alt Hacker NewsThe researchers apparently spend a year or so working on this, and it builds off significant previous work, so it seems like it was a pretty significant amount of work that OpenAI may have trained on
I'd love to see an in depth analysis of how much OpenAI actually did, but I suspect we'll never see that because it would indicate at least some plagiarism which undermines a lot of what OpenAI is putting out in public
The American Mathematical Society credits the Spanish researchers Diego Córdoba and Luis Martínez‑Zoroa with the breakthroughs that eventually led to this solution, and which were published from ~2023 onwards.
This is a good summary:
> In broad outline, the pair’s technique relies on creating an infinite sequence of “layers,” each of which is a non-singular solution to the equation they are studying. (They’ve applied similar techniques to both the Euler and Navier-Stokes equations, as well as to other related systems.) They then combine those solutions in what Martínez-Zoroa calls an “infinite cascade” to produce a new solution. > > That new solution, they showed, contains the desired singularity. However, even though each individual layer relies on a smooth forcing function, combining them together can cause the forcing function to have undesirable mathematical properties. That’s why their solution fell short of satisfying the Millennium Prize criteria. The remaining hurdle was to figure out how to create a similar infinite cascade that resulted not only in a singularity, but also in a smooth forcing function. > > That’s the step that both competing AI groups appear to have had success with.
https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-...
The question is whether OpenAI started out from that published and well known research exclusively, or they also had some insight into the ongoing work of Tristan Buckmaster and Levent Alpöge.
On the one hand, OpenAI have already admitted that they only launched their massive effort after hearing rumours that this particular problem had been solved.
On the other, progress in mathematics research has accelerated significantly over the past months thanks to the availability of newer and more capable AI models. Alpöge himself presented a counterexample to the Jacobian conjecture on July, found with Claude Fable. So if model capability was a bottleneck, that gives credibility to the idea that an even more powerful unreleased model with massive compute would be able to make even faster progress.