> An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.

the post you were replying to quotes Buckmaster specifically denying this: "It is not the direction one arrives at in a few days by giving a model the problem statement."

> And the article states "an insane amount of compute had been used," which implies OpenAI brute-forced their way to a solution. I.e. they searched for every paper published on Navier-Stokes and exhaustively attempted every approach. Such an approach would lead them to a solution.

"implies" is a surprising choice of word here. that's certainly one interpretation of "an insane amount of compute had been used". what came to my mind, considering Buckmaster's statement that the AI would not head down this specific path on its own, is, though, that they prompted it in this specific direction and then used an insane amount of compute. this seems consistent as well with these other statements:

> 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 (...)

>"It is not the direction one arrives at in a few days by giving a model the problem statement."

To be honest, he was referring to routes (c) and (d) to the millenium problem, as far as I understand no more specific. Which is 2/4 routes.

i don't know if i understand what you're saying. but i'm no mathematician. here's the full statement in question once again:

> The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.

so, you're saying that "the direction one arrives at in a few days" is (A) "the route through a smooth force, options c and d in Feffermann's statement of the problem", and no more specific than that, i.e. does not necessarily include (B) "the same path route as Luis and Diego" (quoted from the post i was replying to) (which, as i understand, is a subset of A -- directly from Buckmaster's quote: "the route A is is the route Luis and Diego opened")?

but the post i was replying to claims that "An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work", i.e. that the AI model could independently chose B. but choosing B implies choosing A, since B is a subset of A. and in this case it is irrelevant whether Buckmaster claimed that an AI could not independently choose A or B -- the point which you seem to be contesting.

EDIT: my understanding is that "solving the Navier-Stokes existence and smoothness problem" consists of proving at least 1 of 4 precise statements ("options (a) through (d) of Fefferman's statement of the problem"), and Luis and Diego's work were developments towards a proof of statements (c) and (d), which have been recently further expanded by Alpoge and Buckmaster

I just meant that choosing the same 2 routes out of 4 would not at all be a great coincidence without knowing what Tristan was working on.

if you assume the choice of route is a uniformly distributed random variable, yes. but this assumption does not seem consistent with "Almost nobody else I know of was working on it", from Tristan's quote. nor with "It is not the direction one arrives at in a few days by giving a model the problem statement".

It doesn't really make sense what he said. Everyone expects N-S to have blow-up. If you are going to try to show blow-up, C and D are strictly easier than A and B. So Tristan was not clear about what detail of "route" he is talking about, because what he literally said can not be it.

yeah, it looks like i don't have enough knowledge of this subject to discuss this. but i'd be interested in reading what more knowledgeable people have to say about it -- Tristan's work, how different from others' it was (they claim no one else was following the same path), and how it compares with the AI's

Well, no one arrived in this direction, because no one was sitting and prompting a model. It was 10000 agents working 24/7 for several days, trying millions of different directions.

> "It is not the direction one arrives at in a few days by giving a model the problem statement."

Can they back up this statement somehow?

yes, this is ultimately nothing but a claim.

Buckmaster did also mention, for example, that a team of people was employed to solve the problem, which supports this claim. but that is another claim whose veracity could also be questioned. but at some point we must trust other people, unless we can be satisfied with only believing what we personally see.

(also, IMO, the coincidence of both discoveries in time is pretty suspicious. this one doesn't need you to trust many people i guess)

Please don't say brute forced. It sounds like some form of denial or something. Compute for hard problems drops with models--it just means they threw a huge amount of compute. There's (idk about NS specifically so maybe it's exception) no real way to "brute force" a math proof [ok you can enumerate proofs if you can wait until heat death ]

Sorry for random rant but I don't think these statements help your point