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Did OpenAI solve the wrong Navier-Stokes problem?

43 points tomjakubowski 20 hours ago 17 comments

bmacho 11 hours ago | parent

Article says that there are 2 formulations of the NS problem and both are interesting: one is about fluid behaviour with no external forces, other is about fluid behaviour with external forces.

For a counter-example the latter is easier since you can have a tricky external forcefield.

tomjakubowski 1 hour ago | parent

I learned from this charming lo-fi video that it is actually much easier to find singularities in the Navier-Stokes equation for compressible fluids (which is out of scope for the Millenium Prize problem). The first was found in 1998 by Zhouping Xin.

https://www.youtube.com/watch?v=4wEn9B7pDV4

busssard 9 hours ago | parent

"AI solved it."

"No we almost solved it."

"No way, it was AI all alone"

"no you used our data for train..."

"Guys, Guys calm! You did not produce any useful results!"

rsfern 9 hours ago | parent

I think this is dramatized to the point it’s talking past the article, the math community isn’t really making any of these arguments from what I can tell.

The discourse is (1) models are capable of making really impressive mathematical advances, usefulness is not in dispute, (2) the frontier AI companies aren’t being super transparent about information sources so it’s hard to know exactly how to evaluate the level of capability that was demonstrated, and (3) there are lots of kinds of math that is interesting and there are open questions about how to get there.

In particular this article highlights a particular open question I’ve seen discussed on HN before, which is that the particular proof strategy of finding a counterexample might be more amenable to RL than other strategies of proof that might be needed to resolve the other branches of the Navier Stokes problem (and probably other similar areas of math)

busssard 6 hours ago | parent

yeah i agree its dramatized, but the situation was quite dramatized by the parties involved as well. i just find it quite funny, that the perceived drama might play out like this now.

fmbb 9 minutes ago | parent

Is it really impressive, or just kind of interesting?

If they spent about 10 GWh solving the problem (was it solved?) then that is much much more than 500 lifetimes of a human brain working.

guywithahat 4 minutes ago | parent

> "Guys, Guys calm! You did not produce any useful results!"

That is the best response I've heard to this argument. Assuming the solution is correct, the fact it is not the most interesting solution that could have been solved is besides the point. The team at OpenAI did an incredible job solving the problem.

ChickeNES 16 minutes ago | parent

So what they are saying is that humans, in this case Charles Fefferman (a math prodigy, going by his history), failed to specify the problem correctly?

dgellow 4 minutes ago | parent

No, that not the issue. If you look at https://www.claymath.org/wp-content/uploads/2022/06/navierst..., second page, you will see an option C is one of the four that is asked to be solved. And that option is the one that allows for an external force, which is what OpenAI solved.

IshKebab 16 minutes ago | parent

The goalposts are moving so fast you can barely see them!

Next year's headline: But did Skynet kill all humans?

dgellow 11 minutes ago | parent

That has nothing with moving a goalpost, it’s about understanding the actual result and digging into the details. Obviously when you do that things become more nuanced than at first glance

gr_norm 10 minutes ago | parent

This is mathematicians using the solution, explicitly acknowledged to solve the original formulation of the problem, to pose interesting new questions. That is what mathematics is.

Only someone who has never interacted with mathematics outside a rote-problem-solving capacity would describe it as you have.

ActorNightly 14 minutes ago | parent

Betteridge's law of headlines