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Navier-Stokes Announcement

claymath.org

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Re: Navier-Stokes Announcement

#231

Post by program_whiz »

jacobrussell wrote: post #167
jgalt212 wrote: post #163

Earlier quoted context omitted.

Not including salaries, OpenAI spend $20MM to make $1MM. Very on-brand for a start-up.

I don’t think solving a millennium prize problem can be reduced to some DoorDash economics of “spent Y to make X.” What if it took someone their entire professional career to solve one of these problems, would it not be worth it by the same logic?

Surprisingly this is actually rather fitting in terms of time scale. When you consider it took ~10,000 agents 88 hours, or 880,000 hours to solve. That's 14.5 years in agent time of continuous 365/24/7 processing. Of course, humans solve things much more efficiently (and didn't also need the massive pre-training of every expert on the planet for 1,000,000,000 human years equivalent). But yeah, human researchers can solve a problem like this in a decade or so, while sleeping, teaching, traveling, and taking breaks, only working a few hours a day on the idea.

Re: Navier-Stokes Announcement

#232

Post by MarkusQ »

soperj wrote: post #184
c7b wrote: post #93

Earlier quoted context omitted.

Even funnier that it wouldn't even be the first time that happens: https://en.wikipedia.org/wiki/Grigori_Perelman

He did it because he had principals. OpenAI the opposite.

More likely it's because a million dollars one way or the other won't make a difference in the hole they are digging / mountain they are building.

Re: Navier-Stokes Announcement

#233

Post by famouswaffles »

HarHarVeryFunny wrote: post #203
famouswaffles wrote: post #197

Earlier quoted context omitted.

If you're in OpenAI's position, the PR from the group you're disrupting is rarely relevant. People from the outside will (correctly or not) look at this as "Mathematicians don't want OpenAI to solve problems to keep their status/jobs", and you'll have as much sympathy from them as every other replaced profession in human history - very little to none. Unlike AlphaFold, this technology has the potential to wholesale r…

Most research mathematicians are employed as academics, and it's hard to see universities replacing teaching staff with AI even if that were possible. IMO giving a hypothetical AlphaMath to mathematicians, the same way Google gave AlphaFold to research chemists/biologists, would have resulted in far better PR, and the profit opportunity of attempting to replace the jobs of either research group is minimal. It's downr…

>Most research mathematicians are employed as academics, and it's hard to see universities replacing teaching staff with AI even if that were possible.

If universities come to only need research mathematicians for teaching ability, then it would still gut the profession. You would presumably need far fewer of them for their research ability, and hopefully hire more people who can actually teach. It's strange that you don't see that as a threat to the profession. Lots of research mathematicians would lose their jobs even in this scenario.

>IMO giving a hypothetical AlphaMath to mathematicians, the same way Google gave AlphaFold to research chemists/biologists, would have resulted in far better PR

GPT-N isn't AlphaFold. I'm telling you AlphaFold is a bad analogy! AlphaFold has superhuman capabilities at one specialized subproblem - protein-structure prediction - embedded in a much larger biology/drug discovery pipeline. It doesn't replace the biologist or drug researcher, it just gives them a better instrument, and if you're not in the relevant professions it's essentially useless to you.

GPT-N is general purpose intelligence machine that can increasingly do chunks of work you would otherwise employ the mathematician or software developer to do.

Shanmu Jin is a perfect demonstration. A neurosurgery resident, not a research mathematician, who encountered the Crouzeix conjecture through his transcranial ultrasound research and used GPT-5.6 Sol to solve it (20+ year old longstanding problem).

In the AlphaFold story, the biologist gets a powerful new tool. In the Jin story, someone who isn't a mathematician can obtain research level mathematics and incorporate it into their research/code/business whatever without talking to a single human.

You're asking why they don't market GPT as "AlphaFold for Mathematicians". They don't because it's not.

>It's downright bizarre the way companies like Anthropic (primarily), and to a lesser extent OpenAI and anyone else, are themselves pushing the narrative of this tech may kill you, will take all your jobs, etc.

It's not that bizarre. It only seems strange if you think it's all a facade, "marketing" or whatever nonsense HN is convinced of. These are people who believe very strongly in what they are doing and in the potential of it. For these people, what you are asking them to do is actually incredibly slimy. And it might win some brownie points, but not for long.

Re: Navier-Stokes Announcement

#234

Post by qlte »

swyx wrote: post #2

sounds like they are providing notice that the clock has started on affirming the solution, that it IS presumptively solved, but that they are not commenting on the credit dispute nor the fields medalists open letter. seems appropriate.

Per the rules in their link, the clock starts after publication in a qualifying peer-reviewed journal so, no, I don't think that's the reason.

https://www.claymath.org/wp-content/uploads/2022/03/millenni...

I'm sure they've been getting a lot of press inquiries and don't want anyone to misinterpret their silence as refusing to engage with OpenAI's solution.

Now they have a statement on the record that can be quoted with a gentle reminder of the qualifying criteria (which makes clear they have nothing to evaluate either way yet).

Also to emphasize the original optimistic ideals of the prizes and their role as neutral arbiters who aren't going to litigate anything outside the scope of the prize itself.

Re: Navier-Stokes Announcement

#235

Post by spott »

MarkusQ wrote: post #232
soperj wrote: post #184

Earlier quoted context omitted.

He did it because he had principals. OpenAI the opposite.

More likely it's because a million dollars one way or the other won't make a difference in the hole they are digging / mountain they are building.

It likely cost them more than a million in compute to solve it…

Re: Navier-Stokes Announcement

#236

Post by drxzcl »

famouswaffles wrote: post #177
fragmede wrote: post #87

Earlier quoted context omitted.

No it isn't. Best and worst and ill-defined anyway but the chess ELO score of various LLMs has fluctuated up and down, it's not been montonically increasing. What is the best answer to "how do I make cocaine"? The models are getting larger, with more compute and RAM backing them, but that doesn't automatically make them better if you don't define how you're measuring better-ness.

None of the frontier labs care about Chess as it's already a solved problem. If they did, the models would be much better. It's really not that hard. Google has a paper on grandmaster level chess without search from transformers. Better obviously means better, like how they became better than they were 6 months and a year ago.

Chess is not solved in any meaningful sense of the term. Computers have been better than humans since the 90s, but better chess programs are released all the time.

Re: Navier-Stokes Announcement

#237

Post by syncsynchalt »

auggierose wrote: post #37
adastra22 wrote: post #31

Earlier quoted context omitted.

Publish in academic language means accepted peer-reviewed paper.

Accepted by whom? Peer-reviewed by whom? I guess these little questions are what this article is really about.

Presumably the organization giving away the million dollars is the arbiter of that question.

Re: Navier-Stokes Announcement

#238

Post by avs733 »

Aissen wrote: post #219
eru wrote: post #59

Earlier quoted context omitted.

I'm not sure it actually makes a difference. OpenAI doesn't care about the million dollars in any case. And the judgement that they did it is independent of whether the Clay people agree: you can make up your own mind and so can everyone else. Though it would be funny if no one ever bothers publishing the result in an appropriate journal, and thus the prize technically can never be claimed.

> And the judgement that they did it is independent of whether the Clay people agree: you can make up your own mind and so can everyone else. No I cannot, and I'd argue most people can't either. We rely on mathematicians, peer review, and letting the scientific process run its course.

Can't and shouldn't are at odds here.

Many people, see prior conversation on HN, have already decided that AI solved it. The standards of reasoning and rigor in academia are complex enough that we all argue over them and harumph as we epistemically trespass on each other's domains.

The public, really humans if care for Herbert Simon, are much more apt to evaluate knowledge emotionally and by other standards. We may see them as wrong but standards only matter in context. The NYT, HN, and Annals of Mathematics will always have different standards of truth.

Re: Navier-Stokes Announcement

#239

Post by pwdisswordfishq »

soperj wrote: post #184
c7b wrote: post #93

Earlier quoted context omitted.

Even funnier that it wouldn't even be the first time that happens: https://en.wikipedia.org/wiki/Grigori_Perelman

He did it because he had principals. OpenAI the opposite.

He had principals, while OpenAI had agents?

Re: Navier-Stokes Announcement

#240

Post by mpardalos »

soerxpso wrote: post #223
Aissen wrote: post #219

Earlier quoted context omitted.

> And the judgement that they did it is independent of whether the Clay people agree: you can make up your own mind and so can everyone else. No I cannot, and I'd argue most people can't either. We rely on mathematicians, peer review, and letting the scientific process run its course.

It's formalized in Lean, isn't it? Do you also rely on a community of C++ experts to tell you whether a program compiles or not?

Yes, but there's still the possibility that it's either exploiting a bug in Lean, or that the theorem statement is not set up correctly (i.e. it's actually proved a different theorem).

My understanding is that the theorem statement is quite simple, so i guess the latter is not very likely, but the former is very much a possibility in a proof this large, and it will take some human eyeballs to go over it before convincing mathematicians.

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