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Who gets credit in the AI era? OpenAI maths bombshell sparks debate
Controversy around OpenAI’s claim to have solved the Navier–Stokes problem highlights how researchers could be inadvertently sharing — and absorbing— ideas through chatbots.
OpenAI’s announcement that it used an artificial-intelligence model to solve a major puzzle in fluid dynamics — the Navier–Stokes problem — is likely to change how mathematics is done forever. The claim, made by the AI company in San Francisco, California, on 8 September, has also sparked controversy about whether OpenAI tools have learnt information from human mathematicians who were also racing to solve the problem using AI tools.
The widespread use of AI models across most fields of research, and the difficulty of tracing the origin of the information used to train models, could put the very notion of scholarly credit into jeopardy, researchers warn.
“It is quite possible that academic researchers have not fully grasped the consequences of uploading data and knowledge to a personal AI model account,” says Luke McDonagh, who studies intellectual-property law at the London School of Economics and Political Science.
In an open letter decrying AI companies’ entry into solving mathematical problems, 25 winners of the Fields Medal — which is often considered mathematics’ equivalent to the Nobel Prize — write that AI tools muddy the ability to give appropriate credit: “As in all creative professions, this raises severe attribution and plagiarism questions.”
Chatbot controversy
The day before OpenAI confirmed rumours that it had solved the Navier–Stokes problem — one of the highest-profile questions in mathematics — one researcher was already raising the alarm. Tristan Buckmaster, a mathematician at New York University in New York City, and his collaborator Levent Alpöge, a mathematician at Harvard University in Cambridge, Massachusetts, had been working on an aspect of the Navier–Stokes problem using tools from OpenAI as well as Anthropic. They were told that OpenAI was preparing to announce that it had solved the problem. Buckmaster wrote on social media that the company had jumped on the problem after hearing about the work by him and Alpöge, and that OpenAI's model could have been learning from their interactions with ChatGPT.
An OpenAI spokesperson told Nature: “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.” The company said that it started working on the problem on 1 September and that it had not seen “any of their work through any means until they released it publicly”.
Buckmaster says he had used OpenAI tools to work on the problem for a year. He told Nature that he had three separate accounts on OpenAI’s ChatGPT, and that only on two had he opted out of the setting that gives permission to the company to use chatbot conversations in the training of its models.
Assuming that the OpenAI solution is independently confirmed, it remains to be seen how the maths community will choose to apportion credit — and who deserves the US$1-million award offered by the Clay Mathematics Institute for completing one of seven Millennium Prize Problems that it selected at the turn of the century.
OpenAI says it has verified its proof using a programming language called Lean. The Clay Mathematics Institute, whose scientific headquarters are in Oxford, UK, says it will consider whether a solution is valid only after the results have been published in a peer-reviewed publication and been further vetted by the community.
Researchers who study the Navier–Stokes equations say that a large part of the credit should go to Buckmaster and Alpöge, and also to Diego Córdoba at the Institute of Mathematical Sciences and Luis Martínez Zoroa at CUNEF University, both in Madrid.
Future of research
How to apportion credit in the age of AI will become increasingly complicated, says Andreas Thom, a mathematician at the Dresden University of Technology in Germany. He wonders whether brainstorming sessions that he held with OpenAI’s ChatGPT tool over the past year or so about the theory of groups, a concept that has pervasive uses across mathematics and physics, might have helped to train the chatbot.
He says he was using a particular strategy to try to construct a type of group called non-sofic — something many mathematicians had long thought impossible. Then in August, OpenAI posted a preprint reporting that it had arrived at the first ever example of such a thing — with a similar strategy to Thom’s. In Thom’s opinion, it is unclear whether credit was given appropriately in this case; OpenAI did not comment directly on this question.
The OpenAI paper correctly references earlier works by him and his collaborators, says Thom. But until late June, Thom had not opted out of training of the models, meaning there is no way of knowing whether the company’s tools used the sessions with him — in addition to his published papers — to help with its work.
It’s a problem if such brainstorming is being used to train AI models but it is not being recognized, he says. If a human mathematician wanted to break into the field of non-sofic groups, they would probably have conversations with specialists in that field, he says, and learn tricks of the trade that are not represented in the written literature. Typically, they would then credit those conversations in the acknowledgments sections of their papers. “If a human had sat in my office and then had written that paper, I would be angry if he had not given credit to our discussions and explanation,” Thom says, although it is not established whether OpenAI's model in fact drew on Thom's conversations.
OpenAI did not provide a direct response as to whether its models did so in this case. But a spokesperson said that it was up to users to decide whether their conversations help improve models, and emphasized that once users have opted out, OpenAI does not use that data to improve its models.
Tutoring through chatbots
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