On the Navier–Stokes Millennium Prize Problem

My take:

1. It shows what even this wave of AI can actually do.

2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.

3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.

It's not a meaningful response to the accusations. Any productive new research direction would be expected to lead to a number of different possible proofs of a number of similar problems. (Given their bizarrely compressed timescale here, it's possible that the proofs really are so different it's clear they came independently, and they just didn't have time to come up with that information before hitting publish.)

There's something sinister or crazy good in the article.

OpenAI already has a model that is at the very least twice as smart as Astra.

Oh god.

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used."

One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.