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.

> 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).

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.

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.

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.

>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?

Working with AI on science (not LLMs though), couldn't agree more.

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.

> 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.

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..

[dead]