I find this to be a mean and misguided post. To suggest that Victor Taelin does not know about formal methods. As I understand, he is trying to do something genuinely new and interesting. And he is transparent about his work, which he then gets hounded for. A shame.
It would be weird to stand in line for throwing shit at someone you don't know anything about, and believing that the first guy throwing shit has an actual reason to do so.
There are countless people with essentially no domain knowledge to speak of after working on the domain for a decade.
I have no idea how the original authors competency is, I know nothing about them.
There is however a strong correlation between people being influencers and kinda mediocre at what they're an influencer in - which is frankly understandable, because a large part of their skillset is usually more towards attracting an audience and making the topic interesting.
Usually the true domain experts rarely interface with the public beyond their professional capacity.
What has Victor Taelin made which is any way comparable to Linus Torvalds? I'm not saying it's impossible to be a well-known expert with a shitty google scholar. I'm just not seeing any evidence at all in Taelin's case. He doesn't even have a wikipedia page!
I found the post offputting because he is insinuating a few things about the author which are clearly untrue (eg, unfamiliar with the formal verification landscape) and he's using this untrue speculation as evidence of the dangers of vibe coding. Even the edit where he says swap it out with a hypothetical person who fits the description - it's still leaving in the untrue claims about the author.
It doesn't seem unreasonable to think it mean if I were to make up speculative negative assumptions about you which undermined something you've been working hard on for a long period of time.
I know nothing about the author, I'm just watching this whole spectacle unfold.
It is mean for the last point I mentioned: Taelin is very transpparent about his work which makes it easy to attack him. And what for? This post is not even a proper criticism of Bend 2, it is just trying to paint some story that Taelim is a vinecoder who does not know what he is doing, based on no evidence. If he was not transparent it would not even be known that LLMs have been used.
Because this shitty blogs' author just called someone "vibe-coding a language with no knowledge about the field" who is literally working in that very field for a decade, long predating LLMs, with numerous high-profile works.
You are on the wrong side of this whole discussion, there is only one people here who needs calling out and it's not Bend's author.
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
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
In legal writing, an inline footnote begins with the word "see" in italics, e.g.,"football-related prayer in public schools is now permitted,see,Kennedy v. Bremerton School Dist., 597 U.S.507 (2022)." It's just as easy to make this a footnote but some judges have objected to "excessive" footnotes in legal submissions. Keeping them inline avoids this criticism.
ps On another note, AI legal hallucinations are a solved computing problem. Either a cite or case is contained in the closed universe of materials or it isn't--a simple binary question. Problem is, thos with control of the materials, starting with 1 Dallas (which predates the United States) won't share the list with AI companies.
pps This forum deletes unicode. The word see was gobbled from the original text.
I did not have the impression the proof uses a surprising and novel contribution of fields. I think the proof uses standard application techniques of algebraic number theory towards discrete geometry. If you have a quote substantiating what you said I would be curious.
I know these articles write that it used deep algebraic number theory techniques, which is true, but it may also just be the standard in the field.
You are believing a very unlikely scenario. I think the reason is that you have been convinced of a claim which is unlikely and indeed not true. That is:
>the model seems so capable at doing things like refuting fundamental theorems of mathematics
That is not true and a complete misrepresentation of recent progress of AI in math. It is therefore not necessary to believe the conspiracy theory you described in order to explain recent progress of AI in math.
You should believe that the proof works at least as much as any ither paper in mathematics. The proof has been scrutinized by experts and simplified and improved. If you don't believe that then I'm sorry but you are deluding yourself.
