Did OpenAI solve the wrong Navier-Stokes problem?
Posted by tomjakubowski 1 day ago
Comments
Comment by jonlong 6 hours ago
SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question". This is pure sensationalism. Choosing option (C) (out of an explicit list of four options) is neither a "loophole" nor something "found by the LLM"; everyone involved knew this was the option they were pursuing.
With the grumbling out the way, there is some actual scientific content to the article: there's a strong argument that OpenAI's method will not extend to the unforced case, leaving our understanding of NS incomplete. This negative result is itself new and interesting (and predicated entirely on the solution found by OpenAI)!
Comment by HarHarVeryFunny 5 hours ago
Comment by hotdog1492 3 hours ago
Comment by dist-epoch 3 hours ago
Comment by glimshe 1 hour ago
Comment by hn_throwaway_99 5 hours ago
> It did, however, unambiguously solve the problem according to the Clay Institute’s original formulation. The official problem statement, penned in 2000 by mathematician Charles Fefferman, offers an option called “C,” in which solutions are allowed to use an external force like OpenAI’s.
Comment by p-e-w 3 hours ago
God, it’s embarrassing to read stuff like this. They’re making it seem as if everyone involved was either stupid or dishonest just so they can pretend they have a scoop here.
Comment by bmacho 17 hours ago
For a counter-example the latter is easier since you can have a tricky external forcefield.
Comment by HarHarVeryFunny 6 hours ago
The forced version is easier since you can custom design the force function to get the result (it doesn't have to be a realistic force like stirring), so getting the blow-up might be regarded just as much a function of your bespoke force function as of the fluid dynamics itself, which is apparently what OpenAI did, pushing the definition of the force function being "smooth" to it's limit.
So, it appears OpenAI did legitimately meet the Millenium Prize solution criteria, but in the most unrealistic, and therefore least interesting, way possible.
Comment by adriand 4 hours ago
The title is a bit misleading. The variant with a smooth forcing was one of the four valid variants in the Clay formulation. It is interesting to solve it. It is still an interesting and impressive result. The no force version is also interesting and remains unsolved. It isn’t reasonable to just dismiss the proof on the grounds that 26 years later we claim it was never that interesting. This is the first time I’ve seen this attitude.
Comment by tomjakubowski 8 hours ago
Comment by cpard 2 hours ago
Today, we are discussing if AI cheated by picking the easy problem to solve which means that we at least still comprehend what’s going on.
I wish mathematics and the rest of the human intellect wouldn’t turn into content marketing that is generated primarily to trigger strong human emotions.
I feel that this is going to hurt both AI and the disciplines that can benefit the most from it
Comment by ChickeNES 6 hours ago
Comment by dgellow 6 hours ago
Comment by aesthesia 2 hours ago
Comment by hatthew 6 hours ago
Comment by dragonwriter 6 hours ago
Comment by scheme271 4 hours ago
Comment by ChickeNES 5 hours ago
Comment by dragonwriter 4 hours ago
Surprisingly enough, being chosen by another actor as proxy for some group doesn’t actually resolve the problem that an individual may not always be an accurate proxy for the concerns of the group (and especially for the same descriptive aggregate group a generation after the proxy acts on their behalf.)
Comment by etdznots 4 hours ago
Comment by ChickeNES 6 hours ago
Comment by ChickeNES 6 hours ago
I think you are agreeing with me? My point is that "the larger math community" failed to set the bounds of the problem correctly.
Comment by alkyon 5 hours ago
Comment by perching_aix 4 hours ago
Comment by dragonwriter 6 hours ago
And yet another set of humans—Open AI marketers—made an error in how they sold the result of the preceding errors.
But its not news that computers are mere tools and that any error blamed on a computer involves at least two human errors, one of which is blaming the computer instead of the human(s) responsible.
Its perhaps a bit less obvious that every thing for which credit is given to a computer involves at least one human error—that of crediting the computer—and certainly can be more amusing when it involves a bunch of human errors.
Comment by yababa_y 5 hours ago
Comment by emmelaich 4 hours ago
Comment by jongjong 3 hours ago
It reminds me of a junior coding bootcamp lecture I once gave many years ago before AI coding. One of the first slides said "Computers will do exactly what you say, not what you mean."
Comment by dist-epoch 3 hours ago
Comment by ex-aws-dude 5 hours ago
Comment by jrflo 26 minutes ago
At the current rate (if they keep burning tokens on it, which maybe they won’t given the backlash) RH will be proven within a year and there will be some other thing that means it’s not actually that impressive…
Comment by yieldcrv 6 hours ago
Comment by ActorNightly 6 hours ago
Comment by dgellow 6 hours ago
Comment by davidguda 15 hours ago
Comment by IshKebab 6 hours ago
Comment by gr_norm 6 hours ago
Only someone who has never interacted with mathematics outside a rote-problem-solving capacity would describe it as you have.
Comment by curt15 3 hours ago
Comment by IshKebab 6 hours ago
Comment by gr_norm 6 hours ago
> It did, however, unambiguously solve the problem according to the Clay Institute’s original formulation.
Comment by dgellow 6 hours ago
Comment by busssard 16 hours ago
Comment by rsfern 15 hours ago
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)
Comment by fmbb 6 hours ago
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.
Comment by dgellow 6 hours ago
I’m very anti AI and OpenAI, and do think it’s a pretty interesting finding! Very likely not worth their spend, but interesting and novel nonetheless the less
Comment by busssard 12 hours ago
Comment by guywithahat 6 hours ago
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.
Comment by olliepro 6 hours ago
Comment by dgellow 6 hours ago
Comment by krackers 6 hours ago
Then why was it allowed as an option in the millennium prize statement?
Comment by SpicyLemonZest 5 hours ago
Comment by signatoremo 3 hours ago
What about Tristan Buckmaster and Levent Alpöge, did they also attempt to solve the same challenge? Didn’t they know it wasn’t interesting?