The Navier–Stokes Millennium Prize Problem

(simonwillison.net)

54 points | by tosh 44 minutes ago

14 comments

  • tosh 22 minutes ago
    > My two favourite hypothetical questions regarding this used to be:

    > If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.)

    > If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"?

    > My new preferred hypothetical for this is:

    > If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first?

  • rao-v 1 minute ago
    It’s reasonable to wonder about what chat usage data gets into models (to be honest probably quite little - carefully curating training data and creating higher quality synth data seems to be the current approach) and the implied risk to privacy and creativity (every new patent filed this year probably touched a model before filing).

    What I cannot reconcile is the timeline and the concern in this specific case.

    I don’t think training pipelines are anything close to the level of continuous training needed to incorporate Aug 15th ideas into a model that generates a breakthrough early Sept. Either OpenAI nakedly had someone with mathematical understanding dig into a specific user’s chats (a massive red flag) or this really is poor handling of a more classic parallel discovery situation (with one party clearly having worked on it longer)

  • civvv 3 minutes ago
    LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence», I wonder if we will see similar examples by LLM’s soon. It seems to me currently impossible that LLM’s can replace human mathematicians, because of their (assumption) likely dependence on human input in the sense of enormous amounts of pre-existing attempts/data.

    If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt an LLM would be useful at all on their own. Is this the «ultimate ASI test»?

  • nicce 0 minutes ago
    Can’t wait to see the human verifying the results and then figure out that the AI model actually cheated and the results are not correct.
  • shellfishgene 21 minutes ago
    What's missing from the story I think is the part about "...then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear...". If only the two of them were working on the problem in secret, how did their breakthrough become a rumor?
    • tyre 8 minutes ago
      People talk. If you have a breakthrough solving one of the most famous problems outstanding, you're going to tell people.

      You'll say, "Don't tell anyone", which they will ignore because they get a rush and perceived status by sharing it. So then they tell someone, along with "Don't tell anyone", etc.

      It's a small enough world (both in academic math, one at Anthropic) that you get to OAI in very few hops.

    • dboreham 14 minutes ago
      They weren't working in secret?
  • sdcfgy 4 minutes ago
    My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no.

    I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

  • aadyachinubhai 2 minutes ago
    LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?
  • kdavis 2 minutes ago
    All your datum are belong to us!
  • caughtinthought 14 minutes ago
    Basically no new info here, not really sure why this post needed to be written tbh.
    • kzrdude 0 minutes ago
      On the contrary, a level-headed summary that gathers information from all the different sources is necessary.
    • iso1337 11 minutes ago
      Agreed. This person just loves to shill their blog and their pelican benchmark.
      • jdlshore 6 minutes ago
        There’s no shilling here. The person who posted the link isn’t the person who wrote the blog.
    • fimi 6 minutes ago
      Yes, you have ability to get information very quickly, but not everyone does.
  • octocop 1 minute ago
    Is there a good tldr on this topic?
  • dboreham 6 minutes ago
    The concept that "knowing something has been done" allows others to find the solution to an previously unsolvable problem is an old proven one. For example when Germany launched a rocket (V2 prototype) the British knew its rough trajectory and from spying it's rough size. Although they had previously believed that ballistic missiles weren't possible because no engine could provide the necessary thrust to weight ratio, given the obvious German launching of one, they went through all the known chemical compounds to arrive at the combination (Ethanol and LOX) used. [Story from RV Jones "Most Secret War"].
  • tyre 11 minutes ago
    Yeah, this was pretty shitty by OpenAI. Not surprising, sadly.

    Them being assholes, trying to exclude an author just because he worked at Anthropic, shows the kind of culture within (that part of) their organization. The focus wasn't on supporting academics or expanding research. It was on getting great marketing.

    If they had to burn millions of dollars solving a problem _that they thought was already being solved_ to do so, they'd do it.

  • avs733 5 minutes ago
    I’ll go back to the point about authorship. I’m Not a mathematician but I am in academia. if you are fucking around with authorship you are immediately suspect.

    That aspect alone would/should be unthinkable to any serious academic. Authorship reflects who did the work and changing it for business competition reasons should be a red flag for multiple different reasons. They include, the sheer tactlessness of treating a major theoretical advancement as a competitive posturing first, the norms of academia second, and all the misunderstandings of the culture of the disciplines culture that people will now suspect are hiding beneath the visible surface (insert topography joke).

    Math as a field is fairly unique even in how they list authorship. It was long the norm that authorship to be alphabetical because the idea of first, second, senior etc authorship is harder to define than many other fields.

    “The stated rationale for alphabetical order is that it treats co-authorship as intellectually joint work: every listed author’s name carries equal weight, and no one has to negotiate, or be seen to negotiate, over billing. That is a genuine advantage over position-coded conventions, where disputes over who is “first author” are one of the most common sources of authorship conflict in fields that use them” [0]

    That norm is changing, slowly, but one option people are pursuing is notable: randomized author order. Their is a perception that alphabetical is too biased…that’s the world OpenAI is stepping into when they make that offer of authorship to one scholar with a demand that he exclude his partner.

    I can’t speak to the facts of anything else in this, but if a grad student came to me and said someone made them that offer, I would tell them to run and if they were brave report it.

    [0] a to the point lay description of the history of math authorship can be found here: https://casrai.org/guides/mathematics-alphabetical-authorshi...

  • underdeserver 8 minutes ago
    Skulduggery!