The genius of Edward Witten | Cumrun Vafa and Lex Fridman

Just as a little tangent we mentioned Edward Whitten and he, in a lot of walks of life, to me, as an outsider, comes across as a person who is widely regarded as one of the most brilliant people in the history of physics, simply as a power. uh, from a human like uh, the exceptional places that a human mind can go yes, uh, you've had the opportunity to work with him, what's he like? Yeah, more than that, he was my, uh, PhD advisor, so I got to know him very well. Well, and I benefited from his ideas, in fact, what you say about him is accurate.

Not only is he brilliant, but he is also multifaceted in terms of the impact that he has had not only on physics but also on mathematics. in the field medal because of his work in mathematics and, rightly so, you know that he has used his knowledge of physics in a way that impacted profound ideas in modern mathematics and that is an example of the power of these ideas in physics modern high energy and string theory than the applicability of this to modern mathematics, so he is a pretty exceptional individual, we don't come across people like that much in history, so I think yes, in fact, it is a of the rare figures in this history of The topic has had a great impact in many aspects not only of string theory, in many different areas of physics and also mathematics, so I think what you said about it is accurate .

I had the pleasure of interacting with him as a student and later as colleagues writing articles together etc. What impact does it have on his life? What have you learned from him? If you looked at the trajectory of his mind in the way he approached science, physics and mathematics. How did it disrupt that trajectory? Yes, he actually did, so I can explain it because when I was a student I had the biggest impact from him, clearly as a graduate student at Princeton, so I think that was a time when I was a little confused about the relationship between mathematics and physics I double majored in mathematics and physics at MIT and because I really enjoyed both and I write the elegance and rigor of mathematics and I like the power of ideas and physics and their applicability to reality and what that teaches about the real world around us, but I saw this tension between rigorous thinking in mathematics and the lack of it in physics and this worried me greatly.

That worried me, so I was at a crossroads when I decided to go to graduate school in physics because I didn't like some of the lack of rigor that I was seeing in physics, on the other hand, for me, mathematics, although it was rigorous , sometimes they were, I didn't see the point, in other words, when I see when I see that you know the math theorem alone could be beautiful, but I really wanted more than that. I mean, okay, what does it teach us about more than just math? So I wasn't, I wasn't that enamored with just math, but physics was a little annoying, however, I decided to go to physics and I decided to go to Princeton and I started working with Edward Whitten as my thesis advisor and at that time I was trying to put physics into rigorous mathematical terms. one of field theory, I tried to make it rigorous and so on, and no matter how hard I tried, I couldn't do it and I was falling behind in my classes, I wasn't learning much physics and I wasn't achieving It was rigorous and for me it was this dichotomy between mathematics and physics.

What am I doing? I like mathematics, but this is not exactly there. Ed comes in as my advisor and I see him in action thinking about math and physics. He was amazing at math. He knew that everything about mathematics was no problem for him, but he thought about physics in a way that did not find this tension between the two, it was much more harmonious for him, he drew Feynman diagrams but he did not see it as a formalism. It was seen, oh yeah, the particle goes there and this is what's happening, so wait, you're thinking it's really this particle, it's virtual, this is really an electron going there, yeah, yeah, it's not, It's not the formula, no, you just feel the electron you're moving with this guy and you do that and so on and you're invariably thinking about physics or the way he thought about relativity like you know, I was thinking about, you know , this impulse says that he was thinking invariantly about physics just like the way you think about invariant concepts in relativity that don't depend on the frame of reference.

He was thinking about physics in varying ways, but the way that doesn't give you a broader perspective, so this gradually helped me appreciate the interconnections between ideas and physics supersede the mathematical rigor that different facets reinforce each other. with each other, you say, oh, I can't rigorously define what I mean by this, but this connects with this other physics that I've seen and this other thing, and together they form an elegant story and that replaced for me, what I thought as solidity, which I found in mathematics as rigor, was solid, I found that it replaced rigor and solidity in physics, so I found that it's okay, that's the way you can hold on to it, it's not indecisive, it's not like that. someone just couldn't prove it, he just made up a story, it was more than that and there was no tension with mathematics, in fact mathematics helped him as friends and much more harmonious and gives information about physics, so I think that's one of the main things I learned from interactions with writing and I think now maybe I've taken it to the extreme, maybe he wouldn't go as far as I did, that is, I use physics to define new mathematics in a way that would be much less rigorous than a physicist might necessarily believe because I take physical intuition perhaps literally in many ways that could be taught to us, so now I have gained so much confidence in physical intuition that I make bold statements that sometimes take my friends at school by surprise. math.

So an example of this is mirror symmetry, so we were studying this compaction of string geometries. This is after my PhD. Now, when I came to Harvard, we were studying these aspects of string compaction on these complicated manifolds. The six-dimensional spaces called clavial manifolds are very complicated and I noticed with a couple of other colleagues that there was a symmetry in the suggested physics between different calabias, they suggested that you couldn't actually calculate the Euler characteristic of a calabia or that the characteristic is to count the number of points minus the number of edges plus the number of faces minus, so you can count the alternating sequence of properties of the space, which is the topological property of a space, so the holy cakes of the calabia were a property of space and then we noticed that from the physical formalism if a string moves in a columbia it cannot be distinguished we cannot calculate the Euler characteristic we can only calculate its absolute value now this bothered us because how could you not calculate the real sign unless both sides were equal, so I guessed? maybe for every calabia with other positive characteristics there is one with negative ones, I said this to my colleague yao whose namesake I am making this guess, is it possible that for every calabia there is one with the other opposite characteristics that sound unreasonable ?

I said why I said well we know more claudias with other negative characters than positive ones I said but physics says that we cannot distinguish them at least I don't see how so we conjecture that for each calabia with one side there is the other despite the mathematical evidence despite the mathematical evidence even though the expert tells us that this is not the correct idea, if a few years later mathematicians confirmed this symmetric mirror symmetry between the sign with the opposite sign, so this is actually the opposite view of which physics is so sure. It's that you go against mathematical wisdom by telling them they better look for it, so take physical intuition literally and then have that drive mathematics exactly and now we have so much confidence in many of those examples that they have affected modern mathematics.

This way we have much more confidence in our understanding of what string theories are. These are other aspects. Other aspects of why we believe string theory is correct. He's doing this kind of thing.