About OpenAI's Navier–Stokes Millennium Prize Problem work




fractal based turbulent flow i put at github.com/equational/fractalturbulence2d3d

Some quick remarks on OpenAI's Navier–Stokes Millennium Prize Problem work:
  1. ML does not do mathematics, it does computations that result in mathematical properties. This may seem a pedantic thing to write, but it is very different. One way to describe the difference is that OpenAI discovered a single mathematical fact. Yet now this fact needs to be connected into a broader mathematical space to become true mathematics.
  2. While some mathematicians deny it, innovation is much a search effort (I wrote about it here). So when Tristan Buckmaster writes: "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer", he is highlighting that OpenAI's search may have obtained a hint that came from himself and Levent Alpoege. Most likely they naively clicked on the little dialog that explained that OpenAI could use distilled knowledge from their input. From a standard discovery claim, this little uncertainty sadly much hurts OpenAI's achievement.
  3. The work is outstanding! The reality is that the real world does not care about math, it cares about math being useful! So while I feel the chagrin of the mathematicians that feel the alien entity shooting truths into their space, this does not change that from a real world perspective the OpenAI achievement is monumental. In effect, out of thin air, they have pulled out a mathematical truth. A truth well above the current achievement of mathematicians. And while that hurts our mathematical souls, it is also highly useful to apply into other contexts.
I finish with an anecdote:  years ago I was responsible for the math in a derivative market making system. In this context I hired people fresh out of their PhD to write applied math for me. And one thing I noted was that it took them at least a year to switch their understanding from "math is real" to "the world is real, math just approximates it". In the LLM context, it is good to remember: the world is real, LLMs just approximate it! 

All original content copyright James Litsios, 2026.