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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#301

Post by charm137 »

colinhb wrote: post #122
dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!

Progress in humanity's knowledge now has to play second fiddle to narrow corporate interests as IPO timings near (both of which wouldn't exist anyway if generations of mathematicians hadn't paved the way for AIs to become as good as they have).

Re: On the Navier–Stokes Millennium Prize Problem

#302

Post by mlsu »

munificent wrote: post #217
stefap2 wrote: post #180

Earlier quoted context omitted.

This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and…

> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.

It seems like there were a couple of human mathematicians that were higher on the 'solving complex problems ladder' than this machine.

Re: On the Navier–Stokes Millennium Prize Problem

#303

Post by dgellow »

apical_dendrite wrote: post #271
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Their own tweets are also pretty eyebrow-raising: > One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Why would you offer another researcher the lead authorship on your g…

And why cannot they have someone associated with Anthropic as co-author? That’s not obvious at all. For sure they would prefer to be the only ones, but it’s pretty standard to have co-authors from different companies, even if they are technically competitors. What is inappropriate about it?

Re: On the Navier–Stokes Millennium Prize Problem

#304

Post by hkmaxpro »

colinhb wrote: post #122
dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof.

https://x.com/sama/status/2097385167002415140

https://x.com/SebastienBubeck/status/2097379411691516310

A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

Re: On the Navier–Stokes Millennium Prize Problem

#305

Post by kzrdude »

stabbles wrote: post #84
jgbuddy wrote: post #63

Here's the formalization / lean verification: https://github.com/openai/NavierStokesAndEuler

341k lines of lean without comments

The construction is that there is one file you need read and verify, the challenge file. If you've verified that file and trust that your lean compiler works correctly, the proof will be correct.

That file should be https://github.com/openai/NavierStokesAndEuler/blob/main/Com... in this case (286 lines).

Re: On the Navier–Stokes Millennium Prize Problem

#306

Post by 20k »

raincole wrote: post #144
applicative wrote: post #93

Earlier quoted context omitted.

This is the end of OpenAI

This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.

Are you joking? This is evidence that OpenAI is committing plagiarism en masse of researchers private work and threatening them into staying quiet to re-present their results as their own. This would be one of the largest scandals of all time

Re: On the Navier–Stokes Millennium Prize Problem

#307

Post by tedsanders »

hexomancer wrote: post #222
tedsanders wrote: post #181

Earlier quoted context omitted.

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

So you definitely did train on their data, you just think it is unlikely that it impacted the final model significantly?

I have no idea if their data was trained on. For example, if they used ChatGPT, asked a math question, and clicked the thumbs up button, that could have provided a small reward signal. I highly doubt this sort of feedback made a difference to a problem like Navier-Stokes, but it's not something that's feasible for us to prove one way or the other.

Edit: Also, if they opted out of training, then we didn't train on it.

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