I was and have been sick for the last 2-3 days. I didn’t make the cut in that hackathon even though I did all the work for my team and thought that my presentation was good. But none of that matters right now. I am standing at the gates of literal history here. There are going to be two worlds, at least for me, in my opinion, one pre Navier-Stokes being solved, and one post.
Yes. I can’t believe I am writing this, but Navier-Stokes has been solved. I shouldn’t be here, I should be with the discord guys seeing what they think about all of this. This is unprecedented, and this is insane. I don’t know the math, I only know so less about what this problem is about - but these conditions are just definitive of history being made.
This discovery is chilling in a sense. I read Simon Willison’s thoughts about it, and he’s right - OpenAI’s response to the scrutiny behind this is chilling. Here’s what they have to say:
We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
Well in short two researchers (Tristan Buckmaster of NYU and Levent Alpöge of Anthropic) were working on related problems for almost a year and had used Claude and Codex and then had a breakthrough on August 15th. Again, to summarise this drama this rumor spread that Anthropic had resolved a major open math problem and the researchers realised that OpenAI had been working on similar problems during that time. The OpenAI team offered to wait for Tristan to publish or have him author a paper about their result but they were NOT going to include Levent, since he’s from Anthropic.
What’s most scary is that quote up there:
While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
This is insane. Even the scent of a problem as big as Navier-Stokes was enough for OpenAI to throw $15 million worth of compute at it for 88 hours with the latest and greatest models- no resources an individual researcher can afford - and publish a paper even before the researchers who were originally working on this problem opened their fucking LateX (or Typst) editor.
I read Terry Tao’s thoughts on it too. In my read he’s essentially saying that maybe some connections could’ve been deciphered from problems like these, which would’ve helped in other areas of mathematics. This is so NOT uncommon! This happens all the time in science - you try to solve one problem and while you’re in the process you accidentally stumble upon some hint for some other problem. Using LLMs to bruteforce that process of discovery - is that even okay? Can LLMs decipher connections as well as humans can? What if they’re not able to “mine” a problem completely, and are just bruteforced into finding a solution for the current problem at hand?
Finding good problems is becoming harder. This is history being made. We are most likely standing at the gates of the “singularity”, as Hotz likes to call it. I don’t know how to feel about any of this. This should NOT be how science works, where a researcher is punished for even getting a rumor out that he’s found a new approach to one of the hardest problems in our current models of the universe.
We need to commoditize compute. Or this is going to be a very unfair world that we’re headed into.
Ending with a quote from Tao himself:
In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained.
While it may be technically infeasible to completely prohibit the use of automated tools to perform indiscriminate solution extraction, I believe that we can still designate many classes of problems as being desirous of a careful analysis that not only solves the problem, but identifies insights from the solution process, and learn more about the difficulty landscape for nearby problems, and for which raw solutions without such analysis would be of negligible or even negative value for these purposes. This is analogous to how a modern food donation drive no longer accepts arbitrary contributions even when they are verified to be technically edible, but instead maintains explicit and socially accepted standards on what level of contributions are actually sought.