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  • Hacker News
  • > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models

    This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool.

    But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out does not mean what they imply it means.

  • > But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game.

    Just because something is legal and permitted by terms of service doesn't mean it's morally right.

  • "... The point remains that there is a substantial opportunity cost in converting a historically productive and motivating problem (such as Navier-Stokes regularity) into a mere viral social media post advertising some benchmark progress, rather than actually advancing the field and developing the next generation of both problems to ask, and people to work on them."

    https://mathstodon.xyz/@tao/117219101339291693

  • > A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity.

    And what's a better way of empowering people than robbing them.

  • > And what's a better way of empowering people than robbing them.

    Better than the walled gardens of most journals where you can't even read half the papers without shelling over thousands of $$$

  • It's low-key funny that OpenAI attempted the problem because they thought somebody else had already solved it, but turned it had NOT in fact been solved!

    It's like that story about George Dantzig solving open problems as a student because he thought they were simply homework: https://en.wikipedia.org/wiki/George_Dantzig

    It's also unfortunate that such a potentially momentous occasion is overshadowed by so much drama. Which I suppose is expected given the technology and the people involved are so polarizing.

  • I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits.

    This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able to until LLMs came along.

    Hard to claim at this point that LLMs aren't capable of novel STEM creativity and genius to a degree that will soon far surpass that of humans.

    If anyone has counterpoints to this I'd love to hear them!

  • Eh... OpenAI spent significantly more than $1 million solving this...
    by gpm
  • See I think it’s clear demonstration that OpenAI is ethics-free
  • >If anyone has counterpoints to this I'd love to hear them!

    Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement.

    To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah ChatGPT proved X with 5 years of 24/7 work with 10x Terrence Tao level geniuses" it really doesn't cut it.

    Or why's there's no new branch of mathematics invented by AI? That'd be indubitably _novel_ and _creative_. But to my knowledge (and I'm eager to be educated) there's nothing like that. What are the HARD examples of novelty, creativity and genius you claim? For how people like you talk about AI I'd expect idk, a unified theory on fundamental physics, or a novel engineering solution for material science and nuclear fusion, or at least improve itself to not need a bazillion GPUs to emulate a 20 watts wetware. Sure it would infinitely easier to make OpenAI literally print money with any of the thousand problems easier to solve with such amazing intelligence than the NSE problem right? Honest question

  • Sure, even a 20% chance at 1 million payday after 5-6 years of fulltime work on a project with zero practical application doesn't touch the, say, 200k/year guaranteed our best mathematicians would have to forgo to devote their intellect to the problem.
  • Here you go:

    When you read the detail the compute they are throwing at it is incredible, tens of thousands of agents with different groups competing.

    It's not like a single Gauss as you imply, "just" many, many mathematicians working tirelessly in a completely ego-less way, guided by other agents and ultimately humans, built - allegedly - on recent human insights.

    Stunning, undoubtedly, but this is a "brilliant autistic herd" result, not that of a singular mind.

  • I think the biggest hurdle remaining is that all these landmark results are generally counter-examples.

    Proving something in the affirmative often requires the creation of an entire new sub-field of math, or new tools. Think of Fermat's Last Theorem or something like that.

    These results, while impressive, are clever constructions using existing techniques. It isn't clear that AIs can build new machinery like this. But if/when they can, yeah it is probably game over.

  • > will soon far surpass that of humans

    To be fair, I think it's still an open question about how far it might surpass human capabilities.

    I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and existing knowledge.

    Should this be the case, we would see a rapid broadening of development, and a slow advance in the frontier in such a way that might surpass the collective capabilities of people, but not by very far.

  • Not a counterpoint per se, but I burned $50k recently on a much more modest math problem (result already known, just thought I had a sketch of a more interesting proof), and the LLM thought it had proved it within those bounds but had instead subtly fucked up the Lean definition. Take from that what you will.

    Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or sniped the important details from the researchers it was spying on.

  • From my reading of the announcement:

    - There are at least two versions of a model more powerful than Astra at OpenAI at the moment.

    - The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents.

    - The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents.

    - OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed.

    So the timeline was:

    Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution.

    If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!

  • The entire drama is that OpenAI sniped a Millennium Prize Problem from an Anthropic-affiliated research team who had been working on the problem for nearly a year. In just 5 days. I don't think that can be understated.
  • Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute.

    The dark forest awaits..

  • I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.
  • I guess guys from the opposite side would not work there. So that is what will happen more and more.
  • Indeed, this seems to be the main, albeit hidden, takeaway from all of this.
  • 1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox???

    2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...

    When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.

  • For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915

    Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees

  • And even this version contains the line

    > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .

  • To be fair, the first solved Millennium Prize Problem, the Poincaré conjecture, also had its fair share of drama!
  • Which seems to be entirely true by their own admission! [0] Both the comments about him risking his career and about Levent's authorship seem to have indeed occurred.

    > 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.

    > 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)

    https://xcancel.com/SebastienBubeck/status/20973794116915163...

  • > We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.

    WOW?

  • > WOW

    This.

    I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still.

    If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.

  • This is going to be dramatic in so many different ways.

    - First off, to reiterate, WOW.

    - Second of all, when does this end? Are we at the dawn of the singularity now?

    - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?

    - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead.

    - Do "normies" even know what's happening?

    Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.