Navier-Stokes Announcement(www.claymath.org)
78 pointsby rvz3 hours ago8 comments
  • Legend2440an hour ago
    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.

    • auggierosean hour ago
      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.

      • adastra2222 minutes ago
        Publish in academic language means accepted peer-reviewed paper.
      • raegis25 minutes ago
        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.
    • babyan hour ago
      It’s easy to verify the lean statement, you don’t need to read the proof. That is part of the breakthrough
      • seanhunter14 minutes ago
        You absolutely need to read the lean proof firstly to assess the correctness of the proposition it is proving (ie in this case that it is actually proving or otherwise the smoothness of navier-stokes in R^3 and not something else) and secondly to determine whether the proof is “honest” in the sense given here https://lean-lang.org/doc/reference/latest/ValidatingProofs/
      • rramadassan hour ago
        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.

  • tristanj2 hours ago
    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.

    • num42an hour ago
      "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

      • stevefan199933 minutes ago
        That is so vague you might as well call Windows NT new technologies
    • minimaxiran hour ago
      What makes a man turn neutral? Lust for gold? Power? Or were they just born with a heart full of neutrality?
  • swyx2 hours ago
    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.
  • DrBenCarsonan hour ago
    > 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

    • drexlspivey43 minutes ago
      The “load-bearing” feels claude-slop
    • tgvan hour ago
      What a load od corporate drivel. "Interrogated"? Was their need for words so dire?
  • tristanjan hour ago
    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 OpenAI did) or posting arXiv does not count.

    2) At least two full years must pass after publication in a qualifying journal, before CMI will even consider evaluating it. The intent is to give the maths community time to scrutinize the solution.

    Realistically, they'll be eligible for a prize ~2.5 years from now, or around 2029.

    • ngruhnan hour ago
      > 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

      • tristanj41 minutes ago
        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.
    • tancopan hour ago
      > 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 enough, they just need to do the review by themselves.

      • tristanjan hour ago
        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...

      • noodletheworldan hour ago
        My opinion is that it is pretty clear that they’re not going to do that.

        > The rules governing the prizes describe the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates.

        I think “you don’t get anything straight away for rushing your AI into the maths problems, not even credit” aligns pretty fairly with what the fields medalists are concerned with.

    • vatsachakan hour ago
      Who cares about the prize and the outdated methods?

      OpenAI and Anthropic might have 3 millennium problems by December

  • babyan hour ago
    It feels like a nice post. It’s almost like we’re not supposed to celebrate the fact that mathematics is accelerating.
    • gps37211 minutes ago
      Agree! 'Problems' are getting solved and this needs to be celebrated. Wondering how this will discourage mathematicians at all, since now they have another tool to accelerate their research. Nothing is stopping them from using 'new technologies' or sticking a gun to their head to use the 'new technologies' either.
    • ComplexSystemsan hour ago
      I agree. I found it refreshing to get away from all of the AI drama and just enjoy the advancement in math.
      • noisy_boy32 minutes ago
        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.
  • unknown-unknownan hour ago
    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 signed by 25 Fields Medalists, I became quite concerned. It feels like the mathematical world is changing very rapidly, almost overnight.

    I used to think that before AI, you could spend your entire lifetime working on some of the hardest problems in mathematics. If you were an introvert or someone who enjoyed solitude, all you really needed was a pencil, some paper, and an eraser. You could spend years thinking about a problem, and if you were lucky enough to make a breakthrough, it would be your own journey.

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

    Mathematics has given us so many stories of lonely geniuses and their passions, people like Andrew Wiles, Grigori Perelman, and Yitang Zhang. Their stories are interesting because they show how deeply personal mathematics can be. They spent years working on problems because they were genuinely interested in them.

    I am worried that we might slowly lose some of that side of mathematics as AI becomes more powerful. I do not think change is necessarily bad, but I think it is worth thinking about what mathematics should be in the future and whether it can still remain a deeply personal pursuit of curiosity and understanding.

    • reasonableklout43 minutes ago
      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.

      • trhway41 minutes ago
        >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.

    • drexlspiveyan hour ago
      > 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.

      Currently 0/2 Millenium problem solvers claimed the prize money so clearly money is not their motivation for tackling the problem.

    • trhway43 minutes ago
      > 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.

  • an hour ago
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