And simply knowing a problem can be solved is half the battle.
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.
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.
There is not enough information at this time to reach a conclusion. The best option is to wait for statements from both sides, then reevaluate.
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 (...)
Can they back up this statement somehow?
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)
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.
> 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
Sorry for random rant but I don't think these statements help your point
OpenAI said there [1]: > The method by which the problem was solved is also notable. The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question.
[1] https://openai.com/index/model-disproves-discrete-geometry-c...
Have you done any mathematical research? If not, then no, knowing that a problem is solvable is not “half the battle”.
Homework problems are all designed to be solvable, yet they can vary greatly in difficulty. Research mathematics is even more extreme, because, unlike with homework, you don’t know that it is solvable with the extant mathematics, and you might need to invent new maths.
If not for the rumors that A/ had already solved NS, OAI would likely never have pursued solving the problem with such fervour. The rumors drove OAI to assemble an entire team to crack this.