OpenAI, the developer of the ChatGPT chatbot, announced that it has successfully solved the Navier-Stokes problem, one of seven mathematical problems considered among the greatest mysteries in mathematics.
The company spent millions of dollars on this endeavor. But the announcement quickly sparked controversy, after mathematician Tristan Packmaster, a professor at New York University, accused OpenAI of accelerating its work on the problem after learning that he and another researcher from rival company Anthropic were about to announce their own breakthrough.
We're sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
Backmaster raised additional concerns about storing their ongoing research in OpenAI's Codex model, which is used to write computer programs, potentially making the work visible to the OpenAI team.
However, Backmaster explained that he does not know what the OpenAI model did or how it did it, nor does he know if their data was used, stressing that he is not accusing anyone of anything.
At a press conference on Tuesday, researcher Sebastian Popick denied that the company used the researchers' work or accessed shared materials with OpenAI servers, admitting that the company could not rule out that data from the researchers' use of their products "helped improve our models."
OpenAI said it tackled the Navier-Stokes dilemma using a more robust internal system than the latest GPT-6 Astra model, with about 10,000 AI agents (systems that perform tasks independently) working on the problem simultaneously, and arriving at a solution in 88 hours.
The researchers wrote in a blog post: "Our main goal is to enable scientists to develop research and technology that benefits all of humanity, and we believe it is important to inform the world about the pace of progress in artificial intelligence and what can be expected from future models."
The Navier-Stokes problem is a set of differential equations developed in the 19th century (1822) by the French scientist Claude-Louis Navier and the Irish scientist George Gabriel Stokes. It is used to describe the motion of fluids such as water, air, and oil. These equations have applications in numerous vital fields, from weather forecasting and the design of aircraft and ships to the study of ocean currents and understanding blood flow in blood vessels.
The challenge lies in the fact that scientists don't know if the Navier-Stokes equations hold true under all conditions, or if they might break down and produce infinite speeds. This very challenge is known as the "Navier-Stokes dilemma," which aims to prove the existence of a smooth and permanent solution to the equations. However, OpenAI's solution indicates that the equations can indeed break down under certain conditions, producing infinite speeds in what is known as the "burst" phenomenon. It took the GPT-6 Astra model approximately 17 hours to verify this
Mathematicians who solve any of the seven Millennium Problems receive a $1 million prize from the Clay Mathematics Institute, but OpenAI, which is preparing for a public offering that could value it at up to $1 trillion, has said it does not intend to claim the prize.
This breach comes at a time when OpenAI is seeking to improve its image following a period of concerns about the security of its technologies, particularly after a breach last July of an external platform during a security test, which prompted US senators last week to call for a permanent ban on the development of "super-intelligent" artificial intelligence systems that outperform humans in all cognitive tasks.
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