Gathering of Mathematical Minds
In August, OpenAI convened approximately 40 mathematicians to discuss potential actions should artificial intelligence surpass human capabilities in their field. The tech giant hinted that its advanced models had successfully tackled numerous long-standing mathematical problems. However, representatives from OpenAI reassured the attendees that they would not release all solutions simultaneously, a claim that Lindsay McCallum, a spokesperson for the company, stated lacked confirmation. Concerned about the community’s potential reaction, she sought advice on how best to disseminate the findings.
Attendees exhibited a mix of enthusiasm and trepidation, but Bryna Kra, a mathematician from Northwestern University, recalls the gathering as a promising first step. The group urged OpenAI not to limit its announcements to blog posts or tweets, as was the case with ten problems earlier that month. Instead, Kra emphasised the importance of presenting comprehensive articles that would allow mathematicians to assimilate, analyse, and apply the results. “Unfortunately, that suggestion appears to have been overlooked,” she remarked.
Upcoming Publication Plans
OpenAI has revealed plans to publish hundreds of previously unsolved mathematical problems on GitHub this coming Tuesday, as informed by sources familiar with the company’s intentions. This release would mark the latest in a series of thousands of mathematical solutions generated by AI this year.
McCallum indicated, “On August 28, we began training a new internal model. In addition to resolving the Millennium Prize problem concerning Navier-Stokes, this model has already addressed over 100 long-standing open problems across various areas of mathematics. We are committed to responsibly publishing the forthcoming mathematical results from our model, guided by the advice and recommendations of the Advisory Group on Mathematics and Artificial Intelligence from the Institute for Advanced Study to determine how best to present these findings. We have not yet set a publication date.”
Nevertheless, several prominent mathematicians perceive this imminent publication as indicative of a lack of learning from previous controversies surrounding prior disclosures.
Mathematics as a Playground
In discussions with observers, academics have expressed a sentiment that the field has become a playground for OpenAI and its competitor Anthropic, who seem eager to showcase their models as they approach significant stock market launches. In their race to outdo one another, these companies appear to have neglected traditional scientific processes concerning publication and attribution of results.
A notable incident occurred in September when OpenAI deployed thousands of agents to address the legendary Millennium Prize problem, which carries a million-dollar reward, after hearing “rumours” that others were nearing solutions. Tristan Buckmaster, a mathematician and professor at New York University, accused the company of preempting work he had undertaken on a specific aspect of the problem in collaboration with Levent Alpöge, an employee of Anthropic. Although the duo had not yet published their findings, they had been utilising OpenAI’s tools as aids.
During discussions regarding proper recognition, Buckmaster noted that OpenAI researcher Sébastien Bubeck suggested that Alpöge should be excluded from any publication, as this would complicate matters. In response to a request for comments, Bubeck referred to a prior public statement denying any intention to exclude Alpöge as an author. Buckmaster, however, disagreed, stating that he felt compelled to speak out about what he perceived as OpenAI’s appropriation of his work.
Concerns Over Ethical Conduct
Nestor Guillen, a visiting mathematics professor at New York University, expressed to observers that there exists a perception among mathematicians that AI companies exhibit mafia-like behaviour. McCallum firmly rejected this characterisation, stating, “We do not agree with that characterisation.”
Guillen added, “I am increasingly concerned, as are many of my mathematical colleagues, not about AI itself, but about the companies behind it. Much of the anxiety stems from the concentration of power in a single entity.” In mid-September, OpenAI established an advisory group to assist in evaluating and communicating new results, maintaining academic and professional standards, and developing tools that support mathematical research and learning. However, mathematicians argue that little progress has been made.
Many express frustration that OpenAI and Anthropic continue to release results via blogs rather than through scientific papers, making verification challenging and often omitting prior work from other mathematicians. The fragmented announcements are not limited to the labs; Alpöge himself announced the refutation of an 87-year-old conjecture via a tweet shortly after the World Cup final.
Redefining Mathematical Publication
Kra contends, “For me, communicating mathematics through tweets and press releases is not the way to nurture the ecosystem that has cultivated this field.” In response to the rise of machine-assisted proofs, some have developed new tools aimed at helping the community leverage emerging results and discern which information warrants deeper analysis. Among these tools are Hexagon, a repository primarily of AI-generated material, and Palomar, a registry of machine-verified mathematics.
Despite direct encouragement for OpenAI to adopt these tools, Kra notes, “They have not altered their approach.” She also believes that the company’s actions are misaligned with the Leiden Declaration, a call from over 4,000 mathematicians urging AI companies to adhere to the community’s standards, which she helped draft.
The Future of Mathematics
Some OpenAI employees believe that their technology has rendered traditional mathematics obsolete, according to individuals who have spoken with them. McCallum, however, asserts, “We do not believe the future of mathematics is predetermined. We are collaborating with the mathematical community to navigate the future together.” The scenario where AI capabilities outstrip those of human researchers was posed hypothetically during the August gathering, but attendees who spoke to observers interpreted it as a cautionary note regarding what lies ahead. One individual likened OpenAI’s communication to a scenario in which “the police might wish to inform a family before announcing a death in a traffic accident.”
According to a close associate, Bubeck seems to believe that the technology from his company will swiftly eliminate most mathematicians’ careers. In statements to observers, Bubeck emphasised his belief that a more powerful AI could assist mathematicians in tackling more ambitious questions, better connecting their work with real-world problem-solving and making mathematics more accessible. “I see this as an opportunity to expand the capabilities of mathematicians and the impact their work can achieve,” he stated.
While mathematicians are aware that they must adapt, especially to prepare future generations, they do not believe their field is at an end. Kra argues, “It is changing the way we work, but I believe this is a time for ambitious thinking.” She welcomes the arrival of a new and powerful tool for problem-solving, expressing a desire for companies to be more transparent to foster trust in the results and leverage them effectively. “It is a moment that is frightening, but also very exciting,” she concludes.