mathematical results generated by internal AI models.
This also explains why this advisory group was established at this time. In the past few months, OpenAI's continuous breakthroughs in the field of mathematics should have been an important demonstration of the improvement of artificial intelligence capabilities, but related events have been accompanied by a series of controversies. Some mathematicians believe that when OpenAI announced its results, it did not fully explain the contribution of previous human research to AI results, and it did not always handle citation and priority issues in a manner familiar to the mathematics community. Some researchers have even accused OpenAI of making use of their research results without giving them proper credit.
These controversies ultimately led some mathematicians to question whether OpenAI truly understands how the mathematical research community operates.
Kevin Buzzard, professor of mathematics at Imperial College London, asked: Since there has been a lot of public discussion in the mathematics community in the past few months, mathematicians' demands for AI to participate in mathematics research have been clearly expressed, so why does OpenAI need a committee composed of the world's top mathematicians to understand these issues? In his view, the problem is not that the mathematics community lacks people who can solve difficult theorems, but that AI companies need to better understand the discipline of mathematics and the rules of the mathematics research community itself.
AGMAI is currently gathering input from the mathematics community, including through exchanges with other mathematicians, public feedback forms, and on discussion platforms such as Proofs and Prompts. These platforms have recently become important venues for discussing the impact of artificial intelligence in the mathematics community.
At the same time, the problems faced by OpenAI have gone far beyond how to publish a few papers. As AI begins to independently produce mathematical results that have not been solved for a long time, the most basic questions in mathematical research, such as "who discovered what first", "who should get the signature" and "which human research provided the basis for the final results", all need to be redefined.
This is also a core change brought about by the current entry of AI into the field of mathematics research. Traditional mathematical research usually relies on researchers publishing papers publicly, citing previous work, peer review, and constantly building on existing results. AI can read and process massive amounts of existing knowledge in a very short time, and generate new mathematical derivation. When humans cannot completely trace the paths through which AI obtains a result, traditional results attribution and priority judgment methods become more complicated.
The recent controversy surrounding OpenAI’s solution to the Navier–Stokes problem has particularly highlighted this issue. OpenAI has investigated the relevant controversy and stated that a prompt word submitted by a mathematician using Codex was unlikely to affect the final system's solution to the problem. However, such incidents still worry some mathematicians. In the future, it may become increasingly difficult to accurately determine what kind of human research a mathematical result produced by AI is based on.
AGMAI member Hairer also admitted that the advisory group must be wary that AI companies may interpret or use the advisory group's opinions according to their own public relations needs. However, he believes that after AI has inevitably entered mathematical research, completely refusing to communicate with AI companies will not solve the problem. Rather than isolating the mathematics community from the AI industry, we should try to establish a set of ground rules that both sides can accept.
For OpenAI, the establishment of this advisory group also means that the company is facing a reality that it was not familiar with before: artificial intelligence has gradually transformed from an auxiliary tool for mathematical research into a research participant that can directly produce new mathematical results, and the traditional mathematics community has not established ready-made rules for this change.
In the future, AGMAI may need to solve not only when and how the next batch of OpenAI mathematical results should be released, but also how AI-generated mathematical results should be signed, how to cite human research, how to confirm the independence of the results, and what kind of cooperative relationship should be established between mathematicians and AI systems. With OpenAI claiming that its new model has solved more than 100 long-standing unsolved mathematical problems, these problems are quickly moving from theoretical discussions to real-life problems that must be faced.
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