L E S S O N S - with Lennox Saint

OpenAI says its next-generation internal model helped solve the Navier-Stokes Millennium Prize Problem. Around 10,000 coordinating agents. 88 hours. I wanted to understand what that means without needing a maths degree.

I walk through the announcement, the vortex, and a plain-English explanation from GPT-6 Astra. Then I give my take on what this could mean for AI and scientific discovery.

Watch the video: https://youtu.be/LlAoO5AErJU

CHAPTERS
0:00 OpenAI’s new maths claim
0:29 The internal model beyond GPT-6 Astra
1:09 10,000 agents and 88 hours
2:00 How the agents worked together
2:41 Tokens and the hypothetical cost
3:36 Why OpenAI won’t claim the prize
4:39 Navier-Stokes in plain English
6:06 Five details worth knowing
6:53 My take on AI and discovery

SOURCE
OpenAI’s announcement, with links to the paper and Lean proof: https://openai.com/index/navier-stokes-solution/

CLARIFICATIONS
The $15M and $6.5M figures in this video are hypothetical output-token price comparisons, not OpenAI’s reported spending. $15M refers to all attempted problems; $6.5M refers to Navier-Stokes alone under the pricing assumption discussed. My later references to “spent $15M” overstate what is known.

The concurrent Alpöge/Buckmaster result concerned forced Euler, a different result. My imagined rivalry dialogue is speculation, not a reported exchange. “AGI” is my interpretation, not an established conclusion from this result. The thumbnail vortex is an illustration.

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They've done it, OpenAI, they are sharing a solution to the Navier-Stokes Millennium

Prize problem, one of the deepest problems at the frontier of mathematics.

In this video, I will be showing you exactly what on earth that actually means, why this is

a big deal, and whether this is the end of AI advancement or just the very beginning.

Before we do that, I'm Lenny, I love making videos about AI, it is currently 1.54am in

the morning.

If you want more videos about AI from an Aussie dude with a Mo, subscribe.

So back to the news at hand, if you have been living under a rock, GPT-6 Astra came

out about a week ago now, and it is the best AI model in the world.

What we're talking about now is a next-generation model significantly more capable than the

best in the world right now, which is already smarter than most people on Earth.

The problem at hand concerns whether the description of smooth three-dimensional fluid motion

modeled by the Navier-Stokes equations can break down.

It has remained unsolved for roughly 90 years.

Here is the part that blew me away.

This model represents a step function improvement on many benchmarks, and its training is ongoing.

But here it is.

Our internal model group arrived at the Navier-Stokes solution in 88 hours using around 10,000 coordinating

AI agents.

Here's a graph, performance of GPT-6 Astra and our internal model on a curated set of

open math problems.

We see two lines on a line graph.

One is GPT-6 Astra, one is this unnamed internal model.

GPT-6 Astra is basically significantly lower than the internal model, continuing on with

the post.

The solution, which is the thing that was just discovered, a spinning swirl of fluid that

spirals inward and gets increasingly elongated like spaghetti.

Then there's a link to the official paper titled finite time blow up for Navier-Stokes.

And this is the vortex that was just referred to.

I'll discuss exactly what all of this means in just a second, but we've just got a couple

more things to take a look at here in the official blog post.

Agents were subdivided into groups with the ability to communicate within the group.

We encourage different groups of agents to explore a diversity of approaches.

After some time, we cross-pollinated agent groups by using Codex to consolidate the

most useful insights from each agent group.

These follow-up prompts drew on the agent's own intermediate results, the group that found

the solution to Navier-Stokes was guided in such a way.

The agents arrived at their resolution on Saturday, September 5, about 88 hours after

the first agents were launched.

So that was done by the internal model and then lean formalization and verification of

these results took an additional 17 hours via GPT-6 Astra, which is currently publicly

available.

Here's a cool part.

Across all attempted problems, the agent sent 4.9 million messages and used about 300

billion output tokens.

And in the process of resolving the Navier-Stokes problem, the agent sent 2.7 million messages

and used approximately 130 billion output tokens.

So the way AI is billed is through tokens.

GPT-6 Astra is currently the most expensive AI model offered by OpenAI.

This is an internal model.

Assuming this internal model was publicly available, which it isn't, and was priced at the same

price as GPT-6 Astra.

That means across all attempted problems, solving the Navier-Stokes Millennium Prize

problem cost 15 million US dollars.

And in the process of resolving the Navier-Stokes problem alone, the commercial cost was 6.5

million US dollars.

Our goal in releasing this result is to report on the substantial progress of AI models.

We do not intend to claim the Millennium Prize for this result.

Very interesting.

Noble, I would say.

This is not a culmination, but rather a snapshot in time of progress on AI development.

We believe we are now in the next period of AI progress, and today's results provide

further evidence of this.

What is the significance of this?

We're going to get to that in just a second.

But what the end of that blog post is talking about is just basically saying AI is getting

really fucking smart, really fucking quickly.

Just to put this into perspective, GPT-5 came out 13 months ago.

The chart that we're looking at now, think of it as a good rule of thumb for intelligence.

Higher is better.

One year ago at its peak was 23 out of 100.

13 months later, it's now at 53 out of 100.

And most of those gains came in the last three months.

And that's only going to continue to accelerate and to get faster.

Like we're just at the beginning of what people call the exponential, where things are going

to get crazy really quickly.

Anyway, to better understand this, who better to help us, or what better to help us, than

GPT-6 Astra itself.

Explain to me in super simple terms what the Navier-Stokes Millennium Prize problem is.

It's a challenge about the equations we use to describe how fluids move, like air or water.

The big question is, do these equations always behave nicely, or can they sometimes blow

up and produce impossibly wild results?

In simple terms, it's asking whether smooth fluid motion stays smooth or can break down.

Explain it even simpler.

Sure.

It's asking if you start with water flowing smoothly, will it always keep making sense?

Or could the math suddenly go crazy and stop working?

Simpler again.

It's asking, will the math for flowing water ever break?

What's the significance of solving it?

Give me an example, put this into perspective.

Think of a flight simulator.

It uses maths to predict how air moves around a plane.

This problem asks, can that math hit a point where it stops giving a sensible answer?

Even if everything starts smoothly, OpenAI says it found a carefully constructed case

where that happens.

If that holds up, it settles a question mathematicians have wrestled with for about 90

years, and reveals a fundamental limit and a hugely important tool.

It's not about real water going infinitely fast, and it doesn't mean planes or weather

forecasts don't work.

The AI angle is also big, helping discover new maths, not just answering old questions.

What would you say are the five most interesting or important things to know?

One, they say they also solved a separate major maths problem on the way involving the

Euler equations, which helped point them in the right direction.

Two, in their example, the water starts completely still, and a smooth external force gets it

moving, so it's not starting broken.

Three, the AI was still being trained while this was happening.

They upgraded the agents midway through the project.

Four, another team had a related result, but not the same result.

Those details matter.

Five, OpenAI says it won't claim the million dollar prize.

They frame this as showing how far the AI has come.

Cool, so I didn't actually know that it was a million dollar prize, but yeah, OpenAI

probably doesn't need any more money.

So I heard whispers that Claude and Anthropic had solved the Navier Stokes Millennium prize

problem on X or Twitter.

Wouldn't be surprised if OpenAI got wind of this.

They thought, fuck you, Claude, deployed 10,000 agents at the cost of around $15 million,

and then just solved the thing in a few days.

OpenAI is so back.

Imagine AI teams exploring scientific ideas and helping finding something genuinely new.

I think that is the future.

The headline from this is they deployed 10,000 super intelligent AI agents to solve this

thing.

They just pointed compute at it, spent $15 million and then just broke frontier math.

If that doesn't tell you that we have just entered the AGI era, I don't know what will.

Let me know in the comments below.

Do you think this is the future of scientific discovery, deploying ginormous swarms of super

intelligent AI agents at some unknown problem and getting them to just work 24 seven around

the clock, thinking about multiple different solutions, like Dr. Strange looks at 13,000

different possibilities.

That's what these AI agents are doing to solve new problems.

Do you think that is the future?

Let me know down below.

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