Peter Woit: Theories of Everything & Why String Theory is Not Even Wrong | Lex Fridman Podcast #246

The following is a conversation with Peter Woit, a theoretical physicist at Columbia, outspoken critic of string theory, and the author of the popular physics and mathematics blog called Not Even Wrong. This is the Lex Fridman Podcast. To support it, please check out our sponsors in the description. And now, here's my conversation with Peter Woit. You're both a physicist and a mathematician. So let me ask, what is the difference between physics and mathematics?

Well, there's kind of a conventional understanding of the subject that they're two, you know, quite different things, so that mathematics is about, you know, making rigorous statements about these abstract, you know, abstract things, things of mathematics, and- and prov- proving them rigorously. And physics is about, you know, doing experiments and testing various models and that. But I think, uh, the more interesting thing is that the- there's a- (laughs) there's a wide variety of what people do as mathematics, what they do as physics, and there's a significant overlap. And that, I- I think is actually the much, much- very, very interesting area. And if you go back kind of far enough to- in- in- in history, and look at figures like Newton or something, I mean, they're- at that point, you can't really tell, you know, was Newton a physicist or a mathematician? The, uh, mathematicians will tell you he was a mathematician, the physicists will tell you he was a physicist. But-

He would say he's a philosopher. (laughs)

Yeah. (laughs) That's- that's interesting. But, uh, yeah, anyway, there- there- there was kind of no such distinction then, that's more of a modern thing. And but anyway, I think these days, there's a very interesting space in between the two.

So, in the story of the 20th century and the early 21st century, what is the overlap between mathematics and physics, would you say?

Well, I think (clears throat) it's actually become very, very complicated. I think it- it's really interesting to see a lot of what my colleagues in the math department are doing. They- most of what they're doing, they're doing all sorts of different things, but, um, most of them have some kind of overlap with physics or other. Um, so I mean, I'm personally interested in- in one spec- one particular aspect of this overlap, which I think has a lot to do with the most fundamental ideas about physics and about mathematics. But, um, there's just- it- it- you- you kind of see this- this, uh, re- really everywhere at this point.

Which particular overlap are you looking at? Group theory?

Yeah. So the, um, at least what- the way it seems to me that if you look at physics and look at the- our most successful, um, laws of fundamental physics, they're really, you know, they have a certain kind of mathematical structure. It's based upon certain kind of mathematical objects and geometry, connections, and curvature of the spinors, the Dirac equation. And, uh, that- these- this very deep mathematics provides kind of a unifying set of math- of ways of thinking that allow you to- to make a unified theory of physics. But the interesting thing is that if you go to mathematics and- and look at what's been going on in mathematics the last 50, 100 years, and even especially recently, there's a- similarly some kind of unifying ideas which bring together different areas of mathematics, and which have been especially powerful in number theory recently. And there's a book, for instance, by, um, Edward Frenkel about love and math, and-