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Navier-Stokes Announcement

claymath.org

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Re: Navier-Stokes Announcement

#41

Post by kaffekaka »

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…

I agree. Technological advances can lead to a better world for sure, but I think many people underestimate the human need to create and to find meaning in their work.

If AI can do superhuman math that allows better medicines, cleaner energy etc that is great. But if AI replaces humans in all the creative and intellectual fields that is not only a loss of jobs but also a loss of deeply meaningful activities. This is waved away but I think that is mistaken.

What I fear is really the growing notion that "people shouldn't do math/art/music because machine do it better and cheaper".

Re: Navier-Stokes Announcement

#42

Post by jtpmath »

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…

[flagged]

Re: Navier-Stokes Announcement

#43

Post by kaffekaka »

gps372 wrote: post #36
kaffekaka wrote: post #34

Earlier quoted context omitted.

You mean that every mathematician can assign ten thousands Astra bots and 20 million dollars in compute to their thesis problems now?

If it works (something they need to be convinced about), if it accelerate mathematics and solve complex problems for humanity, then why not? Aren't they already using computers, mobiles, calculators, etc. already?

Yes, but a big part of the problem right now is that two big labs have monopoly on the resources and they for sure are not working for the benefit of mankind.

The Startrek future is still a long way out.

Re: Navier-Stokes Announcement

#44

Post by famouswaffles »

seanhunter wrote: post #40
tristanj wrote: post #27

Earlier quoted context omitted.

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.

That’s a big if. In the maths community, there has been a feeling that Navier-Stokes was close to being solved for a while now. I don’t know of anyone credible who feels that way about the Riemann hypothesis. Here’s what Terrence Tao had to say about it https://youtu.be/vuT-2_e4NHg Edit to add: The fun part about the RH since people mentioned lean in a sibling thread is that in lean’s mathlib4 there is verified state…

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 announced soon too.

Re: Navier-Stokes Announcement

#45

Post by mi_lk »

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.

I really like this style of writing for some reason. Not sure how to put it but it’s a rare combination of a vague post and confidence

Re: Navier-Stokes Announcement

#46

Post by TMWNN »

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.

> Their rules PDF says they won't accept any solution until at least two years after publication in a qualifying outlet.

A similar rule existed for the 100-year Wolfskehl prize established in 1906 for solving Fermat's last theorem; two years after publication.

Re: Navier-Stokes Announcement

#47

Post by phtrivier »

rramadass wrote: post #18
baby wrote: post #10

Earlier quoted context omitted.

It’s easy to verify the lean statement, you don’t need to read the proof. That is part of the breakthrough

If the Lean initial-problem-setup/statements/assumptions/etc. aren't correct then the proof is meaningless. Lean does not know what it is that it is proving i.e. it does not have any semantic understanding but only executes formal logic. Humans need to verify everything.

Also, and sorry if it's been discussed to death (pointers welcome), but, what is the probability that the proof holds in lean becaude of... A bug in lean ?

Re: Navier-Stokes Announcement

#48

Post by d0mine »

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.

> “The ultimate decision as to whether a publication qualifies as a “Qualifying Outlet” shall reside in the sole and unfettered discretion of CMI.”

Re: Navier-Stokes Announcement

#50

Post by ButlerianJihad »

kaffekaka wrote: post #43
gps372 wrote: post #36

Earlier quoted context omitted.

If it works (something they need to be convinced about), if it accelerate mathematics and solve complex problems for humanity, then why not? Aren't they already using computers, mobiles, calculators, etc. already?

Yes, but a big part of the problem right now is that two big labs have monopoly on the resources and they for sure are not working for the benefit of mankind. The Startrek future is still a long way out.

The Star Trek future may be right on schedule.

https://memory-alpha.fandom.com/wiki/World_War_III

  World War III was the last of Earth's three world wars, lasting from approximately 2026 to 2053. The conflict involved nuclear cataclysm as well as genocide and eco-terrorism. The post-atomic horror in the aftermath persisted as late as 2079.

  The war was preceded by the Eugenics Wars and the Second Civil War, all of which were sometimes regarded as parts of a single escalating conflict. It resulted in the deaths of some 30% of the Human population, at least six hundred million people, and the extinction of six hundred thousand species of animals and plants. By the end, most of the major cities had been destroyed and there were few governments left.
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