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Navier-Stokes Announcement

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Re: Navier-Stokes Announcement

#171

Post by rramadass »

Panzer04 wrote: post #139
Tanjreeve wrote: post #124

Earlier quoted context omitted.

I present to you my new theorem as follows: If 1 == 3 then 3 == 3 ---- This statement is 100% logically coherent internally. But it also doesn't matter because we know that 1 does not equal 3 so this proof is completely pointless. I could also say 3 == 5 and it would still be logically sound but completely useless information.

For a laymen, I don't follow this. Are you proving for some arbitrary definition of == that isn't what we commonly consider the definition? How is it logically coherent? You mean only in the sense that you say it is and you haven't provided any rules to disprove it?

It is just the definition of "Logical Implication for Material Conditional" and its truth table; see Material Conditional - https://en.wikipedia.org/wiki/Material_conditional

I highly recommend the following two books to study Logic from the beginning (for a layman);

Logic: An Introduction to Elementary Logic by Wilfrid Hodges.

Introduction to Logic: and to the Methodology of Deductive Sciences by Alfred Tarski.

Re: Navier-Stokes Announcement

#172

Post by qwja8176 »

DrBenCarson wrote: post #4

> Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled. We hope to see waves of new human understanding unleashed as the innovations behind this work are analysed and interrogated. That “apparently” feels load-bearing

Unless CMI is playing a double game, hard to tell with academics, this is indeed a giant f-you to OpenAI.

Re: Navier-Stokes Announcement

#173

Post by perching_aix »

TL;DR:

- "yeah we know"

- "looking into it"

- "will ping you"

- "might take a while though"

+ preemptive linguistic cushioning in case they feel socially (politically) compelled enough to forbid clanker proofs in their solution acceptance criteria, or in case they decide against conceding to such pressuring

Re: Navier-Stokes Announcement

#174

Post by pred_ »

Legend2440 wrote: post #7

Their rules PDF says they won't accept any solution until at least two years after publication in a qualifying outlet. This allows time for the mathematical community to review and accept new results. As the OpenAI proof hasn't been officially published yet, the clock hasn't started ticking.

And chances are they never will publish it in any kind of useful format. Right now, the scientific community is outraged at OpenAI for going about their announcement in the least productive fashion they could have. It really does seem like they have no interest in progressing our understanding of maths outside of mining it for marketing material.

Re: Navier-Stokes Announcement

#175

Post by aeve890 »

moffkalast wrote: post #109
auggierose wrote: post #11

Earlier quoted context omitted.

The Lean proof is published, you can download it. The clock definitely is ticking. Edit: Oh, didn't see the "qualifying outlet" condition. But Poincare was ever just put on arXiv, so arXiv must count as well.

Anyone can put anything on arxiv, it counts the same as printing it on tissue paper.

>Anyone

Strangely enough, the crackpots seems to prefer vixra.org to publish their work. I've never seen something like "4D wormholes can cure cancer" in ArXiv

Re: Navier-Stokes Announcement

#176

Post by SiempreViernes »

kaffekaka wrote: post #35
noisy_boy wrote: post #29

Earlier quoted context omitted.

We should enjoy the advancement. I also think the AI companies solving this or such problems with rewards shouldn't get any cash - that's the least they can do for human advancement having stolen the entirety of human knowledge and continuing to swallow never before seen amount of energy.

FWIW I think OpenAI have stated they will not claim the award. They did not do it for the money obviously, but for the PR, that much everyone must agree on.

> They did not do it for the money obviously, but for the PR

Doing it for the PR is still just doing it for the money, only they have a much bigger pile in mind.

Re: Navier-Stokes Announcement

#177

Post by famouswaffles »

fragmede wrote: post #87
famouswaffles wrote: post #58

Earlier quoted context omitted.

Yes. This is the worst the models will ever be. Perhaps you should start paying attention to that now.

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.

Re: Navier-Stokes Announcement

#178

Post by famouswaffles »

black_knight wrote: post #84
famouswaffles wrote: post #44

Earlier quoted context omitted.

It's really not that big. Yeah Navier-Stokes was easier than Riemann but that's not really the issue. AI has and will improve at a much greater rate than human mathematicians. So it's really a question of if AI gets good enough to tackle it before any human does. It doesn't look like humans will be solving it anytime soon but where will AI be in 2 years ? Hell, it looks like at least one other result will be announce…

The thing about mathematics is that it can be arbitrarily hard, including impossible to prove a given theorem. I don’t know the details of RH, it might very well be solved soon, but it could also be impossible or just so difficult that even orders of magnitude more intelligent AI can’t solve it even. If it is impossible to prove, it might be possible to prove that it is impossible to prove, or that itself might be di…

I mean if it's impossible to prove then the bet is still valid right ? The Clay institute won't be giving out any prize still in that case.

Re: Navier-Stokes Announcement

#179

Post by pred_ »

AnimalMuppet wrote: post #159
Razengan wrote: post #131

Earlier quoted context omitted.

Seems like artificial and maybe bitter gatekeeping

For giving away a million bucks, you get to gatekeep however you choose. But no, peer reviewed and published in a reputable journal is a fairly normal standard.

And just to spell it out, since it looks like HackerNews is flooded by people who are new to science these days: even if a result doesn't come with a price, scholarly peer review is the norm across all of science: https://en.wikipedia.org/wiki/Scholarly_peer_review
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