AI may have just solved a million-dollar math problem. The field will never be the same

Artificial intelligence may have just solved a million-dollar math problem, potentially changing the field forever. A mathematician compared the achievement to the historic chess match between IBM's Deep Blue and Garry Kasparov in 1997. The problem concerns the Navier-Stokes equations, which govern the flow of fluids, from tiny whirlpools to massive storms.

Mathematicians have struggled for centuries to determine if these equations accurately describe reality in every situation or if they occasionally produce aberrant mathematical blips that cannot occur in real fluids. The Clay Mathematics Institute offered a $1 million prize to anyone who can solve this problem. Two mathematicians, Diego Córdoba and Luis Martínez-Zorúa, discovered a potential method to approach the issue by focusing on a seemingly insignificant part of the equations, known as "forcing."

Mathematician Tristan Buckmaster continued this work with help from Anthropic's research team. However, the method was slow until Buckmaster and his colleague used large language models from OpenAI's rival company, Anthropic, to analyze mathematical possibilities. Progress accelerated in August when they used their method to prove that the Euler equations, a simplified version of the Navier-Stokes equations, could produce such mathematical blips.

Buckmaster alleged that OpenAI, after learning about their work, quickly focused on the forcing method and used its internal model to further prove the Navier-Stokes equations blow up. Buckmaster claimed that OpenAI offered sole authorship for the result, excluding his collaborator. He threatened to reveal the situation publicly, but OpenAI denied the allegations.