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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#131

Post by emp17344 »

naasking wrote: post #101
raincole wrote: post #86

Earlier quoted context omitted.

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. "People" are just misinformed and keep…

> The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to O…

You can expect the OpenAI defenders to be out in full force here.

Re: On the Navier–Stokes Millennium Prize Problem

#132

Post by contemporary343 »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

"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."

- This, from Tristan Buckmaster's writeup yesterday, indicates to me that there was more than incidental inspiration from Alpoge and Buckmaster.

Re: On the Navier–Stokes Millennium Prize Problem

#133

Post by mlcrypto »

Yajirobe wrote: post #124
peri-cl wrote: post #58

Earlier quoted context omitted.

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

Why would Anthropic employee even use OpenAI's models? Cross-polination would have been avoided

They should have used a zero data retention agreement, user error

Re: On the Navier–Stokes Millennium Prize Problem

#134

Post by [deleted] »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#136

Post by simianwords »

aizk wrote: post #52

People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon

https://news.ycombinator.com/item?id=38433655

> Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief that an LLM can't do that, and will never be able to. LLMs can barely solve elementary school math problems reliably.

https://news.ycombinator.com/item?id=42331654

> An LLM is like a well read college student with a nearly photographic memory that sometimes mixes things up. It's great for bouncing ideas off of and getting feedback on them. And yeah, it might product "novel ideas" by mixing and matching existing ideas, but LLMs will never create truly novel ideas. Not in their current form.

The paper didn't really answer the question sadly: their conclusion was just that humans rate LLM answers as more novel than human ones, but less feasible.

https://news.ycombinator.com/item?id=41522605

> Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.

https://news.ycombinator.com/item?id=38435909

> LLMs cannot reason or use mathematics - in a way, they don't know what they are talking about. Why would such technology lead to superhuman smarts?

https://news.ycombinator.com/item?id=35752293

> But still, the questions in that test are "solved" in the sense of "I can take a dictionary and answers these questions with full certainty". Beyond established knowledge LLMs are monkeys with typewriters, at best.

> I agree but I have tried many times to intersect two ideas with a LLM that would be novel and the LLM can not do this at all. We shouldn't expect the stochastic parrot to be able to do this though and it is unfair to the stochastic parrot.

> It is like expecting a real parrot to say words it has never heard before.

> No one asks that of a real parrot because we don't anthropomorphize a real parrot like we do the LLM

https://news.ycombinator.com/item?id=41525962

Re: On the Navier–Stokes Millennium Prize Problem

#137

Post by cmiles8 »

>>“we cannot rule out that de-identified data derived from their usage of our products helped improve our models”

Other simpler words for this sort of thing are “IP leak.”

There’s some quite concerning issues burried in this rah rah PR post that seems like potentially the real story here.

Much more clarity is needed on what happened here beyond this eh, some strange stuff could have happened comment.

Another way of reading this is never give these models anything that’s not already public knowledge as otherwise OpenAI is admitting it could, potentially, steal your IP or idea. Thats quite scary for anyone in the business of IP generation and explains why the maths community seems quite upset today.

Feeding it your paper and asking for help (even just editing and grammar) now looks like a terrible idea.

Re: On the Navier–Stokes Millennium Prize Problem

#138

Post by rfgplk »

imbusy111 wrote: post #83
Reubend wrote: post #66

It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.

I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.

Skill issue. Also lean is meant to be executed, not read.

Re: On the Navier–Stokes Millennium Prize Problem

#139

Post by achierius »

raincole wrote: post #86
echelon wrote: post #53

Earlier quoted context omitted.

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. "People" are just misinformed and keep…

Have you read the actual statement https://cims.nyu.edu/~tristanb/statement.pdf ?

> I should say here why I interpreted their statement the way I did, the in- terpretation I will discuss below. 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.

...

> I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. > I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

It's not a direct accusation, but it's not far off.

You shouldn't accuse other people of spreading misinformation when you haven't read the actual sources in question, it's possible that they might know more than you.

Re: On the Navier–Stokes Millennium Prize Problem

#140

Post by causal »

lambda wrote: post #130
peri-cl wrote: post #58

Earlier quoted context omitted.

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

Good chance their whole training pipeline is vibe coded so yah they probably don't actually know.
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