"Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens." At a conservative estimate of GPT 6 Astra pricing, this would have cost upwards of 15 Million dollars for anyone using the OpenAI API! To me this is the one silver lining. Yes, they can solve millennium prize problems, but it still costs a fortune.
On the Navier–Stokes Millennium Prize Problem
961–970 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#962Diagram of a swirling vortex illustrating inward spiral and axial stretching. A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching."
Hmmm, isn't that interesting!
(Side note: Apparently we can't "compress" something, but apparently we can move more units of that thing over a specific space in a specific time... hmmm, I wonder what the difference between those two concepts could be...)
Main Observation: The image on OpenAI's web page above, looks sort of like the one for the Hopf Fibration:
Re: On the Navier–Stokes Millennium Prize Problem
#963Earlier quoted context omitted.
Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.
I tried to build a procedural 3d asset pipeline for a specific use case. Before the Opus upgrade in November it was basically no way of doing this. I gave up very quickly. After November i tried again, and no model could build me anything relevant. Now it just works. Took me an hour to progress to a point were i'm happy. Whatever they do, progress is still real, still way faster than I assumed The list of Ubuntus 240…
Re: On the Navier–Stokes Millennium Prize Problem
#964Earlier quoted context omitted.
This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.
I agree. Nobody cares and will care about the drama, it is just marketing. This is the point where were definitely have reached AGI.
Re: On the Navier–Stokes Millennium Prize Problem
#965Earlier quoted context omitted.
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
#966[flagged]
Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.
Not exactly...
From here:
https://cims.nyu.edu/~tristanb/statement.pdf
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem".
Re: On the Navier–Stokes Millennium Prize Problem
#967Earlier quoted context omitted.
But that lead happened to be the same approach Levent and Tristan had found... Meaning they would have found it first if OpenAI hadn't spent millions in compute on following their lead to its conclusion faster than them.
It's forced vs unforced Euler, so it's not exactly the same. Since OpenAI has access to their training data, they can probably scrub through the data to find out whether there have been any mentions of the similar approach, and whether it only comes from Tristan Buckmaster or if it is in the training data before that. They'll probably have to kick off another fleet of agents to scrub through the training data to answ…
They did check and it was in the trainingset but they could not confirm if it was the /cause/ of it, which is a bit of a cop out.
Re: On the Navier–Stokes Millennium Prize Problem
#968created a simulation of the solution to describe what's happening and why it's important for engineers, climate modeling, etc : https://navier-stokes-singularity-simulator.netlify.app/ (updated so that it works better on mobile)
In reality you can't have things like infinite velocity, so if Navier-Stokes is predicting blowups, then isn't this a problem with Navier-Stokes not handling some edge cases, not a problem with reality that engineers need to be concerned about?
Re: On the Navier–Stokes Millennium Prize Problem
#969Earlier quoted context omitted.
What makes you think they were coherent?
They managed to solve a problem that was beyond current human ability.
Re: On the Navier–Stokes Millennium Prize Problem
#970Earlier quoted context omitted.
How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.
Because it seems like most of the work may have been done by human mathematicians and cribbed by OpenAI at the last minute
Any way you cut it, this is a major achievement for AI, besotted with human drama over whose prompt should be recognized by the history books.