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 result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development.
Those problems can’t be formally verified with an automated theorem prover. 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 because otherwise they’d be too computationally expensive, or we just don’t have the right data to parameterize them beyond describing qualitative behavior. Agents are helping accelerate research in these fields but I think it’s mostly a different class of problem that’s a lot harder to specify and verify
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.
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.
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.
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...
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.
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.
“relying on” is misleading here relative to what the researchers have said.
If I write a book and pass it through a spelling and polish checker, I still wrote the book and its core IP. I didn’t “rely on” the tool to create the IP.
it’s much more like you come up with the premise and someone else writes the book. the released prompts for other foundational problems (like unit distance) prove that.
The tools the researchers used though was much more than an spellchecker, because spellcheckers don't come up with chains of reasoning for the arguments in the book. The LLMs did in the case of the Navier-Stokes problem.
that's not how AI was used in this case. It's more like a professor with assistants.
Professor says the assistants - why don't you dig in this direction, I have a hunch it might produce something valuable. And AI assistant does just that, proving or disproving a hunch. This would take the professor a lot of time if doing by themselves.
Yes, and keyboards also save a lot of time over handwriting. Numerical methods and proof engines save even more time. LLMs are just another tool in the kit.
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.
This is straight up misleading. When you press your K key on a touchscreen, your keyboard program may decide you meant to press the neighboring L key (by dynamically inflating the collision geometry on it) because it was statistically far more likely that you meant to press the L key next.
This likely doesn't happen exactly on an analog keyboard, but then many text-processing environments that do the same thing in post. My keyboard just edited 'yuor' to 'your' even though I successfully input the prior string.
The researchers were driving prompts and trying to actually do math.
The OpenAI effort was a pure brute force attempt. I'm not even sure an LLM was actually involved. I think they just used their hardware to run the matrix multiplies required by the search for a counter example. Perhaps some clever approach guided the search but that seems to be about it.
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.
Agree all. And as the revenues become questionable, the frontier labs practices will necessarily become (more) questionable. Vicious cycle.
To avert that dynamic, the frontier labs must deflect and otherwise act to prevent this controversy from breaking through. Both to the general public, but also more specifically to the firms' decision-makers. All of whom are generally aware of the IP issues, and some of whom are aware of what happened with Cursor and Figma, but with few exceptions have not yet themselves acted to protect their property.
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?
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.
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.
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. 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.
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.
Didn't OpenAI make a Lean proof?
https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
"This repository contains Lean 4 formalizations of the results presented in “Finite time blowup for Navier–Stokes” and “Finite time blowup for the Euler equation” by OpenAI."
The efficacy of applied NS was never in doubt. "Checking the box" is downplaying the magnitude of the discovery quite a bit as it has been unsolved for almost 100 years. Yes, this particular problem with NS no real-world applications, but that's true for 99.9% of math research.
Agreed, but i think this underscores my point. We have numerical simulations in materials science too, but that doesn’t mean formally verified theorems about the underlying equations automatically translate to formal (or even informal) verification of simulation results. That’s not to say you can’t make progress with agents, but I think it’s less well defined how you write the goal and progress assessment for an agent
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.
> 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).
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.
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
>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?
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
Those problems can’t be formally verified with an automated theorem prover. 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 because otherwise they’d be too computationally expensive, or we just don’t have the right data to parameterize them beyond describing qualitative behavior. Agents are helping accelerate research in these fields but I think it’s mostly a different class of problem that’s a lot harder to specify and verify
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