Tuesday, September 22, 2026

AI mathematical proof not without its detractors

OpenAI has solved one of the thorniest mathematical problems still left unsolved. And not everyone is happy about it.

The Navier-Stokes Problem was one of the $1 million Millennium Prize Problems established by the Clay Mathematics Institute in 2000. Without going into too much technical detail that would be way above my pay-grade anyway, the problem concerns a set of equations used to describe the flow of fluids. While the equations are already in regular use in everyday applications in physics and engineering, scientists don't really understand how or why they work, knowledge that would allow them to be used much more extensively in a wider range of applications. In order to do that, they need to understand scenarios where the equations break down or stop working, and that is the essence of the Navier-Stokes Problem.

Some scientists have welcomed the AI proof and see it as the start of a new golden age of mathematical advances. Others are a bit nonplussed that, while the proof is generally considered to be correct, the 166-page manucript is written in such opaque and obscure terms that no-one really actually understands it. It may take months or years more work to interpret it in a way that humans can understand and actually use. "The paper is not written for humans", as one mathematician put it. "It's a terribly written paper", says another. "Virtually unreadable", bemoans another.

But it gets murkier. Two mathematicians claim they were getting very close to a proof, and that the OpenAI proof uses their preparatory work. They accuse OpenAI of rushing out a muddled and poorly-argued paper in order to steal the accolades. 

Well, it wouldn't be AI if it weren't controversial, right?

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