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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#701

Post by demibabs »

boshalfoshal wrote: post #544
20k wrote: post #310

Earlier quoted context omitted.

Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it Edit: OpenAI have now admitted they were training on prompts at the time they made their breakthrough: https://mastodon.social/@tristanbuckmaster/11723647135247030...

lol, the "other work" was also probably 95-99% AI generated. By a similar breed of OpenAI (and some Anthropic) models, as well. I dont know why this monumental achievement is being drowned out by some arbitrary drama. No matter which way you slice it, AI solved this problem. Doesn't matter if it was some internal OpenAI model, or whether it was Astra + Fable.

Yeah but the mathematicians are claiming that the key insight that made the problem tractable for AI in the first place, came from them.

Re: On the Navier–Stokes Millennium Prize Problem

#703

Post by robryan »

concinds wrote: post #510
Eridrus wrote: post #465

Earlier quoted context omitted.

Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?

His issue is more nuanced than that. Most of the value was in humans reaching new insights or new math during failed attempts to solve these problems, whereas AI is basically "too efficient" in beelining to the goal and discards potential new insights reached along the way. I assume this is solvable.

Surely it is. Ask it to keep a list of all the promising sub paths, reprompt the collections of agents again on these after the main problem has been addressed. Or even release a list of them and let others investigate.

Re: On the Navier–Stokes Millennium Prize Problem

#704

Post by btilly »

The problem that I want to see them tackle is formalizing the classification of finite simple groups.

Everyone uses the classification. Nobody has great confidence in the proof. Nobody understands it. There are attempts to reprove it.

If it can be formalized, that would demonstrate that AI is ready to formmalize all of mathematics.

Re: On the Navier–Stokes Millennium Prize Problem

#706

Post by zem »

AlexErrant wrote: post #242
recitedropper wrote: post #10

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..

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…

the projectnash link claims it's mathematically valid, the noahpinion link says that it's invalid and has a marvellous proof that the non-walled section is too small to contain.

Re: On the Navier–Stokes Millennium Prize Problem

#707

Post by semi-extrinsic »

sobellian wrote: post #668
semi-extrinsic wrote: post #633

Earlier quoted context omitted.

This is a wrong interpretation. Physicists have a shit-ton of models that produce "aphysical singularities", they just work around those to get meaningful answers anyway. This is a whole trope and stereotype. Some of the most successfull and accurate predictions in all of physics come out after you discard a bunch of singularities. See e.g. https://en.wikipedia.org/wiki/Renormalization Nobody who actually works in fl…

Whether or not ways exist to work around the singularities, that they exist is surely of note. Before von Neumann formalized QM people were still doing QM, okay fine. But it's wrong to then say von Neumann was doing no physics of note.

"Does there exist a pathological combination of smooth body forces and initial conditions for this set of PDEs, where singularities appear, which by the way is completely impossible to actually create in the real world unless you are a literal God?" is a question of math, not physics. This is a hill I will die on.

Re: On the Navier–Stokes Millennium Prize Problem

#708

Post by danielmarkbruce »

brettdev wrote: post #659
hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

There are lots of startups creating labs that can be managed e2e by agents. That will connect reasoning to the physical world and dramatically speed up the plan, experiment, reflect loop beyond what humans currently do in science R&D.

Maybe. Maybe not. Look at AI drug design - it's not really speeding up the important part - drug trials. There isn't really a coherent plan to use AI for the most complex part of drug discovery at all.

Re: On the Navier–Stokes Millennium Prize Problem

#709

Post by jiggawatts »

rfgplk wrote: post #107

Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at fronten…

I can't find a good way to articulate this point to other people. What the LLMs lack in depth in a speciality field they more than make up for in breadth!

It feels like the "tide is rising" where the minimum level of skill applied to every aspect of everything will inexorably rise to "whatever an LLM can do", which is already pushing past PhD level.

Re: On the Navier–Stokes Millennium Prize Problem

#710

Post by danielmarkbruce »

vatsachak wrote: post #356
hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

Lol what? Everything is computation. The natural sciences will soon start breaking too. I will concede that AI seems likely to not invent a "research program" anytime soon. It has no taste

No, it won't. How do you verify some causal claim in biology?

The reason AI is doing so well in math proof writing is that it can verify every idea it has, quickly.

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