New York University mathematician Tristan Buckmaster published evidence on Monday suggesting that a simplified version of the Navier–Stokes equations can break down—an important development in the search to solve one of the Clay Mathematics Institute’s Millennium Prize Problems. Buckmaster and Alpöge reportedly spent nearly a year investigating the problem with publicly available models from OpenAI and Anthropic.
OpenAI has now released what it describes as a proof that the full Navier–Stokes equations can also break down. The work was reportedly produced with the help of an internal artificial intelligence model released just last week, which the company says significantly outperforms its already capable Astra model. OpenAI has stated that it does not plan to pursue the $1 million prize associated with solving the problem.
Although the mathematical claims are significant, much of the attention has focused on questions about how the research was produced and who deserves credit. In a statement supported by evidence, Buckmaster described his interactions with OpenAI employees after learning about the company’s work.
According to Buckmaster, OpenAI employees presented him with two options: he and Alpöge could publish their research, after which OpenAI would release its Navier–Stokes solution the following day, or Buckmaster could collaborate with OpenAI on a paper that would exclude Alpöge because of his affiliation with Anthropic, one of OpenAI’s major competitors. Buckmaster also said he asked whether OpenAI’s AI agents had accessed records of the work he and Alpöge conducted with OpenAI models. He said the employees denied having access, although OpenAI has not publicly explained whether those conversations were used to train its models. MIT Technology Review reported that Buckmaster did not respond to requests for comment before publication.
The allegations raise questions about whether OpenAI’s models may have benefited from Buckmaster and Alpöge’s research. That possibility appears plausible because both sets of work use an approach to the Navier–Stokes problem pioneered by mathematicians Diego Córdoba and Luis Martínez-Zoroa. Javier Gómez Serrano, a mathematics professor at Brown University, said the method is one of several promising strategies for addressing the Navier–Stokes equations.
It remains possible that the two teams independently selected the same approach. However, the similarities also leave open the possibility that Buckmaster and Alpöge’s work influenced OpenAI’s results. Mark Chen, OpenAI’s chief research officer, again denied during a press conference that the company’s employees or AI agents had access to the researchers’ records. Still, past incidents—including revelations surrounding the Hugging Face hack—have raised concerns about how fully OpenAI understands and monitors the actions of its AI systems.
If OpenAI’s models were trained on Buckmaster and Alpöge’s research, or if its agents accessed that work directly, the company’s failure to establish what happened and properly credit the researchers would raise serious concerns about transparency and attribution. At the same time, the controversy may offer an important insight for mathematicians and AI researchers.
Researchers have long identified “research preferences”—the ability to select promising questions, methods, and directions—as one of the biggest challenges for artificial intelligence in science and mathematics. If OpenAI’s system independently chose the Córdoba–Martínez-Zoroa approach, that would still highlight the importance of human mathematical judgment. Buckmaster and Alpöge had already identified the same promising direction, suggesting that human research insight may have played a crucial role in advancing AI-assisted work on the Navier–Stokes Millennium Problem.
Source: www.technologyreview.com