0:000 seconds	Open eye claims to have solved the Navia Stokes Millennium problem. It's not a secret that I've been working on the same problem in the past year with
0:088 seconds	OpenMai's models and I'm sure so have many others. So, what are we to make of the solution? And is it really as
0:1515 seconds	useless as the critics complain? Let me say that I've been struck by how extremely negative the reaction has been
0:2323 seconds	to the open eye proof. Like you'd think that mathematicians and physicists would be interested in how the proof works,
0:3131 seconds	how openi managed to get it done, what else can be done with it. Instead, everyone's complaining that OpenAI
0:3838 seconds	didn't leave it to humans. For decades, they've complained that private business has no interest in pure maths. Now, they're complaining private business does have an interest in pure math.
0:4848 seconds	Okay, but first, let me tell you what we're even talking about. The problem to be solved is the question of whether a
0:5555 seconds	fluid that's described by the Navia Stokes equation can develop singularities or blowups in finite time.
1:041 minute, 4 seconds	The Navia Stokes equation is the key equation that describes realistic fluids and gases and it's for example used for
1:121 minute, 12 seconds	the weather forecast. The equation looks like this where use the fluid itself and P the pressure. This new is the
1:201 minute, 20 seconds	viscosity. That's a constant. And this F here is what's called the forcing.
1:241 minute, 24 seconds	That's the force that acts on the fluid in each point. Now, it's of course possible to get the fluid to blow up if you make the forcing large enough. So,
1:321 minute, 32 seconds	if you want to solve the problem, you have to show that the forcing itself remains regular. The cleanest way to do this is to use zero forcing. That's also
1:421 minute, 42 seconds	the hardest way. The Omei proof now instead starts with a fluid field that has a blow up. You just insert this into
1:501 minute, 50 seconds	the equation and call whatever's left the forcing. Then you have to prove that the remaining forcing itself remains regular. The entire proof is 160 pages
1:591 minute, 59 seconds	or so. I did not check it. I'll leave that to competent people. But I can make some incompetent observations. The
2:062 minutes, 6 seconds	construction works by supplying the fluid with pulses that come in at specifically chosen time intervals that
2:142 minutes, 14 seconds	adapt to the fluid dynamics. So, it's a deliberately engineered driving of the fluid into a singularity. The simple
2:212 minutes, 21 seconds	singularity they looked at is a type of vortex that becomes increasingly stretched and focused on its center axis. This is what the image shows. This
2:302 minutes, 30 seconds	is totally allowed by the criteria of the millennium problem, but it puts the burden on having to prove that the forcing does not supply unlimited
2:382 minutes, 38 seconds	energy. This means they have to somehow keep track of what the pulses do and sum them all up and estimate the errors and
2:452 minutes, 45 seconds	so on. This is what most of the proofs about. It's lema after lemma about how to estimate the total contribution from
2:532 minutes, 53 seconds	the forcing. Now look, going by what Open AI said, they had literally thousands of AI agents working on this.
3:013 minutes, 1 seconds	o it seems highly unlikely to me that the proof is directly wrong. However, what I've noticed is much more likely to happen with the publicly available
3:093 minutes, 9 seconds	OpenAI models is that they run into circular arguments where they implicitly assume what needs to be proved. They
3:163 minutes, 16 seconds	might for example assume a certain regularity or solvability condition for a lema that actually contained the bound
3:233 minutes, 23 seconds	they had to prove. The issue is that this sort of argument has no actual mistake in the stepbystep procedure. You
3:303 minutes, 30 seconds	see it's like saying if pigs can fly then the laws of gravity are broken and if the laws of gravity are broken then pigs can fly. And that's totally
3:393 minutes, 39 seconds	correct. But it doesn't prove that either pigs fly or the laws of gravity were broken. Just that both are consistent with each other. So it might
3:473 minutes, 47 seconds	be that the proof is consistent in that sense and yet circular in not proving the thing they need to prove. I found
3:553 minutes, 55 seconds	that even GPT 5.6 still struggles with this. By the way, my impression is that the new Astra is worse than GPT 5.6 when
4:034 minutes, 3 seconds	it comes to maths, but that's just an aside. Let me put it like this.
4:084 minutes, 8 seconds	Personally, I think that the Navia Stokes equation does have blowups and the class that they looked at in the proof is the case that most efforts in
4:164 minutes, 16 seconds	the past decade have focused on. So, it's plausibly correct. Still, I'll not take it for granted that the proof's correct until humans have checked it.
4:274 minutes, 27 seconds	Then, let me say something about the question of whether this is relevant.
4:324 minutes, 32 seconds	I've seen a lot of people commenting, "Oh, no one cares. this isn't useful for anything and so on. Well, the reason I've been interested in this besides the
4:414 minutes, 41 seconds	million-dollar prize is that the Navia Stokes equation has a known relation to some problems in general relativity,
4:484 minutes, 48 seconds	especially concerning the physics of black hole horizons. Now, you could say again, okay, but this isn't useful for anything. At which point, I'd like to
4:574 minutes, 57 seconds	ask, well, what's the use of kicking a ball into a net? Personally, I think if some people find it interesting, that's
5:045 minutes, 4 seconds	a use in itself. Can you make money with it? I mean, other than winning this prize, probably not. And I guess that
5:125 minutes, 12 seconds	this will soon dampen open maths enthusiasm. But Sam Outman said he'll now be looking at room temperature superconductors, which I think will keep
5:205 minutes, 20 seconds	GPT occupied for a while. That problem is on a completely different level because it's not mathematically well
5:285 minutes, 28 seconds	defined to begin with. Finally, let me add that I'm aware there's some controversy about whether a rope open my
5:355 minutes, 35 seconds	eyes model sneaked in on someone else's research. I have to admit that I'm super not interested in people's stories. I
5:435 minutes, 43 seconds	really just care about science. You might say, "Okay, but if you care about science, you need to keep people motivated to do it. So, you must care
5:525 minutes, 52 seconds	about people, and if their results get stolen, they won't continue doing it." Well, I guess that's the question we
5:595 minutes, 59 seconds	have to answer. Do we need to keep people motivated by giving them a million dollar prize? Or do we just
6:076 minutes, 7 seconds	leave it to AI to begin with? And will AI companies continue to be motivated if they notice there's no money to make
6:156 minutes, 15 seconds	with it? In summary, I think there's a 90% chance this proof is correct, but a 99% chance that mathematicians will
6:226 minutes, 22 seconds	continue to complain about it. If you haven't yet reached your daily limit of uninformed opinions about useless topics, please subscribe and buy a t-shirt. Thanks for watching.