Openai’s AI agents solved a math problem that has been a mystery for 90 years in 88 hours. Oh, and it comes with beef.
The seven millennium prize problems were established by the clay math institute to celebrate mathematics in the new millennium. The directors at the institute put up a total of 7 million dollars’ worth of prize money, one million dollars being assigned to each impossible math problem being solved. One of the prize problems was recently settled by 10,000 of OpenAI’s advanced AI Agents: the navier-stokes problem.
Put simply, navier-stokes equations model fluid motion. Because gases and liquids can not be strictly defined by Newtonian equations, Euler came up with a different equation for expressing fluid motion, which was then refined by two mathematicians named Navier and Stokes, ultimately becoming the Navier-Stokes equation we know today. However, for a long time, there were certain components of the Navier Stokes equations that remained a mystery, such as whether a smooth solution exists for all time, and whether there is a point where the solution shoots up to infinity when a smooth external force is applied. That part-the “whether there is a point where the solution shoots up to infinity when a smooth external force is applied” is what OpenAI’s models solved.
Although the Navier Stokes equations do have limitations in scope, such as only considering incompressible liquids (liquids that do not change in density), it has been widely used by engineers and scientists to model fluid motion. The equation is particularly important because the alternative to this method would be modeling the movement of particles in the fluid one by one, which would make most computers lose their sanity.
The problem arose when a mathematician named Tristan Buckmaster released a statement suspecting that the work he and mathematician Levent Alpoge had done using OpenAI’s codex had leaked into the OpenAI agents that solved the problem. The statement sprawled into a massive debate between OpenAI and the two mathematicians on the ownership of the proof. Buckmaster and Alpoge had taken on the work of Diego Córdoba and Luis Martínez-Zoroa to solve the forced version (the problem where the force is applied) of the navier-stokes problem. As they were working on the problem and making real progress, there was a rumor that Anthropic, Alpoge’s employer and OpenAI’s direct competitor, had come up with a solution to a major mathematical problem. OpenAI’s attempt to solve the problem was chronologically right after the rumor was spread, and it had the same niche angle (the version of the problem with applied force) that Buckmaster and Alpoge had been working on.
Almost everybody attempting this problem were attempting the no-force version, which was why Buckmaster raised the possibility of his work getting leaked. It was too much of a coincidence that the AI models came to attempt that specific angle on its own. This led to an ownership dispute, which was amplified by the fact that Alpoge worked for a rivaling company.
Besides problems on the ownership of the resolution of the problem, some researchers have raised concerns on the automation of the process of proof generation. Terrence Tao, a renowned mathematician, expressed disapproval on the “flattening of the difficulty landscape”. Back in the good ol’ days when humans had to think everything through, they could develop a comprehensive understanding of the field, often developing new questions worth exploring. Automated tools like AI models, however, tend to over-optimize the process for finding the answer, which could cause a scarcity of “problems worth exploring”. He pointed out that the Anthropic rumor incident demonstrated this. Even something as uncertain as a rumor can trigger a mass deployment of automated tools in a race to get the answer as fast as possible.
The nature of academia is changing quickly in this AI-dominated world. Debates about ownership and the flattening of research are on the table. It is unclear whether the traditions that are deeply embedded in academia will still hold against what can flatten in 88 hours that once took a lifetime.
By. Seojin Yun