Princeton Mathematician: Wormholes Can’t Survive Einstein’s Math

A Princeton mathematician says wormholes cannot survive Einstein's equations, and the AI apocalypse is absurd. A solution that vanishes under a small nudge is a ghost, not physics. Sergiu Klainerman is a mathematician at Princeton University. With Demetrios Christodoulou, he proved that empty spacetime is stable. We cover: What makes a solution of Einstein's equations physical, why slowly rotating black holes pass the stability test and wormholes fail it, why shocks form no matter how small the perturbation, whether AI can reproduce a landmark proof, and why he calls the AI singularity absurd. Mathematics is discovered, not invented. CHAPTERS 00:00 Are wormholes real? 08:38 What happens at an event horizon 12:06 God does not know about coordinates 17:32 What Maldacena would say about wormholes 21:48 Why extremal black holes matter 28:56 Einstein and the 1919 eclipse 33:52 Terry Tao and Fermat's Last Theorem 43:04 Can universities be reformed? 48:16 What to tell a 19-year-old 50:48 Kip Thorne and the movies Support the show and get the full transcript, bonus content and my Monday M. A. G. I. C. Message: https://briankeating.com/yt Have a .edu email and live in the USA? You automatically win a meteorite: https://BrianKeating.com/edu Subscribe: https://www.youtube.com/DrBrianKeating?sub_confirmation=1 Follow on Spotify: https://spoti.fi/3vpfXok Apple Podcasts: https://apple.co/39UaHlB Support Into the Impossible on Patreon: https://www.patreon.com/drbriankeating Join this channel for perks, monthly Office Hours and your name in the Member Roster: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join Sponsored by me. My three books: Losing the Nobel Prize http://amzn.to/2sa5UpA Think Like a Nobel Prize Winner https://a.co/d/03ezQFu Focus Like a Nobel Prize Winner https://a.co/d/hi50U9U Amazon affiliate disclosure: links above marked to Amazon may earn a commission for the channel at no cost to you. As an Amazon Associate I earn from qualifying purchases. X: https://x.com/BrianKeating Substack: https://briankeating.substack.com Blog: https://briankeating.com/blog Audio-only: https://briankeating.com/podcast #blackhole #generalrelativity #wormhole #Einstein #briankeating #intotheimpossible Learn more about your ad choices. Visit megaphone.fm/adchoices

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• 0:00Speaker 00

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• 0:45Brian Keating?

  What's your opinion on wormholes?

• 0:46Speaker 03

  From my understanding, they are extremely unstable. If it's unstable, mathematically, it has relatively small perturbations. It disappears. Then it's like a ghost. The part inside is pure mathematics now, right? Because we cannot go there. The AIs is going to become more intelligent and it's going to reproduce itself at a huge speed and then And kill us all. It's just absurd. It's ridiculous.

• 1:05Brian Keating?

  Serge Klaiverman is an mathematician at Princeton University. More than 30 years ago, he and Demetrius Christodolo proved that empty spacetime is stable. That sounds simple, like almost a technicality, but it isn't. Every exact solution of Einstein's equations has to survive that test before it even can count as physics. Slowly rotating black holes pass. Wormholes, they just don't. And at the end, he takes the same scalpel to the AI apocalypse that we're all confronting these days. And it all started one question after a talk he gave.

• 1:29Speaker 03

  I was in Berkeley. I came as a postdoc and Yau invited me to give a colloquium at Stanford, which I did. And at the end, so I talked about my thesis. At the end, he came to me and said, well, did you have you consider the stability of Minkowski space? Or something. He knew about it. I mean, even his own interest is also Riemannian.

• 1:51Brian Keating?

  Yeah.

• 1:51Speaker 03

  It's not the answer.

• 1:52Brian Keating?

  But why would that be a question? I mean, why would somebody think, I mean, we don't think of Newtonian Jayson's thing unstable. So why would we think that Minkowski space would be

• 1:59Speaker 03

  Might be more difficult. Right. Because you could say that there is a positive energy, the positive mass, which if he actually, Yau has contributed, this was maybe a little bit later, but about the same time that he and Sean proved the positive mass. And indeed, from a point of view of physicist, you could say, well, okay, that proves stability. And in fact, actually, I remember later on, when I was at Koran, after we proved the stability of Minkowski space was Christodolo. Ed Witten gave a talk in which he said that he had another proof of the stability of mass in, I mean, of the positivity of mass in general relativity. And he claimed that this proved the stability of Minkowski space. So I went

• 2:44Speaker 03

  to him, said, what do you mean? And, well, you know, the dynamical systems, you have positive energy, Hamiltonian, that of course shows. Of course, I mentioned to him the Burger equation, right? You hear about Burger equation. It's an equation in which you also have positive energy and that it's shark forms. And he just smiled, superior, I remember, and just, and he didn't really answer the question. That's the sort of thing. I mean, you know, for finite dimensional system, Hamiltonian systems, having positive energy is good enough. But for infinite dimensional systems, like the case of general relativity, it's not enough.

• 3:23Speaker 00

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• 3:32Brian Keating?

  What does it mean fundamentally that something is stable versus unstable, starting with classical mechanics and then we can go into Minkowski mechanics?

• 3:39Speaker 03

  Yeah. So that means that you have a solution and starts to some initial conditions. You perturbed the initial conditions a little bit. You'd like overall asymptotically for all time, the new solution to be either converging to the one you perturbed or to stay nearby, right? So stability would mean it stays nearby. It doesn't change very much. The profile looks similar, which is of course extremely important because you never have exact solutions in anything, right? In order for that solution to have some kind of physical meaning, it has to be stable.

• 4:13Brian Keating?

  In terms of perturbing it, if you were to perturb it, you could put mass in there or you could send in radiative, you know, excitations like gravitational.

• 4:20Speaker 03

  That's a good question. Obviously, that depends on the problem. So stability can mean lots of things. But within the context of a specific equation, say, I'm interested in compressive Euler equations, right? So I expect that I have shock waves. If I perturb just the flat, the trivial initial condition, stability would mean that you have solutions which stay nearby, which stay close to constant, or I don't know, even converge to the original one. Let's say zero solution, right? The solution is converge back to zero or at least stay nearby. But of course, that's not the case. And the best example is the Burger equation,

• 4:59Speaker 03

  right? Which is the simplest possible compressible equation where shocks form. So you're starting at constant. Let's say also UT. So this is the derivative of U with respect to T plus U times derivative of U with respect to X in, you have one space and one time dimension, so two dimension. It's not a finite dimensional dynamical system. And shocks form no matter how small, you know, whatever perturbations you make, no matter how small, shocks will form, right? So that means the solution, the derivative solution blows up in finite time. You are very far from stability.

• 5:35Brian Keating?

  If we think about, you know, shock waves and sometimes associated with turbulence or, you know, Mach number, Reynolds numbers and things like that, in an empty spacetime, what is a shock wave in that case in Minkowski space?

• 5:46Speaker 03

  You mean in the context of an equation?

• 5:48Brian Keating?

  Yeah.

• 5:48Speaker 03

  The Einstein equation.

• 5:49Brian Keating?

  What, no, physically, what does it represent? Like, what would happen to an observer? What does it do to observers in covariant coordinates? Say you have a population of observers in Minkowski and there's a shock wave. What is being shocked? What's effectively, because this is classical, right?

• 6:04Speaker 03

  Right. So again, I mean, the Burger equation, that's a simple, specific example, right? So you take initial conditions and particles follow characteristics which are very simple, right? They are just straight lines.

• 6:16Brian Keating?

  Yeah.

• 6:17Speaker 03

  But the straight lines can change depending on where you start from, right? It can be a straight line at an angle. If I start here, so this is the line, I start at this point, I get one straight line at this angle. But if I go here, right, the same initial condition, then I get a straight line in this other direction. So they obviously, and the solution remains constant along the straight lines, right? So obviously, at that point, I have I have a solution with two different, two distinct values, right?

• 6:49Brian Keating?

  Depending on initial conditions, yeah.

• 6:51Speaker 03

  Depending on the initial condition. That's a value from the first line and the value from the other line. So obviously, this doesn't make any sense. Something wrong has happened, right? So what happens is that in fact, first derivative of the solutions blow up, become infinite, and then you have to continue the solution. So all of the shock wave theory is a way of continuing the solution past this. And, you know, Riemann is the first, I mean, people may not know, but Riemann, among many things he did, he was also played a very important role in the development of the shock wave theory.

• 7:24Brian Keating?

  I didn't know that. Yeah, I didn't. I mean, we associate him with geometry and then eventually with relativity, general relativity.

• 7:30Speaker 03

  But he also, yeah, he also had a major impact.

• 7:33Brian Keating?

  That's very interesting. Yeah, it sort of makes sense. I mean, Mach was also, you know, very interested in shock waves, turbulence, sonic phenomena. And he came up with Mach's principle. Maybe the last of the philosophical kind of physicists where you could do philosophy, you know, maybe Einstein was the last, you know, think philosophically and then derive something interesting in the physical universe. I mean, we physicists typically look down, you know, with some derision at philosophers. Oh, they don't do anything. They don't produce anything. Although now they're having a renaissance, your fellow, you know, Professor Princeton, Tom Griffiths and others have written, you know, basically philosophers are getting a renaissance now with AI, which we definitely have to talk about in the context of how do we actually know these 800-page proofs that you generate? And is your kind of the

• 8:15Brian Keating?

  Klaiverman brand are valid? And without tools like Lean and other things, I want to get your impressions of, we'll get there. I think the first thing I want to do now is take the reader through something more realistic, add some mass to the problem and you get a black hole, get a Schwarzschild solution, which was first, you know, represented by Schwarzschild, you know, soon after the creation of GR. And it was really kind of late dormant and Einstein didn't really know if it would ever have applicability. But what happens when you add mass? When you add something, you add some point mass, you add something that you can, you still solve exactly. And then it also becomes unstable, correct? So talk about stability in the context of general relativity with

• 8:53Speaker 03

  So you're actually talking about just the vacuum equations or you add the

• 8:56Brian Keating?

  Well, now I want to add a Schwarzschild measure. Yeah. So the stability of a Schwarzschild solution.

• 9:01Speaker 03

  Yeah. So the Schwarzschild solution, of course, is still a solution of the vacuum equation. So you are talking about the vacuum equation was no, it was no sources.

• 9:08Brian Keating?

  Physics was there is a source. It's a point mass of some mass capital M and that's, I mean, otherwise you don't generate, you know. It's not perfectly imaginable, but it's a delta function, right? I guess the point I'm trying to make is black hole solution has a mass, it's a point mass, the Schwarzschild solution, and then you generate things like the event horizon and so forth, right?

• 9:26Speaker 03

  This point of view of void mass and so on, of course, I find it not realistic. I mean, you know, the way we think about the black hole, and I'm more interested in the extent of the black. So you had a black hole is separated. It has a part which looks like Minkowski space, right? So at least far away from the black hole itself, it looks like Minkowski space. But as you approach the black hole, if you are lucky to goes in the direction of the black hole, at some point you pass the event horizon. So this event, the event horizon is a mathematical boundary between the visible part, let's

• 10:08Speaker 03

  say the Minkowski part, in which we live, we believe, right? And the part which is in the black hole. And of course, as you pass the horizon, nothing happens. You don't even know, right?

• 10:19Brian Keating?

  It's like passing the South Pole, which I've done many times. Nothing happened to

• 10:23Speaker 03

  But once you are in, that's it. You can never come out. And then at some point, there will be a singularity. That kind of, the issue of that singularity is more murky. So the visible part of the black hole is sort of thing that, you know, makes sense astrophysically, makes sense mathematically, makes sense astrophysically. The part inside is pure mathematics now, right? Because we really, you know, we cannot go there. Can't access it.

• 10:49Brian Keating?

  Right.

• 10:49Speaker 03

  Cannot access. So if you accept that the Einstein equations are correct and that you have this exact solutions of the Einstein equations and you can speculate what happens inside the black hole. And one thing that you you can easily see mathematically, you can see that at some point there will be a singularity. That that singularity is, you cannot describe it as a point. It's not a point, you're right. It's more like a space, like in fact, if you if you draw a geometric. I mean, you have to be very careful. Once you are in this kind of extreme regimes, you have to be very careful with the with your geometric description. So in reality, it's a space like a hypersurface, right? So that corresponds to, I don't know, r equals zero, let's say, in

• 11:30Speaker 03

  coordinates, let's say, t r, t dot five, which are called the boiling with coordinates. So in those coordinates, r equals zero, the curvature becomes infinite. So then obviously something terrible has happened, right? The problem with general relativity, which is something that really buzzed Einstein, I think, Einstein had promises it also. But many people had, is this coordinate dependent, right? So any kind of description, if you are to describe a solution, you have to pick up some coordinate system, but the coordinate system itself can create problems, right?

• 12:00Brian Keating?

  Right. Yeah, the cross-coordinates.

• 12:02Speaker 03

  Because that's what I was, for example, that's the best example, right? So it took people, I don't know, forty years, maybe more, I mean.

• 12:09Brian Keating?

  In nineteen sixty-five, yeah.

• 12:11Speaker 03

  Right. You took two fifty years to actually understand. Einstein, same was buzzed, I remember that. He was in Paris, actually, where people were asking him about it and he he looked very fancy. They had a lot of issues with this, right? So that's why I'm saying, so coordinates, this, the geometric description is very much coordinate. If you want to visualize things, you have to pick up a coordinate system.

• 12:33Brian Keating?

  That's right.

• 12:34Speaker 03

  And then you.

• 12:35Brian Keating?

  And then that's, listen, he's sort of philosophically at least committing, you know, hate crime against the the notion that all the laws should be coordinate invariant, right? So you'd like to think so, but in the universe as a whole, you can't create such coordinates, right? It's a cosmology, there's no such thing, right?

• 12:50Speaker 03

  And there is, I mean, God doesn't know about coordinates, but you could say, but we as humans are, in order to solve a problem that has to do with general relativity, we actually have to look at the coordinates, right? So, so for example, the stability, both the stability of Minkowski and even more stability of Schwarzenegger. The coordinates play a fundamental role in the proof, the coordinates play, the choice of coordinates play a fundamental role. You couldn't do anything without them. In fact, actually, I would say the, maybe the principal role, I would say, almost.

• 13:21Speaker 00

  At Edward Jones, we believe rich is more than caring about the latest and greatest. It's also taking care of what gives your life meaning. That's why your dedicated financial advisor meets you where you are with personalized financial strategies that help protect what matters. So you can preserve your progress while creating a path forward. The key to being rich is knowing what counts. Let's find your rich together. Edward Jones, member SIPC.

• 13:51Speaker 03

  I mean, there are many things that go into the proof, but one of the fundamental issue is a problem of gauge. Your description of stability is based on a choice of a gauge, additional coordinate condition.

• 14:03Brian Keating?

  And there's no unitary way.

• 14:05Speaker 03

  Right. It's highly non-trivial, because you cannot, you cannot impose it, no, actually, any proof presumably would have this issue. You cannot impose it from the condition, from the initial conditions. You you cannot say what the correct coordinate system should be.

• 14:17Brian Keating?

  Should, should be.

• 14:18Speaker 03

  You have to, you also find it dynamically, right? As you solve the problem for long, you you have to solve the problem for long time, infinite time, you, at the same time, is solving for the solution of the Einstein equation, you actually solve for the gauge in which the solution is is described. That's what makes it very hard.

• 14:36Brian Keating?

  It's not that you choose the gauge and then that enforces the form of the solution. It's that the gauge will change.

• 14:40Speaker 03

  The choice is dynamical itself. In other words, you you constantly change the gauge as you as you evolve.

• 14:46Brian Keating?

  So that's unlike any other approach. I mean, in in particle physics and electromagnetism, you have one, you know, you'll choose a gauge, you'll choose Newtonian, you'll choose whatever, you don't, you don't continually dynamically change it. So that's unique. That's at least as far as I understand. I'm not an expert, but.

• 15:00Speaker 03

  There is a modulation theory that that people have used also in describing as a kind of nonlinear equation. I mean, it's a nonlinear fact. In linear theory, you don't have to worry about, I mean, you choose a gauge and you stay with it. But for some nonlinear problems, if you want to describe some non-trivial solutions, you you have to also do some modulation, which means sort of picking up the correct physical, the correct mathematical description of the solution, right? The solution usually depends on some parameters, depends on coordinates, and so, in this case, coordinates, in other cases, depends on other things. In that case, you also have to find a solution together with the correct modulation to describe.

• 15:41Speaker 03

  So, but this was done usually for equations which are much, much simpler than the Einstein equations, or which the the choices are finite dimensional. The Einstein equations, the the gauge condition is infinite dimensional. So it's a fully coordinate, I mean, the full diffeomorphous group, right?

• 15:58Brian Keating?

  That's such a monster. You perturbed this, you perturbed spacetime, you sent in gravitational radiation, you send, you look at its behavior, its stability in space. What if you sent in other excitations, electromagnetic gauge, you know, you want.

• 16:10Speaker 03

  So you, you, so that would be now, right? So when you talk about stability of care, right?

• 16:15Brian Keating?

  Instability.

• 16:15Speaker 03

  That's the next level. When you are talking about the Einstein equations in vacuum, right? If you, you can talk about Einstein equations coupled to, say, Maxwell field. And then you have the Kähler Newman, instead of Kähler, you have the Kähler Newman problem, which, you know, it's another it's another problem, but you would like to prove stability. There's been some progress, but there is no yet solution, like say, our, my solution is Jeremy Seftal and

• 16:47Speaker 03

  Alina Georgi and and another student of, there are five papers, I mean, anyway, it's a long, it's a long project. But the ideas from that one can of course be used also for the the the case of the Kähler Newman solution.

• 16:59Brian Keating?

  But you talked about, you know, these these problems, these problems of ghosts or artifacts. What does that mean in a mathematician and in a solution? Is it what, you know, Einstein was saying, you know, the kind of, you know, subtle is the lord, but not, he's not malicious, you know? What is a ghost? What is a, what is an anomaly?

• 17:14Speaker 03

  Yeah, this, I mean, I used it as a sort of

• 17:20Speaker 03

  metaphor for instability, right? So, you you know, in the case, again, let's go back to stability of care. You have an exact solution of the Einstein equations in vacuum, right? I mean, so mathematically, if you accept mathematics always accepts something, right? I mean, it's always in the context of some, something, either an axiom, a system of axioms, or in this case, the axiom would be that you accept the Einstein equations, and therefore, we are in the realm of general relativity.

• 17:49Brian Keating?

  Yes.

• 17:49Speaker 03

  Right? Classical general relativity, we don't talk about quantum.

• 17:52Brian Keating?

  Right.

• 17:52Speaker 03

  Right? Talk about classical. So in that context, you solve the Einstein equations, you find an exact solution, which is a Kev solution. So it's extreme, I mean.

• 18:00Brian Keating?

  This is for, as you say, it's a rotating massive black hole.

• 18:03Speaker 03

  It's a very large black hole, which you you can write down explicitly, you can check, right? Either by hand or you can use AI nowadays, you can check that it's indeed a solution, exact solution. So there is no issue. Mathematica, the mathematical reality of the Kev solution is uncontestable, right? Okay, but turns up the question, is it physically relevant?

• 18:25Brian Keating?

  Yes.

• 18:26Speaker 03

  So my metaphor about that is that, but somehow, if it's unstable, mathematically, in other words, very little to small perturbations, it disappears. Then it's like a ghost. It's a physical ghost that doesn't have any.

• 18:39Brian Keating?

  Manifestation.

• 18:40Speaker 03

  It doesn't have manifestation. So that that would be the.

• 18:43Brian Keating?

  So let's talk about the curved black holes, because it's going to dovetail into a conversation ahead when Juan Maldacena, your, you know, fellow Princeton dweller, was sitting in that chair. And it has to do with wormholes and and sort of the work that he's done, which does branch, you know, away from, I would say, what a physicist would call real or or important even. So talk about wormholes, let's let's stop there for a second. To build a wormhole, it it seems almost impossible. It seems, it seems actually logically contradictory, even though they appear in movies and my friend Kip Thorne won the Nobel Prize for, you know, his work with black holes, but he's the one who popularized it for movies like Contact and Interstellar. Right? So tell me, is a wormhole not just possible? I mean, of course, things are possible. We go into the impossible here.

• 19:28Brian Keating?

  But is it a real object in the sense that a black hole could be considered, whatever extent you consider a black hole real, is a wormhole? Because to build a wormhole, you need to build multiple black holes, you need to sort of have them be traversable, you need to have them be stable, you need to have them admit, you know, certain, certain dynamical properties. But you could think of a unicorn also, right? So, and just because you can think of it doesn't mean it exists. So what's your opinion on wormholes? Are they constructed of curved black holes? I mean, are these even possible?

• 19:55Speaker 03

  From my understanding, is that they are extremely unstable, right? So there are probably zillions of solutions of the Einstein equations that are unstable, mathematically unstable. But of course, I I think, so for, in the context of what I said before, classical general relativity, they are clearly unstable as far as I I can see. Right? So so you you can construct a solution. I mean, even Gödel constructed some cases.

• 20:22Brian Keating?

  Rotating, sliding universe, right?

• 20:24Speaker 03

  Clearly, it's unstable. So in other words, if you want to understand dynamically, in the context of the dynamic social affair, it's clearly unstable, right? So it's it's it classically doesn't make any sense. Now, I think what Maldacena would be saying is that.

• 20:41Speaker 03

  But quantum mechanically, they do make sense and they are useful quantum mechanically. But of course, it's way beyond my gray. Right? I mean, I, I can't say anything whatever what he really wants to do. Quantum mechanically, I mean, I, I, you know, quantum mechanics is very, it's not that I, I would be, if I had another life, maybe I would be. But unfortunately, you know, we are all limited in terms of what we can do.

• 21:05Brian Keating?

  Yeah. What is your taste say that makes a problem interesting to Sergio Kliman versus me, Brian K, an experimental physicist? When do you get interested in a problem?

• 21:13Speaker 03

  The part of mathematics that I, I think is interesting is the one that has something to do with the physical world, right? But it's maybe a shadow of the physical world or a, yeah, there is some complicated intimate relationship with the physical world. I mean, I think all beautiful mathematics started like this. I mean, we even say numbers theory or, or geometry, right? They will start from numbers and, and shapes which are physical. I mean, physical. Numbers, of course, are abstractizations of physical things, one, two, three, right? And, and shapes are also there.

• 21:46Brian Keating?

  There's no triangle. Give me a triangle. You can't do it.

• 21:49Speaker 03

  Right. No, but, but geometry started however, this need somehow to describe things which are physical. But then it went to different levels and good mathematics started to follow its own logic. And, and you know, you can start up with triangles and circles and so on, which, which have some connections with the physical world. But then of course mathematics takes over and you, you know, after a thousand years or more, you get to Remarion geometry. And then Lorentz and Minkowski and, and the special relativity, and all of a sudden it has enormous impact on, back in physics. So, so I, what I wanted to say is that, uh, on one hand, like the kind of mathematics that, that has its origins in the physical world.

• 22:31Speaker 03

  But also like the freedom of mathematics to follow its own logic and its own path and.

• 22:36Brian Keating?

  Hey, do me a favor. I know you're enjoying this on YouTube, but make sure you follow me on Spotify too and leave a review. That helps out more than I can tell you. But you're not immune to it either. I mean, looking at your, looking at your career, it would seem to me, I could predict with almost, you know, a hundred percent certainty what you're going to work on next. Because there's these unanswered questions from the real physical universe. I'll just tell you, I think maximal black holes. I think extremal black holes, incursion black holes, you haven't done that yet. I mean, you've done incredible gel. And I, I'm like, that's, you got it. You did it for slow rotating black holes. So explain why it's, it's natural, not just because well, fast is better than slow. But why are extremal black holes kind of the, the final, you know, the event horizon of black hole stability theories?

• 23:18Speaker 03

  I mean, I, I think they're stable and to start with, the physics is like them.

• 23:22Brian Keating?

  Yeah. They seem to be relative. They seem to power black holes, jets, accretion discs, quasars and so forth. Not, not, not truly maximal. I don't think, I don't know if truly maximal black holes can even exist.

• 23:32Speaker 03

  Oh, close.

• 23:33Brian Keating?

  Curves Kirk. Yeah.

• 23:33Speaker 03

  Oh, yeah. No, large, large triangle. Yeah. This, this is one of the major problem that, you know, many people are still working on, right? It's, it's a stability of care for large A. So in principle, you could go all the way to what is called the subextremal care, right?

• 23:48Brian Keating?

  And your theory would still hold, your proof would still hold.

• 23:50Speaker 03

  I think there's been a lot of work. It's my, my, my former collaborator, Jeremy Seftel.

• 23:55Brian Keating?

  Yeah.

• 23:56Speaker 03

  Has, has done some recent work which really indicates that the problem would be solved. In other words, that you, you could prove the stability for the subextremally.

• 24:08Brian Keating?

  In classical mechanics, we have the notion of the Poisson bracket. We can make a Poisson bracket. We can take the conjugate variables, momentum and position. And then we can form, you know, the mixed partial differential, you know, kind of, uh, relations between them. And we get Lagrangians and we get Hamiltonians and we get their dynamics. And if you do that, um, in classical mechanics, it works out and you get equations of motion. And you can't do it in quantum mechanics without adding the square root of negative one. And it's just so bizarre to me that adding in the square root of negative one, now you get the Heisenberg equations, you get quantum account. Why should that be? And then if that's true, Sergio, are there other levels of abstraction analogs of the square root of negative one? Quaternians, octonians, sextuppians, or whatever comes beyond them.

• 24:53Speaker 03

  Yeah.

• 24:54Brian Keating?

  Are, are they all manifest? And in other words, are all mathematical objects manifest in the physical world?

• 25:00Speaker 00

  At Edward Jones, we believe rich is more than caring about the latest and greatest. It's also taking care of what gives your life meaning. That's why your dedicated financial advisor meets you where you are with personalized financial strategies that help protect what matters. So you can preserve your progress while creating a path forward. The key to being rich is knowing what counts. Let's find your rich together. Edward Jones. Member SIPC.

• 25:30Speaker 03

  I wrote actually an essay about this, which to Wiggs, yeah. So, yeah, we're going it. Which I don't have a solution of the weakness mystery, as I say in the essay, but, but I, I tried to somehow understand it on my own terms. So one conclusion that I, I got sort of reflecting on these things is that what we call, it's concerning what we call reality. What, what is reality, right? I mean, you know, you can start with, with things that you can see, touch and hear. And you can share information about it, right? I can see these flowers, you, right? So there is objectivity, direct objectivity associated with it, which is given by the senses, right? So we call that real, right?

• 26:07Brian Keating?

  Yes.

• 26:07Speaker 03

  But then you go further, right? And you, you start talking about things that are far away and you need a telescope to see them. Or, or black holes which are not even bright, I mean, you know, so clear. Or you have very little, uh, direct information or microscope and so on and so. So, so, so those that we consider real also, why? Because they are consistent with everything else that we started with. So it's like running sort of circles of reality. You have the first circle, which is the most direct connected with our senses.

• 26:37Brian Keating?

  Right.

• 26:37Speaker 03

  And then the next one, which is further away and, and it's all direct already. But, but you know, you, you can relate to a microscope.

• 26:46Brian Keating?

  It's, it's reliability. You're bringing up a good, excellent point that when you have something that is trustworthy, it's to an experimentalist, it's always subject to falsification, but we don't have Gödel in physics. We don't have an incompleteness theorem. The best we have is falsification, which means the violation of reliability, doesn't it?

• 27:02Speaker 03

  That's exactly my point. So my point is that there's these circles of realities which are further and further removed from, uh, the center. They are connected by, as you say, reliability or consistency or what I call objectivity. As they go further and further away, they become more and more mathematical. I mean, you know, surprise, surprise. I mean, the, the.

• 27:21Brian Keating?

  More abstract, more.

• 27:22Speaker 03

  It becomes more abstract. Now mathematics, okay. So this is on one hand. On the other hand, mathematics is also very objective, right? That we, we deal with things which again are very consistent.

• 27:31Brian Keating?

  Yeah.

• 27:32Speaker 03

  So do I have any right not to call them real?

• 27:34Brian Keating?

  Right. Even now, concept is real numbers, imaginary numbers, rational numbers.

• 27:39Speaker 03

  And they, how do they, and then mathematics develops in this very strange way, right? I mean, it starts with numbers and, and the, you know, basic properties of numbers, computativity, associated and so on and so forth. So then somehow for me, algebra comes out, equations, and then, you know, we start solving equations and you get the I at that point. And the mathematics evolves through this, it starts again from, from basic objects like numbers and shapes. But it builds up, uh, uh, levels of, I mean, these concepts and which are very far, I mean, which seem apparently very far away. I mean, you know, we talk about an equation. I mean, what does it, an equation, it seems like something very abstract.

• 28:24Speaker 03

  It has nothing to do something that we see, right? Not to speak about the Einstein equations.

• 28:27Brian Keating?

  No, it's true. C equals mc squared, even simpler. But Pythagorean theorem seems much more real than any physics equation, right? Even though we can't touch a triangle, right? Hand me a triangle. You can't do it. You can think of it only in your mind, which maybe segues to the next point, which I want to talk about AI and computation.

• 28:44Speaker 03

  Yeah. But, but just to finish this, so, so anyway, so for, for me, mathematics is real as, not any kind of mathematics is directly connected to the physical world. Some people say that everything that is consistent mathematically is real, right? It has physical significance.

• 28:58Brian Keating?

  Right.

• 28:58Speaker 03

  I, I'm not going to go so far, but everything that has, has developed naturally, starting from, from the basic physical objects. Through, I don't know, through the natural developments of, of mathematics, which I, I talk about it in this essay.

• 29:16Brian Keating?

  Yeah.

• 29:17Speaker 03

  There's a clear idea about how, how, I mean, I, I should say clear, but I have some idea about how this, how this works out. So that, that's, that's the kind of mathematics that should not surprise us that it has a huge impact back into physics.

• 29:31Brian Keating?

  But it, it does shock one when you think that you're using Fourier's, you know, theorems. He described originally to describe, you know, heat flow in a, in a metal plate in 1800, 1820, whenever he was working. And then you're sending Fourier modes into a black hole, you know? I mean, that's kind of shocking that these things couldn't be more removed on a physical scale. And yet they have identical pedigree mathematically. It's, it is shocking. And I don't think anyone can really, I mean, Wigner didn't answer it either, right? I mean.

• 29:59Speaker 03

  Thing that doesn't answer, and actually he, he makes him our opinion mistakes that many physicists make, which is to claim that somehow mathematics is come of an invention of the human mind. He says it very clearly and he says it completely reject. It's not, it's not an invention. It's discovered. I mean, mathematics is discovered, right? It's just like the physical. World discoveries, we also, you know, mathematically discover.

• 30:22Brian Keating?

  Let's talk about, you know, how we know what we know. In the case of these proofs, some of which, you know, are in excess of, you know, 500, 800 pages, and it's not uncommon in mathematics. I mean, first of all, it reminds me of what Einstein said, you know, when they made the 1919 eclipse expedition, the Eddington expedition, to see if the, the sun's mass bent rays of light in from distant stars. And of course, he confirmed it. And Einstein was asked, well, what would you have done if they couldn't confirm it? He said, well, I would have felt sorry for God. Because on the other hand, you know, four years earlier, he was wrong. He had the new, he had the factor of two wrong. So it was a good thing that the eclipse of 14, 1914 was, was eclipsed by war in the Crimea.

• 31:06Brian Keating?

  Just a quick interruption from today's sponsor, me, Brian Keating. Since it's Nobel Prize season, I can't resist advertising my three books. First book I wrote is called Losing the Nobel Prize. It's a cosmology story mixed with a memoir of what it feels like to do science at the highest level, and spoiler alert, fail. But my next book, Think Like a Nobel Prize Winner, tells the story of nine Nobel laureates who will reveal their insights and actions, how to take your science, or just your job in general, to the next level. It's full of insights and tips that I never would have thought of. And lastly, my book published last year, Focus Like a Nobel Prize Winner, is written for students of all ages to learn the tools and the tricks to compete with yourself,

• 31:51Brian Keating?

  which sometimes can be the hardest competitor of all. Get all three of them, Amazon affiliate links in the description below. And if you've read them already, I'd love it if you leave a review. Every single review helps. Now, back to the episode. But tell me, Sajju, when you look at this, who could possibly check the proof? And how is that possible? And was that the sort of the last human check proof of that magnitude? Or are we just going to lean, talk about, we'll talk about AI proof checking, but, but who, like, who could referee such things?

• 32:19Speaker 03

  Yeah, okay. So it's a long paper because, for many reasons in particular, because we wanted to be very thorough, yeah, very thorough, and we complete, right, without, I mean, many papers refer to other papers, results from other papers. We want to have, essentially, you can read the whole paper from beginning to the end. It's completely self-contained. So that's one thing. And also, we try to put all the calculations. I mean, again, many papers, people don't really put the calculations, right? I mean, you just write down the conclusions. So anyway, we wanted to be very complete. That's one thing. The second is that the proof, these proofs are very conceptual. The only reason you can do a proof like this is because it's very conceptual, right? It, you know, you

• 33:03Speaker 03

  can split it into various parts. Now, this is an only, Einstein questions are more linear, which means that all, every part influences another part in some way. So you, you have to develop a language of how to put these pieces together. But it's very conceptual. I mean, at the end of the day, it's very conceptual. That's second answer. The third answer is that many of these long proofs, if a result is important, then the proof will simplify in two ways. I mean, first of all, some of the things that are used in the proof will become standardized, right? So they are part of the field, right, that every student that works in that field would have to know. So in that sense, it's.

• 33:44Speaker 00

  At Edward Jones, we believe rich is more than caring about the latest and greatest. It's also taking care of what gives your life meaning. That's why your dedicated financial advisor meets you where you are with personalized financial strategies that help protect what matters, so you can preserve your progress while creating a path forward. The key to being rich is knowing what counts. Let's find your rich together. Edward Jones, member SIPC.

• 34:14Speaker 03

  A paper later on will be simplified, and instead of having 2000 pages, will have only 400 pages, right? Which is what I expect to happen. So this is, I mean, so that's, that's my answer. I mean, things, things to simplify in many, many ways. But if the result is important, people will try to simplify, will try to go beyond, right? I mean, other people will take over and do something else with an method which we use. And that's how in time is, I mean, the, the best way for, for something to, to, to be verified. In the short run, I mean, if you're asking how the paper was accepted, obviously, a lot of people looked at it, they, different people read different things. In the future, it will become much easier, as you say, because of AI. I mean, I think AI is going to presumably

• 34:59Speaker 03

  be very good. Maybe not, not to delude a whole proof, but let's say, somebody who wants to check the proof would ask AI to check. First of all, we'll have to have some idea about the whole. And then if that person would be unsure about one thing or another, we'll ask AI to help. So I think AI is fantastic from this point of view. I think it would be a great, a great.

• 35:23Brian Keating?

  What's the, what's the most complex proof that AI has reproduced? Because we hear a lot about these Erdos problems. I was pouring your coffee earlier, and I said, you know, we have to make, pay homage to Erdos. You do fewer amphetamines than he did. You know, he said to Ron Graham, who was my colleague here, as you know, when Ron asked him to give up taking amphetamines for a month, that he did it, and then he collected the $500 bet and told Ron, you set back mathematics for one month. So you don't use math, but but other mathematicians have, but you like coffee. But we hear about the Erdos problems falling every day now from, you know, different, different models. But to my knowledge, I talked to Terry Tao, as you know, you gave me a couple of hints, questions, and me prep

• 36:05Brian Keating?

  for that interview last year. You know, he told me that it can't, quote unquote, even do things like reproduce Andrew Wiles, you know, proof of Fermat's Last Theorem. That's not something simple. But what is the most complex, I mean, can it do the piano?

• 36:18Speaker 03

  It can, it cannot.

• 36:19Brian Keating?

  It cannot. He said it cannot. I mean, if you know, if it's changed since then, it could have with the progress rate that's happening. But tell me, what, what is sort of the most impressive, just reproduction of like the piano axiom? What has it done that is, you know, beyond like helping you, like a good graduate student can help you, I'm sure, and you must have billion ones. But, but tell me, like, can it reproduce things we call, in the art world, it's called copy work? Like, before you want to be the next Picasso, show me you could paint everything he did, or Rembrandt, or whatever. Don't just start off, I'm the great. And we both know mathematicians that think that they have theories of everything. And before you do that, show me that you can reproduce it. And I don't know, is there anything that AI can do that just straight up reproduce a proof that a genius mathematician, or, you know, not prove the Riemann hypothesis,

• 37:03Brian Keating?

  but prove some things that have been landmark proofs in mathematics without human intervention?

• 37:08Speaker 03

  I mean, I would argue that that's probably not possible. I mean, you know, Peter Sana, who is my colleague, he has this, called it Alpha Zero Test. He calls it, which is, so he connects this with chess. So, you know, chess, there are two ways now to automatize chess. There is a procedure which is based on creating large libraries of openings, movements, that AI knows and then is going to use. And of course, it's so fast that it will beat everybody. But then there is this, this Alpha Zero model that starts from nothing, right? So it just, you just give it the rules, the rules, and then it starts clear by itself. And then after a while, it beats everybody. In fact, it beats even

• 37:53Speaker 03

  the best computers apparently, from what I understand. So then is Alpha Zero Test is, is, can you give to AI, give it just the piano axioms, let's say, and then develop whatever, you know, you ask, you have to do mathematics. I mean, that's the, AI do it? Most probably not. I, yeah, I mean, I have reasons to think, you know, AI intelligence, it's remarkable, as remarkable as it is, I mean, it is impressive. I mean, I'm using it more and more also myself. And it's just pretty stunning what it can do. But still, it's, it's not, I mean, to claim that somehow LLMs are at the same level with what happens

• 38:35Speaker 03

  in the human mind, it seems to me a huge, a huge stretch.

• 38:39Brian Keating?

  Yeah. I've tried to do what I call the Einstein test. If you take LLM now, if you take Claude, or, you know, OpenAI, or whatever, and you say, you know, tell me about the multiverse, or tell me about this and that, it knows so much, not just from, you know, the physics, but also from the culture. In other words, there's, there's the movies about wormholes, like we just talked about. There's movies about, you know, Stephen Hawking and Hawking Radiation, right? So you can't even trust the, the training data, which is a large fraction of what makes these things unique. So, so we, we tried asking the following quote, what if you gave, what if you gave it an LLM lobotomy? What if you took everything about the, you know, physical world, just trained it on stuff before 1900? You know, could it come up with quantum mechanics and relativity? And of course, there are other people working on this, and there are people that have

• 39:24Brian Keating?

  actually made these LLMs and actually denatured them, denuded them of any pop culture references after 1930. But that's even too late for quantum mechanics, right? And relativity. And it really, we tried to do it with just giving a data from the planet Mercury and just this orbital history over thousands of years that JPL has. And it gave us back, you know, it couldn't derive, you know, the Riemann curvature, couldn't derive the Ricci tensor. What it gave us back is this very discretized, you know, hyper fine resolution, and it matched the planet. But it was just, it was just copying, it was just mimicking it. And I think until that's passed, I'm not going to be, because you know what Einstein said was the happiest moment of his life, was that in free fall, I wouldn't feel any gravitational field. So that led to the.

• 40:06Speaker 03

  That's a kind of, exactly. How does it, that's about, you know, I know another thing to talk about.

• 40:10Brian Keating?

  It's happily, yeah, I'm going to talk about the AI, about their thinking and.

• 40:13Speaker 03

  And that's exactly my, so I have, I made various points about the fact that, you know. AI, I could very well imagine that AI can do all sorts of things, but it doesn't change itself, right?

• 40:25Brian Keating?

  Yes.

• 40:25Speaker 03

  You know, humans are able somehow to design something new. I mean, can it design another version of itself based on different principles? Like, for example, when we invented the, you know, flying, right? I mean, it was, you know, an invention that completely changed the world. I mean, you cannot say that it was continuous

• 40:44Brian Keating?

  privilege, right?

• 40:45Speaker 03

  Of something else. Or the same thing with Keppler's laws, for example, right? You could imagine based on periodic approximation, the epicycles.

• 40:55Brian Keating?

  Epicycles, yeah.

• 40:55Speaker 03

  So if it's epicycles, you could approximate everything.

• 40:58Brian Keating?

  Perfect.

• 40:58Speaker 03

  I don't know.

• 40:58Brian Keating?

  It was better, yes.

• 41:00Speaker 03

  Epicycles, you could absolutely everything, right? So I say, but would you discover Newton, you know, Keppler's laws? And even more important, Newton's law?

• 41:07Brian Keating?

  Right.

• 41:07Speaker 03

  And Einstein goes, come on, I mean, give me a break.

• 41:10Brian Keating?

  Right.

• 41:10Speaker 03

  It's, it's just not even close, based on what we know so far. And also, you, you can go to, to more specific things, like, for example, it's pretty clear that our thoughts, I'm not, I'm not talking about all thoughts, but

• 41:24Brian Keating?

  Yeah.

• 41:25Speaker 03

  But the one that matter predate the language, right? We, we have an intuition about something and then we find the words to explain it.

• 41:32Brian Keating?

  Right. It's like a proto-language, right?

• 41:34Speaker 03

  I mean, that, that, that's something that, that AI doesn't have. I mean, AI is completely based on guessing the next word, the next token. In other words, it's completely based on, on words.

• 41:44Brian Keating?

  Yeah. Language, yeah.

• 41:45Speaker 03

  On language, right? But as I said, I mean, I, I think our thoughts are predate the language, right? We, we can say, yeah, we, we have intuitions about things, which

• 41:55Brian Keating?

  We have a physical embodied motion, like Einstein falling in space. He doesn't, I don't have to tell, I can't describe that to you, but you know exactly what it feels like to go in a roller car or fall in love and what.

• 42:04Speaker 03

  Like his embodiment, right? Embodiment problems is huge.

• 42:06Brian Keating?

  But I mean, how, you, you know? It's like, well, maybe we blow a capacitor, you know, and the computer, when it gets the wrong answer, you know? How do you train it to have pain or loss or quinancy? What does that even mean?

• 42:17Speaker 03

  And then these absurd notions that, that people have, including very smart people, right? They claim that somehow, you know, we passed the event horizon or the

• 42:28Brian Keating?

  Yeah, the singularity, they call it, yeah.

• 42:30Speaker 03

  You are going to see, right? The AI is going to become more intelligent than everybody and is going to reproduce itself at a huge speed and

• 42:36Brian Keating?

  And kill us off, whatever, you can.

• 42:38Speaker 03

  I mean, it's just absurd. It's ridiculous. I mean, even this business was, was killing ourselves. We can stop it in every moment. I mean, if it becomes dangerous, we can stop it.

• 42:47Brian Keating?

  Right.

• 42:47Speaker 03

  We can destroy it. We could, you, you know, we just, we, we just stop the internet and that's it.

• 42:52Brian Keating?

  Exactly. And, and another thing, I always joke, what's the first thing you do every morning that use AI? Push here to update to version 1.974. And then you go to, push the update to 4.327. Every single day they're updating, they're responding to attacks. If there was, it's kind of like the grandfather paradox, you know? If, if a time machine was possible, you could go back and kill your grandfather, which would prevent you from inventing a time machine. Here, let's assume artificial superintelligence, you know, the most powerful intelligence that'll ever be made. It wouldn't make itself. It wouldn't allow itself to be made because the next thing after it, version 1.9, is going to be more powerful than it. Turn it off. And so, yeah, I think these things are overblown, but they do have a very important purpose.

• 43:30Speaker 03

  Yeah. Oh, no, certainly.

• 43:31Brian Keating?

  They, no, no, the purpose is to generate revenue for these closed model AI leverage.

• 43:35Speaker 03

  Well, but they also scare everybody.

• 43:37Brian Keating?

  They, they scare everybody to get more money. So the government will protect them as a natural resource, like the, like uranium stockpiles.

• 43:43Speaker 03

  No, but, but the problem is now lots of people are calling for, for the destruction of data centers.

• 43:48Brian Keating?

  That's a separate issue, I think, yeah. I mean, I think Musk has, you know, they're saying very far, I see.

• 43:53Speaker 03

  Yeah. But does Musk really believe? I mean,

• 43:56Brian Keating?

  Well, if he, if he does want to build, I mean, he changes his mind, yeah, more frequently than my toddlers that, you know? But, you know, it went from going to Mars, now then it was going to the moon. Now it's not important anymore because we can have AI reproduce everything. But sticking with, you know, kind of this, this thought about, you know, where, where does humanity come in? Your tablet essay, I think it's, it's, it does stress the kind of uniqueness of humanity, but it's not, it's not something like, you know, Pollyanna, you know, everything's going to be okay, everything's wonderful. No, I mean, I think there's huge, there's huge benefits and you and I know how powerful it is and how fast science can change. I guess we don't have that much time, we both have other things to do later on today, but I do want to talk about being a professor nowadays in the age of AI. Is it really worth being a, I mean, do students need to pay? What is your tuition? $70,000? I mean, our state tuition's about that now.

• 44:41Brian Keating?

  I think Princeton's about that, one of the highest levels. But with all these tools, with all these wonderful things, with self-teaching, with, with all the available things on the internet, including conversations with you and your writing and, and the podcasts and stuff that you do and I do, do we need to pay $70,000? What are you really getting for your money?

• 44:57Speaker 03

  No, no, of course. I think it's ridiculous, I mean, universities.

• 45:00Brian Keating?

  How would you restructure Princeton?

• 45:01Speaker 03

  I'm very, if you were I, you know, I, I used to be more optimistic. That's how I got more involved in, in

• 45:08Brian Keating?

  Reform and

• 45:10Speaker 03

  doing, yeah, reforming and so on. I am very, I'm becoming, actually quite pessimistic that universities can be before, except by creating new universities. I mean, creating completely new institutions that will have to compete with this, this other ones. I mean, in science, it's not so bad, of course, but I'm a firm believer that a good education should involve also humanities and social sciences. I mean, I don't think you can be a good scientist without sort of a firm foundation and so on. You have at least some understanding of basic philosophical issues.

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• 46:10Speaker 03

  Anyway, so, yeah, I mean, I, to be a good scientist, you also have to have a broad view.

• 46:15Brian Keating?

  Yeah, I said, Galileo was one of the best writers, period, you know, in human history. And he happens to be, you know, a scientist as well. Einstein was phenomenal. Newton wasn't quite as good. I mean, he was much more dry, I think, Newton. You know, in terms of university, politics and so forth. I mean, when you and I started, you know, a year older than me, but, but when you started university, it was very different. I mean, it was sort of the, the best job I could possibly imagine. And nowadays, I don't know if I could advise my children

• 46:38Speaker 03

  To become

• 46:39Brian Keating?

  to become a professor, an academician. It's not necessarily only the life of the mind anymore. It's become so much more. You know, I want to give you credit for inspiring me personally, but, but also doing incredible work as a scientist, but also a scientist and speaking out on behalf of people that you don't agree with. I mean, you're unique in that you, I, I don't know if I have the same courage as you or maybe the same intellectual honesty. After October 7th, you said that, like, the protest, the students should have a right to protest and, and the anti-Israel, you know, factions on campus were very vocal there and here. I mean, we had an encampment here that lasted, you know, a couple of days and I testified in Congress about how evil and destructive and, and anti-intellectual it was. But you wrote that they should have a right to protest, but it, it should have limitations.

• 47:22Brian Keating?

  So let's talk about, what is your view on students participating in protest? I agree, they should, students should. I give concern when I see my colleagues doing it for different reasons, but, but where, where do you fall? Like, what, what rights do students have to kind of, you know, advocate as they did, you know, that your university's racist or it's, you know, and it should be, you know, more pro-Palestinian? What level of, of, you know, kind of impact do you seek to have in these debates?

• 47:46Speaker 03

  You know, on, on one hand, yeah, I mean, there's the freedom of thought is, is, is extremely important. On the other hand, what do you do in a situation where universities have become so unbalanced in terms of what is being taught, what is being accepted? What the kids really becoming more and more expressing radical ideas, anti-American, anti-American ideas? I think the universities have lost their ability to frame what their mission is. I mean, they, they are completely confused. About the mission is to find the truth and to educate the, the, the kids in the best that Western civilization or the world civilization has to offer. None of this is true anymore.

• 48:31Speaker 03

  Like, I mean, they, they, kids are educating all sorts of crazy things about, about human nature, lie. I mean, truth doesn't seem to matter. There is a lot of relativism, a lot of political advocacy for certain causes, which the left considers sacrosanct, right? I mean, Diversity, diversity, inclusion. Diversity. As Israel, I think this business with Israel is just ridiculous, right? So what? Singling out one country versus the hundreds of other. The right, I mean, huge deal about about the situations where Israel was attacked, right?

• 49:10Speaker 03

  But by, you know, more than two, and you know, or Iran essentially surrounding Israel by factions that really want to destroy it. Anyway, it's, yeah, I have a huge problems. So I don't know where I may, I do think that this is probably going to happen, that universities become more and more, I mean, the university that we have today will become more and more irrelevant. Another thing that really bothers me is that you would think that in a capitalist system like United States. Yeah. That if a university goes very much on the left, then there will be another one that wants, will get an advantage, right? Will get the advantage by going the other way, right? Because it just doesn't happen. I mean, how do you explain that? How do you explain that all universities go in the same? One exception, yeah.

• 49:54Brian Keating?

  Yeah, you're seeing it with capitalism. You're seeing it like Palantir and you're seeing in corporations that will, you know, take the people that were, you know, too unwoke for Google and hire them. And there are also some of the people that are supporting new institutions. But yeah, I'm also pretty pessimist. The thing that made me most pessimist, I thought COVID would be the end of the current university system, going through that, charging the exact same tuition for Zoom lectures that you could, you know, basically get online for free from past years. The fact that it was so resilient to that kind of just horrible product delivery and service provided for the vast amount of money that far exceeds inflation. I mean, the amount of tuition that's being raised at all of our colleges vastly dwarfs it. And then the debt you take on can't be discharged and bankruptcy. It's a cartel.

• 50:39Brian Keating?

  I mean, basically, we in the university system operate in a cartel system. No, I think there's, there's a lot that's troubling about the university system. And like I said, I don't know if I want to return to this life, you know, there are other things you could be doing, there are other things I could be doing. But let's, let's, let's assume that there's a 19 year old, maybe not in Bucharest, like you were in 1969, but let's say there is some young person, maybe they're living in a slightly repressed, you know, state. I like to ask the following question, you know, what would you tell that 19 year old version of yourself to do to give him the courage to do what you did to go into the impossible, the namesake of this podcast? What kind of, you had 20, you know, 20, 19 seconds with a 19 year old Sergio Clonan, what do you tell him? Would you change anything?

• 51:23Speaker 03

  In science, it's still the best place to go, to go to the top universities. I mean, it's still true, right? I mean, it's true in astrophysics, it's true in astrophysics. Even though, even there, you could see signs of decline, right? But if it comes to something else, I mean, if you really want to do humanities or social sciences, you, I presume you have to do it all your own. I say no, no advantage to go to university. You can read the best books. Now you have AI, AI will direct you. And the same thing with school, right? I mean, even more radical, right? What do you do with the kids? Do you, you have your, do you have kids? Should you send them to school? Or I don't know, maybe frame some kind of, some kind of education system for them?

• 52:05Brian Keating?

  I think it's both. I think you have to do both. You have to socialize them. They have to network. They have to understand how to interact and maybe do sports or athletics or arts. And then, and then there's stuff that, yeah, only I'm not going to let them, you know, only learn in a public school, you know, the basic mathematics, you know. One of my kids is, you know, taking advanced calculus now and he's not even able to drive. So, you know, but that's on us.

• 52:27Speaker 03

  But it was, they're great, they're all the great scientists, they learn by themselves. They're autodidactic, yeah. Right? Yeah. The same thing with art, the great artists and stuff. I don't know, maybe we will, maybe AI will help us to go back to situations where people have.

• 52:43Brian Keating?

  Personalized tutoring.

• 52:45Speaker 03

  And personalized things, right?

• 52:46Brian Keating?

  Exactly. Yeah, I think that's a, that's a wonderful thing. And it's a good place to stop. And I just want to thank you again for being the scientist you are, the citizen that you are, and the citizen scientist. Those always don't go together. And I think it's, it's rare and it's refreshing that, that you take all these roles so seriously. And that you're not afraid to go after these, you know, monstrous, challenging, difficult problems. And it just seems like you have no bounds, no limits to what you're gonna, willing to take on. And I think that's a sign of your courage. So Sergio Plonerman, thank you so much from Romania to the heights of academia and beyond. Thank you for coming on the show.

• 53:20Speaker 03

  Thank you, thank you, thank you very much.

• 53:22Brian Keating?

  Sergio just told us that wormholes don't survive Einstein's own equations and that the AI apocalypse is quite frankly absurd. If that changes how you think about what's real in physics, subscribe, turn on notifications and tell me in the comments whether you think an unstable solution counts as physics or only mathematics. And for the man who put wormholes into the movies, here's my conversation with Nobel laureate Kip Thorne, the man who worked on Interstellar with none other than Christopher Nolan. Link right here. Thanks for watching.

• 53:43Speaker 00

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• 54:12Speaker 01

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