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)!
It seems to me that formulating problems at the boundary of human knowledge precisely is always going to be challenging and situations are bound to occur where you look back with the benefit of hindsight and wish that you had posed the question slightly differently based on some knowledge you didn’t have at the time.
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.
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> 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.
What's interesting is that there are a set of people who are "in charge" and can as they wish arbitrarily set the goalposts to the thing that they happen to be best at. While this might be satisfying for an Humanity vs AI narrative, it's concerning for an us vs them one. Are these people really special? or do they just change the rules of the game so that outsiders (human or AI) can't win.
If it was you or I that solved this problem our would our rewards stop at $1M? Or would we get authority? If the achievement earns that for an insider but becomes 'just a solved problem' when an outsider does it, what exactly is being rewarded?
For a counter-example the latter is easier since you can have a tricky external forcefield.
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.
Maybe something interesting will fall over because of that, who knows?
We should either see the effect or get to understanding of how to correct the model.
Note that the force is finite and doesn't "know" the vortex config. The singularity should be achieved in a finite time.
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
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…
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."
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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)
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Only someone who has never interacted with mathematics outside a rote-problem-solving capacity would describe it as you have.
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.
Almost never do people judge situations entirely on merit.
If you want to abide by your own words and judge the situation on it's merit, then you need to look at the specifics, meaning the OpenAI proof itself (166 pages), and the analysis of it that is only just beginning. Assuming that the proof is wonderful and provides much insight into Navier-Stokes is just as dumb a take as assuming that it doesn't. Judge it on its merit.
The Scientific American article is sadly paywalled, but at least part of the discussion is based on the paper below, whose work the OpenAI proof appears to build upon.
https://arxiv.org/pdf/2609.20803
When discussing the proof itself, below, with Sonnet, and asking it to explain the distinction between a function being smooth and analytic, one aspect that appears interesting is that the OpenAI forcing function is apparently constructed out of "bump functions", meaning that it is not a uniform force acting upon the flow but rather a highly engineered pattern of pokes, localized in time and space, which as another commenter in this thread notes sounds similar to Maxwell's Demon - another theoretical force, that neither tells us anything about Brownian motion nor the 2nd "law" of thermodynamics.
So, we'll have to wait for mathematicians to continue to analyze the proof, and determine to what extent is does deliver on providing insights into Navier Stokes, and any potential improvement to it, that was the goal of setting it as a Millenium Prize in the first place.
https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
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I think you are agreeing with me? My point is that "the larger math community" failed to set the bounds of the problem correctly.
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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.
OAI should just get on with it and more importantly - produce more stuff that positively benefits the vast majority of the population.
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.
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
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.
> It did, however, unambiguously solve the problem according to the Clay Institute’s original formulation.
Then why was it allowed as an option in the millennium prize statement?
Extrapolating on that, I'll take on the biased hope that almost none of the 100 solutions to be released will have any applications for at least 30 years.. (besides PR wins for AI companies)
In order to counter the fear (my own lonely one) that the 9 big names will not be able to hold the execs to account or get openAI to act "more responsibly" (whatever that means).. in the form of direct hits to new subs or partnerships or funding
I plead guilty to any accusations of (vicarious) sour grapes or sympathy for the weak
Point to you, because.. the committee would make more sense if they also bring Ant to the table.. unfortunately nerds will be nerds, so perhaps, to you, and I'll reluctantly concede, mathematicians deserve to be serfs
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What about Tristan Buckmaster and Levent Alpöge, did they also attempt to solve the same challenge? Didn’t they know it wasn’t interesting?
Yes, they were working on what is considered a niche case, the option C from the millennium statement for Navier-Stokes. The article explains that clearly, you can just read it and get the details
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.)
Let's say they do not much on Ant's findings but edge on the NDA with OpenAI. That might even be PR victory for mathematicians
(I'm proAI (for the masses, but green) BUT antiopenAI and a bit less antiAnthropic. For me it's all about the personalities.. the people in oAI are deeply uncool. not so in Ant. Dario is still dangerous, but I guess sexily dangerous lol
https://www.linkedin.com/posts/corywarfield_aigenerated-humo... )
Just the idea of making a conscious digital being, to then get it to process excel files for its whole existence is such an immoral concept