4 ms·

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes resul

• rakejake 18d ago
  Yeah, I think you can't just throw money randomly at problems and expect results unless you know a line of attack that can get you all the way. OpenAI chose the line of attack only after it became known to them via rumors. They "front-ran" the researchers.
  • dcre 18d ago
    Worth noting they claim they did not choose the line of attack. Of course we don’t know whether that is true.
    • rakejake 18d ago
      Plausible deniability - The line of attack is in their sessions/prompts data. Just make the prompt pointed enough that the search space is tractable and use your ginormous compute. > "Of course we don’t know whether that is true" Yep. Who is verifying these claims? We all know how trustworthy Altman & Co are.
    • freejazz 17d ago
      Yeah, they didn't choose the line of attack, the person they copied it from did..
  • cmiles8 18d ago
    Yes. What the headlines hailed as an AGI discovery the facts show more to be someone spending years mining for gold, rumor gets to OpenAI that there might be gold in this specific place, they mine there and instantly discover gold, then tell the world they’ve developed the worlds best gold finding/mining machine. Separate from all the allegations of more nefarious actions and ethical issues, that’s the most charitable version of what happened here.
    • Romario77 18d ago
      they threw it on all the millenial math problems (I think there are 6 at this point unsolved, well, 5 now). And according to them at some point they saw that one was close to being solved, so they pointed all the agents at it. The same thing happens to humans - at this time there are no simple problems left, so solving the hard ones requires using prior knowledge and attempts at solving things.
      • nrdvana 18d ago
        Yeah but the one they decided the AI was close to solving may have been so because the researchers' progress on this problem became part of the training data for that AI...
  • whimsicalism 18d ago
    but the researchers were also largely relying on AI
    • pphysch 18d ago
      In the same way you rely on a keyboard or touchscreen to type this comment. It doesn't mean the tool is the brain behind the work.
      • whimsicalism 18d ago
        frankly don’t know how to reply to these sorts of comments anymore
        • pphysch 18d ago
          That's usually a good sign you are on shaky ground!
          • logancbrown 18d ago
            Obvious false analogy in your earlier argument.
            • buellerbueller 18d ago
              No so obvious to this guy.
              • whimsicalism 18d ago
                it is truly not obvious to you why keyboard isn’t a good analogy for LLM?
      • vouaobrasil 18d ago
        Keyboards don't suggest chains of reasoning or words to type. When I press the K key, I know exactly what will happen. It's just a translation layer that gives an output known ahead of time and thus does not impinge upon the creativity of putting words together. A better example would be playing chess against a player slightly stronger than me and using a chess computer to suggest some good moves. I could win, but it certianly wouldn't be just my brain that wins. It would be an amalgamation of my brain with a machine that suggests good moves. One cannot simply reason by analogy.
  • eieje1 18d ago
    You can’t do anything novel with these models from scratch and let it fly. I’ve observed something over the past few months Work on something novel -> llm is kinda useless and low value-add -> Keep at it and in the process feed it more information -> keep doing this periodically -> a few months go by and you realise the model outputs are almost like-for-like regurgitations of what was inputted in some prior period. Once it’s accumulated new info can it produce something automated that is somewhat useful? Sure. But by itself - absolutely not. I clearly see humans will be needed - the best ones that is. For ‘rote work’ and stuff that is not IP sensitive firms will be ok with employees putting that as inputs into models. But I’d wary about trusting the labs. They will push the letter of the law to the max. Personally I’ve stopped doing anything novel with these models. If I do use a model on something adjacent but not totally novel I have to craft the inputs in a strategic way not to give much away. I’d wager firms will soon realise this and that growth rate of revenues of the frontier labs will become questionable. The economic cost that firms have brought out thus far is only financial. There’s a whole bunch of other costs people aren’t talking about.
    • vonneumannstan 18d ago
      This doesn't follow for me. There are what, Dozens or Erdos tier problems that got solved with no progress for decades? How does that factor in to your view?
      • fc417fc802 18d ago
        IIUC the argument is that while unsolved there was much work done on them that shows up in the training data. The idea being that the LLM is limited to a small amount of inference over externally supplied data.
        • eieje1 18d ago
          [dead]
        • vonneumannstan 16d ago
          And yet the best humans could not use that same available data to solve the problems.
  • chermi 18d ago
    Almost but not quite I think. You can throw money at parts of problems. I think it's helpful to think it kind of like supercomputer MD/MC or electronic structure calculations. A tool that can get you valuable answers but not necessarily aid understanding. Simulations can be used to aid understanding also, and are integral to theory development. In the same way the approach to this result is.
• harhargange 18d ago
  I’m pretty sure that OpenAI has some of the best mathematicians prompting the models and analysing the results. While they are marketing as if the model solves problems themselves.
  • nayroclade 18d ago
    Prompting them yes, suggesting potentially fruitful research directions and so on, but the actual research was conducted by hundreds of agents swapping millions of messages and using billions of output tokens over 88 hours. The result being a huge Lean proof: https://github.com/openai/NavierStokesAndEuler https://github.com/openai/NavierStokesAndEuler. It's not just possible for humans to manually guide such a process in a meaningful way. They can set the direction and attempt to understand the result, but they solution itself must emerge (or not) from the agent swarm. So yes, the models do seem to be "solving" the problems themselves, but not necessarily in the way we think of mathematical discoveries happening. Academic mathematics has historically been resource constrained: There are a limited number of top-level mathematicians, and they only have so much time and brain power to spend. So when approaching a problem, they are essentially forced to be as efficient as possible, not just searching for a solution, but for one that can be achieved within their cognitive budget. This induces them to develop novel techniques and abstractions, and it is actually those techniques and abstractions that tend to be the valuable part for further research, not the proof itself. An agentic swarm is like getting a single skilled mathematician, cloning them a hundred times, then locking them in a room with the single objective of solving a problem. No longer constrained by time or brain power, they can approach it differently, using pre-existing techniques to gradually build their way to a solution. This process might not require a single intuitive leap or new discovery, and the solution will not be simple or elegant, but they will probably get there. It is more like a process of intelligently guided search than invention.
    • hunterpayne 18d ago
      The OpenAI team didn't make a Lean proof. They brute forced a counter example. The "other" team was doing what you described but they haven't "finished" their work yet. Also, their Lean proof was for a simpler version of the problem, not the full NS. Also, OpenAI wanted the actual mathematician taken off the resulting paper. I'm not sure I would describe what OpenAI did as research. What the other team was doing does seem to be more like research but the hardware was still in those cases mostly brute forcing things and then doing something like a genetic algorithm to compose an actual proof based upon the results of a large set of brute force attempts.
• sigmar 18d ago
  >We have a lot of physics based simulation tools, but they tend to focus on small subsets of the full design problem and they make limiting approximations Do you think it is possible that better math will lead to better physics models?
  • tantalor 18d ago
    It might but the math results from GenAI so far have been limited to finding counterexamples to known conjectures, not building new mathematics.
    • cma 17d ago
      > results from GenAI so far have been limited to finding counterexamples Not all. Ehrhart’s volume conjecture Quantum parallel repetition for general two-player quantum games Erdős Problem #183 on multicolor Ramsey numbers Erdős–Sárközy Problem #12(i)/(ii) Erdős Problem #125 Log-concavity of codimension-3, type-2 pure O-sequences Optimal O(1/t) last-iterate convergence for Anchored Gradient Descent-Ascent
      • tantalor 17d ago
        True, these results are from last month. My info was a little out of date. Prior updated :)
  • rsfern 18d ago
    Yes, definitely! There’s a long history of this and I think there’s tons of opportunities for more. Both for improving the exactness/physical fidelity of models and for developing new approximate theories and simulation methods
• u1hcw9nx 18d ago
  For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.
  • robotpepi 18d ago
    you're as sure of what you say as wrong about it.
    • Toutouxc 18d ago
      Note that your reply has exactly 0 value for anyone who doesn’t already know where and how the parent poster is wrong.
      • robotpepi 18d ago
        fair enough
    • jgalt212 18d ago
      which part is wrong? > For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. or > This proof is just checking the boxes for mathematicians.
    • hyperbovine 18d ago
      The same could be said of your post. OpenAI (claim to) show the existence of *a* finite time singularity. It could stimulate more research in PDE solving, and maybe physics, but it has zero impact on practical applications, that I can see. The Millenium problems were chosen based on hardness not practical relevance.
      • robotpepi 18d ago
        I was referring to the "it's just mathematicians checking boxes" claim
    • CyberDildonics 18d ago
• jhrmnn 18d ago
  Working with AI on science (not LLMs though), couldn't agree more.
• jgalt212 18d ago
  > Those problems can’t be formally verified with an automated theorem prover. It certainly seems like any problem that is amenable to reinforcement learning will be solved.
  • rsfern 18d ago
    It does, yes. So designing objections functions and making sure you can afford the training rollouts becomes really important in defining which problems are tractable. It will be really interesting to see how that shapes the kinds of problems people choose to work on
• fxj 18d ago
  [dead]
• alansaber 18d ago
  The TL;DR is still "AI helpful, but not end of the line". The live discussion about these matters is always ridiculously inflated by hyperbole.
• _zoltan_ 18d ago
  > same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development." you're not actually spending that money. it's sunk cost, as you already bought the hardware. at least for the big pharmaceutical companies for drug development. then you run your own local model, trained on special data, with special etc, etc... to the end of buying GPUs for what, 3.5-6.5M/rack or so (GB300 NVL72, Google AI summary pricing quote) becomes a bargain (vs the double digit billions you need to spend on a new drug R&D).
• 00ze 18d ago
  Solve logically? Sure. Solve for how to implement and synthesize physically? Not likely. Humans solved for launching rockets to the Moon on paper decades before it happened. Pareto type thing; the logical work is the easy 80%. The last 20% is fighting physics. There is no beating physics but there is still plenty of room for us to improve our understanding of it. Which we weren't focused on at all sitting millions primates at well understood physical computers searching for Shakespeare Python and Ruby code yet merely getting same old contemporary software outputs.
  • eieje1 18d ago
    [dead]
• chermi 18d ago
  I think a lot of people don't understand, with respect to a mathematical theory, the relation between a carefully stated conjecture requiring formal proof vs. using the objects in the theory effectively. Could better understanding of NS lead to better practical tools? Almost certainly, even if only to give us bounds on performance. Has its unresolved status stopped us from using NS? No. Almost no one using it cares. Resolving it is valuable, especially if it comes with mathematical and/or physical insight leading to greater understanding. But it is not this is grand result that like instantly unlocks 100+ day weather forecasts. It would be like saying proving ergodicity more generally for physical systems would unlock condensed matter physics, ignoring how well stat mech has served us regardless. I am not anti-AI and I don't think we should stop throwing them at conjectures. I'm against this fundamentally misleading type framing that's become prominent. Millennium prize problems are important. Treating this specific aspect of NS as the one missing piece is just harmful. If we just throw compute at formal conjectures voila cancer and fusion. I think the better example of "AI" usefulness toward solving problems is AlphaFold, and immensely powerful tool. But also suffering from a false framing/marketing problem as "solving protein folding". It feels like the right use of compute. Considering many factors that we can't hold in our head at once. "Solving" something that was already "solved" via computation (simulation) but now much more efficiently. The output is a valuable tool itself, it was not about "solving the protein folding problem", which it didn't do. It is a tool to solve problems requiring a sequence->ground state calculation. Which is a very broad set. Formal verification of a conjecture we set up as a benchmark we set to test human understanding is not valuable in the same way. I'm failing to make multiple points and gotta run, but i think that final point is important. The millennium prizes are not about technological/practical value, at least not intentionally. They're about shit that seems fundamental to us, things that feel[1] to us based on our understanding are important AND feel like they should be solvable in a human-comprehensible way. So formally resolving them with pure compute is not really the point. It seems closer to that story about one of those prime conjectures where some guy just ran brute force enumerations to find a counterexample. Valuable for sure, time-saving. And knowing the answer makes it a lot easier to solve a problem. TL:DR science and math are more than formally resolving conjectures, they're about building up understanding and tooling that you can then build more on. AI should be an increasingly big part of it, but declaring "AI will solve fusion because it's smart" is like the rest of the fucking owl meme. I have no doubt it will help, most likely via simulations/quicker testing/calculations and verification. Maybe partly via reactor designs. Maybe partly being fed conjectures about bounds/limits that would be useful as inputs for the next iteration. And maybe even in the form of resolving some formally stated conjectures (I don't know enough plasma physics to name any). [1] obviously to the mathematicians it's more than a feeling..
• SwtCyber 17d ago
  [dead]