Millennium Prize Problems
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Search complete. 156 mentions across 97 episodes found for "Millennium Prize Problems".
Oct 28, 2026
LeahHOST
The models also proved a 35-year-old wave conjecture in physics.
AminHOST
Yeah, and solved a portion of a $1 million Millennium Prize problem in mathematics.
LeahHOST
And to ensure this isn't just an AI hallucinating complex math, they have Nobel laureate David Gross leading the independent review.
AminHOST
What is particularly notable is OpenAI's approach to publishing this.
AminHOST
But you hear this old critique all the time, right? That AI is just a plagiarism machine, a stochastic parrot that just remixes text that's scraped from the Internet.
LeahHOST
Oh, constantly.
AminHOST
But you cannot plagiarize the solution to a millennium prize problem that no human has ever solved.
AminHOST
This is net new human knowledge.
Dhaval KapadiaHOST
Now, Navier-Stokes is essentially a conjecture.
Dhaval KapadiaHOST
It's part of the Millennium Prize competition that was basically given very brief background.
Dhaval KapadiaHOST
There are eight problems.
Dhaval KapadiaHOST
that in year 2000, hence the name Millennium Problem, they basically came in and said, you know, math as a collective described these Millennium Problems as so extensive that you essentially had to invent new mathematics to solve each of these problems.
speaker_0HOST
In physics, OpenAI claims a rigorous proof that quantum chromodynamics and pure Yang-Mills theory exist in four dimensions.
speaker_0HOST
That is one part of a Millennium Prize problem.
speaker_0HOST
OpenAI does not claim to have solved the other part, the mass gap.
speaker_0HOST
A group led by the Nobel laureate David Gross is holding back the AI-produced material for now and is writing up the work itself.
ParzivalHOST
And PSI isn't alone.
ParzivalHOST
In September, 10,000 AI agents cracked Navier-Stokes, a Millennium Prize problem.
ParzivalHOST
OpenAI's model wrote more than 700 math papers.
ParzivalHOST
And on three of these five problems, you saw other teams, many of them with AI, land closed results within weeks.
ParzivalHOST
Five papers at once, each with a proof a computer checked, from about 25 people, with models that will look ancient in a year.
ParzivalHOST
So give it a better model, a better harness and more compute, and the batch gets bigger and the problems get harder, it's the staircase math just climbed.
ParzivalHOST
From homework to Olympiad gold to open problems to a millennium prize in about two years.
ParzivalHOST
I want to end on why this matters outside physics departments.
Josh PoertnerGUEST
It's a set of equations.
Josh PoertnerGUEST
A lot of what's going on here is that we – and part of like what the Millennium Prize is, is like we still don't – and I think we've talked about it on this show before.
Josh PoertnerGUEST
Like – There's a lot we don't understand about turbulence.
Josh PoertnerGUEST
We don't really understand why laminar flow transitions to turbulence.
Josh PoertnerGUEST
But what I will say from the The people I have talked to in the CFD world, they are still pretty skeptical and apparently the quote-unquote proof, the paper that OpenAI dropped kind of claiming to have solved this is – pretty brutal even for like the most serious mathematicians.
Josh PoertnerGUEST
So I think the current – I cannot remember the group.
Josh PoertnerGUEST
There's a group that kind of audits the Millennium Prize and I'm just blanking on their name.
Josh PoertnerGUEST
But they have come out and said that they – it will likely take two years to figure out if this – if the proof is a real proof or not and if it's true.
Nilay PatelHOST
And even though I have set off agents to do all kinds of things, there's a brittleness to it that feels inherent to the technology to me.
Kevin RooseGUEST
Did the Millennium Prize problem solution change that view at all?
Nilay PatelHOST
Only in the sense that finding the next thing that has some objective verifiability seems very rich for these tools, right? And so obviously mathematics has a verifiability and the tools got so capable that they could run at it really, really hard.
Nilay PatelHOST
And the brittleness that I'm describing is a lot of the world around us does not have that kind of verifiability.
Igor KravchukHOST
But...
Igor KravchukHOST
A few weeks ago, I think at this point, OpenAI dropped that they had a Millennium Prize solution and that they had found like a particular solution of a like a Navier-Stokes problem.
Igor KravchukHOST
And there was drama afterwards about their approach possibly having been lifted from human mathematicians who were developing the proof in CGPT.
Igor KravchukHOST
And Opmeyer couldn't rule out that the model had been trained on their approaches.
Igor KravchukHOST
response to them?
Jacob HamesHOST
And it was two weeks after-ish they say that they have solved Navier-Stokes, which is, of course, not actually what they did.
Jacob HamesHOST
They met the conditions to unlock the Millennium Prize for the Navier-Stokes Millennium Problem, which means that they had a counterexample for it.
Jacob HamesHOST
Now, that's not to say that that isn't like its own achievement um whether it is their achievement is in question um but it isn't the claim that seems to be said often at the very least
JimmyHOST
yeah So so I think if you look at the rate at which I was accelerating and the fact that if you look at what's happened in the last month and we're going to talk about the PHP stuff later, I won't talk about that.
JimmyHOST
But what I will talk about, because we haven't talked about it, is the Millennium Prize stuff, right? So AI has solved Navier Stokes, essentially.
JimmyHOST
I mean, mathematicians say it looks a bit ugly, but it is a solution.
JimmyHOST
It's advanced the Riemann hypothesis, and they've produced a paper with more than 700 mathematical, at least partial proofs or, you know, things that have advanced mathematics, shall we say.
Connor LeahyGUEST
And given that we now have like, you know, I don't know if you heard this, for example, that OpenAI used a not even finished model that was still growing.
Connor LeahyGUEST
It wasn't even done cooking yet to solve a millennium prize problem, which is the kind of like, not even the Olympics of math.
Connor LeahyGUEST
It's like...
Connor LeahyGUEST
even higher than that.
Connor LeahyGUEST
When was this? Like two weeks ago.
Julian DoreyHOST
Can we Google this, Steve?
Connor LeahyGUEST
Yeah, you can look up the Millennium Prize Navier-Stokes equations.
Connor LeahyGUEST
And so the Millennium Prize are a set of math problems that have been considered like the hardest, greatest math problems for the last 100 years, roughly.
Michael HansonPANELIST
I mean, I can't imagine the scenario.
Joe GettyHOST
So among the major findings, and this might mean something to you, it doesn't really to me, but reported by OpenAI, advances related to three of the five remaining Millennium Prize problems, including the Ryman hypothesis, which I believe is it takes one to know one.
Joe GettyHOST
They've proved that through algorithms.
Joe GettyHOST
Anyway, so AI is now freaking out the world of math.
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