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Navier-Stokes Announcement

claymath.org

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Re: Navier-Stokes Announcement

#21

Post by vatsachak »

tristanj wrote: post #8

It's worth mentioning that OpenAI will not be eligible for the Millennium Prize for quite a while. Per the rules listed https://www.claymath.org/wp-content/uploads/2022/03/millenni... , Clay Mathematics Institute have some requirements to make this process deliberately slow. 1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenA…

Who cares about the prize and the outdated methods?

OpenAI and Anthropic might have 3 millennium problems by December

Re: Navier-Stokes Announcement

#22

Post by tristanj »

tancop wrote: post #15
tristanj wrote: post #8

It's worth mentioning that OpenAI will not be eligible for the Millennium Prize for quite a while. Per the rules listed https://www.claymath.org/wp-content/uploads/2022/03/millenni... , Clay Mathematics Institute have some requirements to make this process deliberately slow. 1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenA…

> The ultimate decision as to whether a publication qualifies as a “Qualifying Outlet” shall reside in the sole and unfettered discretion of CMI. CMI may, in its discretion, relax or remove one or more of the conditions listed in Section 6(e) above if it has received advice from experts in the field of the Problem, chosen by CMI, that a published solution is likely to be correct. Looks like even a blog post is good e…

Interesting. It seems this carve-out was added when they rewrote the rules in 2018. In the original rules [0], it says:

   Before consideration, a proposed solution must be published in a refereed mathematics journal of world-wide repute, and it must also have general acceptance in the mathematics community two years after that publication. Following this two-year waiting period, the [Clay Mathematics Institute] will decide whether a solution merits detailed consideration.
There's no option for CMI discretion. They probably rewrote the rules to avoid another Poincaré conjecture situation, where the paper was only published on arXiv and not in a mathematics journal.

[0] https://web.archive.org/web/20000622023328/http://www.clayma...

Re: Navier-Stokes Announcement

#23

Post by trhway »

unknown-unknown wrote: post #9

In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory. However, after reading the open letter sign…

> It feels like the mathematical world is changing very rapidly, almost overnight.

...

>Now AI is changing that. I wonder what this means for the kind of mathematics that people have traditionally done.

Mathematics becomes engineering. I think it is great and long overdue. Saying that as a Math PhD dropout :) Of course like manual craftsmen had to adapt to Industrial Revolution, the same would need to be done by the mathematicians. And other scientists too.

Re: Navier-Stokes Announcement

#24

Post by drexlspivey »

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

[flagged]

Re: Navier-Stokes Announcement

#25

Post by reasonableklout »

unknown-unknown wrote: post #9

In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory. However, after reading the open letter sign…

Yes, mathematics has been perhaps the purest human intellectual pursuit. Sure, many theorems turn out to have important applications in science and engineering, but the mathematical community has mostly escaped corporate interests. And for the reasons you mentioned about not needing any resources except your brain, it has been a uniquely human activity which showed us talent can come from anywhere, with stories like Ramanujan and Galois.

I hope that pure mathematics research can retain a strongly human component forever. It would sadden me immensely for human understanding of our mathematical world to wither and die, and for us to become ignorant consumers of wonders beyond our understanding just because our robots can do it better than we can. As far as applied research goes, I hope we will always be able to understand what we want to, but I have less qualms about becoming more scalable and efficient.

Re: Navier-Stokes Announcement

#26

Post by trhway »

reasonableklout wrote: post #25
unknown-unknown wrote: post #9

In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory. However, after reading the open letter sign…

Yes, mathematics has been perhaps the purest human intellectual pursuit. Sure, many theorems turn out to have important applications in science and engineering, but the mathematical community has mostly escaped corporate interests. And for the reasons you mentioned about not needing any resources except your brain, it has been a uniquely human activity which showed us talent can come from anywhere, with stories like…

>for us to become ignorant consumers of wonders beyond our understanding just because our robots can do it better than we can

all this fantasy books with magic artifacts should have mentally prepared us. Time to study the prompts Potter was giving to his magic wand.

After all, one of the main work the top AI companies are doing rigth now is developing AI to further develop AI. After several layers of AI developing AI we probably wouldn't be able to understand much there.

Re: Navier-Stokes Announcement

#27

Post by tristanj »

ngruhn wrote: post #13
tristanj wrote: post #8

It's worth mentioning that OpenAI will not be eligible for the Millennium Prize for quite a while. Per the rules listed https://www.claymath.org/wp-content/uploads/2022/03/millenni... , Clay Mathematics Institute have some requirements to make this process deliberately slow. 1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenA…

> or posting arXiv does not count The Poincaré conjecture guy also broke that rule. They wanted to give him the prize anyway but he refused. OpenAI announced they would also not claim the prize. Looks like no one wants this prize lol

You might be right. At this rate, if AI solves the remaining five problems, we're heading towards a hilarious situation where all the Millennium Problems are solved, but nobody wants to claim the prize money.

Re: Navier-Stokes Announcement

#28

Post by stevefan1999 »

num42 wrote: post #6
tristanj wrote: post #3

Smart move by them for waiting until the drama died down before making a completely neutral statement. The statement is so sterile they don't even mention who solved it. The word "OpenAI" doesn't appear at all.

"In recent years there has been an increasing sense of anticipation as breakthroughs in the surrounding field (some recognised by the Clay Research Award) have raised hopes that the Navier-Stokes problem might soon be resolved. The increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation." Keyword: New Technologies

That is so vague you might as well call Windows NT new technologies

Re: Navier-Stokes Announcement

#29

Post by noisy_boy »

ComplexSystems wrote: post #16
baby wrote: post #12

It feels like a nice post. It’s almost like we’re not supposed to celebrate the fact that mathematics is accelerating.

I agree. I found it refreshing to get away from all of the AI drama and just enjoy the advancement in math.

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.

Re: Navier-Stokes Announcement

#30

Post by raegis »

auggierose wrote: post #11
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.

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.

If I recall (too lazy to check) folks made slight improvements to Perelman's work and published it in mainstream journals, satisfying the "qualifying outlet" requirement.
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