Did OpenAI solve the wrong Navier-Stokes problem?

OpenAI claimed a solution to the Navier-Stokes problem, one of the most significant unsolved mathematical issues, earning a $1 million prize from the Clay Mathematics Institute. However, a new controversy has emerged regarding whether OpenAI solved the correct Navier-Stokes problem. The AI-generated proof uses a variant of the problem that many experts argue is disconnected from reality and therefore less interesting.

In fact, a group of three mathematicians recently posted a proof showing that OpenAI's method cannot be extended to solve the full problem. The Navier-Stokes equations describe fluid flow, but mathematicians question their reliability, particularly when it comes to "blowing up," or causing infinite velocities at certain points. The problem involves whether the equations can ever blow up, which would be impossible in the real world.

Some experts focus on a specific piece of the equations, where an external force like gravity affects fluid movement. Mathematician Diego Córdoba and his colleague developed a method to create a specific external force that could trigger a blowup. OpenAI finished the job less than a day later, leading to a heated dispute among the mathematicians.

However, a new study released last Thursday shows that OpenAI's method cannot work without a contrived equation for the force, which is unlike anything that could occur in the real world. This result does not answer the Navier-Stokes problem that mathematicians care about and may even support the idea that the equations can blow up only with an external force.

The Clay Institute's original problem statement, from 2000, allows solutions to use external forces like OpenAI's, which has raised questions about the problem's formulation.