by liberal japonicus
The NYTimes Headlines reports that an OpenAI has just solved one of the Millenium problems, the Navier-Stokes equations. Yay, us!
Err, just a second. Quanta has this at the end of their article.
OpenAI admits that their work on the Navier-Stokes equation was inspired by rumors that Alpöge and Buckmaster had solved a Millennium Prize problem. (They hadn’t quite, though they say they have an unverified proof of blowup for a somewhat easier version of Navier-Stokes.) Using a new internal model, OpenAI employed groups of autonomous AI agents of various sizes to attack variants of the Euler and Navier-Stokes problems. “Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof,” the company wrote in a press release. They then deployed an even bigger group of agents — 10,000 or so — to attack Navier-Stokes. After 88 hours, the agents running on the internal model had a proof of a singularity in Navier-Stokes, and after an additional 17 hours, another AI model had formalized the result. In total, the agents sent almost 5 million messages to each other. Sébastien Bubeck of OpenAI estimates the computational cost at several million dollars.
Are you sure that you solved it? Here is an article discussing the problem
According to the four-page public statement from Buckmaster, after OpenAI learned that the two sides’ research directions were close, it proposed two publishing plans to him.
The first plan:
Buckmaster and Alpöge publish the Euler equations results first, and OpenAI releases the Navier–Stokes proof the next day.
The second plan:
Buckmaster writes the paper on behalf of both sides, and publishes the Navier–Stokes results obtained by OpenAI’s internal model.
But Buckmaster claimed that OpenAI researcher Sebastien Bubeck stated twice that he hoped to exclude Alpöge from the author list.
Why?
The reason is very simple, Alpöge works for Anthropic.
Mathematical achievements can be discussed, but it is not convenient for people from competing companies to be on the same author list.
Here is the pdf link to the 4 page statement mentioned above. God, OpenAI sucks.
AI is the current global version of a gold rush, and OpenAI are just doing a bit of bushwhacking and claim jumping to get a seam to work. We’ll just ignore for the moment that these epoch defining achievements are not sustainable, and their claims that everyone will have an AI like this working for them is a transparent lie.
On a related note, my wife’s publishing agency is busy finalizing the details of her Anthropic settlement claim – which comes to less than she made on a single advance for any of the books that Anthropic fed to their models without securing any permissions.
The entire Anthropic settlement is only fifteen times the total amount that OpenAI threw at one math problem just so that they could beat the first team to publication and claim all the prestige.
Chump change for the would-be masters of the universe.
I truly hope there is a singularity so that we can drop them all into it.
My first question, when AI (or anybody, for that matter) claims to have found a “result” like this: OK, you say there is a singularity. For what values of the variables do you get a denominator of zero? (That being what it takes to get an infinity singularity.) Generally a lot of handwaving results.
The Navier-Stokes equation isn’t one that can be solved in the mathematical sense — it’s a second order, non-linear, partial differential equation** after all. But if you think you have a solution, you can plug in the numbers and see if it works.
** The joys of a masters in Fluid Mechanics. Although at the time we made simplifying assumptions (dropping some patameters, e.g. viscosity, to zero so as to make the simplified equation solvable). The first time I got paid for programming (i.e. not in class) was writing FORTRAN to graph ideal fluid flows. Simple ones: laminar flow plus sources and sinks.
If AI can accurately calculate p(doom) we’ll be getting somewhere.
The claim about the Navier-Stokes equation is that the AI has answered the smoothness hypothesis — whether solutions to the NV equation are always smooth with respect to time. The AI’s proof is that the hypothesis is false, by providing a counter-example. I suspect that this will be one of those peculiar things that happen in calculus like Gabriel’s horn, a surface of revolution that has a finite volume but infinite surface area. Interesting in theory but doesn’t matter in practice.
Although I passed Fluid Dynamics in college, last millenium, my understanding of what it means to “solve” the Navier-Stokes equation is amateur-level, even after reading the links. I mean, “solving the equation” given a specific configuration of sources, sinks, boundaries and body forces, to calculate the fluid velocity at any point as a function of time, makes sense enough. So I guess the problem is either to show that every specific configuration can be solved, or define a configuration that demonstrably cannot be solved even in principle. My level of understanding is a couple of orders of magnitude less than what I need to even imagine how you’d go about either task. I was never in the running for a Millennium Prize, I guess. Didn’t lose any sleep over that. Let “AI agents” have the glory for all I care.
Navier-Stokes has to break down at a small enough scale anyway, as a practical matter. In a universe where it’s continuum all the way down, and you can completely fill Gabriel’s horn with a finite amount of paint while needing an infinite amount to paint its inside surface, human intuition is hopeless. If AI has anything like “intuition”, I wonder whether Gabriel’s Horn would blow its mind too.
–TP
Some of the non-intuitive parts of physics/math have become important. The nonvolatile memory in the phones we all carry around depend on the quantum mechanics view of an electron’s position as a probability distribution rather than a continuous function. For GPS to produce the current degree of accuracy, time dilation due to relative velocities has to be accounted for. We know N-S is at least incomplete: any set of equations with mass and velocity that doesn’t include general relativity is incomplete. I wonder if we’ll ever find an application involving N-S where relativistic mass and velocity effects will have to be included?
nous:
I hope not, nous, some occasional posters on this board might work in that industry…
Tom H – I have friends in AI development. Workers gotta eat. Only the broligarchs and their venture capital sugar daddies get chucked into the cosmic oubliette.