I feel like something is being lost in the drama here.

First of all, there has been published work from Diego Cordoba and Luis Martinez-Zoroa that will be in every training set. It was suggestive of the pathway to solve Navier-Stokes.

Then Tristan Buckmaster and Levent Alpoge built on this work using LLMs from OpenAI and Anthropic. Possibly internal models were used from Anthropic. And of course Anthropic wants to credit for solving the first Millennium Problem just as bad as OpenAI. It seems they were getting close and were aware that they might get to Navier-Stokes.

OpenAI swoops in. At a minimum they are aware that Anthropic has either solved a Millennium problem or is close to it. At a maximum they may have Tristan and Levant’s unpublished proofs of related problems.

They then throw a truly staggering amount of compute at Navier-Stokes. They seem to be aware it is the best candidate problem. And they crack it. They are the first with a verified proof.

So the outcome here is that we have a solved Millennium Problem. It’s not the extremely simple narrative that would be easy to understand, “solve Navier-Stokes make no mistakes.” It was a messy race to finish against two unpublished frontier models, a whole bunch of brilliant mathematicians and enough compute to drain a lake. It’s kind of irrelevant which company got there first. They were both within a few months of being capable. I think the thing to remember here is that without LLMs, I don’t think we would have a proof to Navier-Stokes in hand today.