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From Buckmaster's text: The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route

by dbdr 25d ago

From Buckmaster's text: 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. This is much more than the knowledge than the problem can be solved, it's also the specific, non-obvious approach to solving it. That's much more damning for OpenAI, if confirmed.

Keyframe 25d ago
[flagged]
tristanj 25d ago
That's a stretch. The Luis and Diego paper was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work. 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.
- mishellaneous 25d ago
  > 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 (...)
  - shrx 25d ago
    > "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?
    - mishellaneous 25d ago
      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)
  - golol 25d ago
    >"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.
    - mishellaneous 25d ago
      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
- Davidzheng 25d ago
  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
seeall 25d ago
I want to point out that almost all previous AI discoveries in math were made in almost the same way. The ideas were there in the community, but weren't considered mainstream/worth pushing forward. Read Tao's comments on the unit distance problem, for example (sry I can't find a link right now). 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-conjecture/ https://openai.com/index/model-disproves-discrete-geometry-c...

by dbdr 25d ago

Keyframe 25d ago

[flagged]

tristanj 25d ago

That's a stretch. The Luis and Diego paper was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work. 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.

mishellaneous 25d ago
> 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 (...)
- shrx 25d ago
  > "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?
  - mishellaneous 25d ago
    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)
- golol 25d ago
  >"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.
  - mishellaneous 25d ago
    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
Davidzheng 25d ago
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

seeall 25d ago

I want to point out that almost all previous AI discoveries in math were made in almost the same way. The ideas were there in the community, but weren't considered mainstream/worth pushing forward. Read Tao's comments on the unit distance problem, for example (sry I can't find a link right now). 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-conjecture/ https://openai.com/index/model-disproves-discrete-geometry-c...