Full text of A Rare Interview With the Mathematician Who Cracked Wall Street: Jim Simons at TED Talks
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Chris Anderson: You were something of a mathematical phenom. You had already taught at Harvard and MIT at a young age. And then the NSA came calling. What was that about?
Jim Simons: Well the NSA — that’s the National Security Agency — they didn’t exactly come calling. They had an operation at Princeton, where they hired mathematicians to attack secret codes and stuff like that. And I knew that existed. And they had a very good policy, because you could do half your time at your own mathematics, and at least half your time working on their stuff. And they paid a lot. So that was an irresistible pull. So, I went there.
Chris Anderson: So you were a code-cracker.
Jim Simons: I was.
Chris Anderson: Until you got fired.
Jim Simons: Well, I did get fired. Yes.
Chris Anderson: How come?
Jim Simons: Well, how come? I got fired because, well, the Vietnam War was on, and the boss of bosses in my organization was a big fan of the war and wrote a New York Times article, a magazine section cover story, about how we would win in Vietnam. And I didn’t like that war, I thought it was stupid. And I wrote a letter to the Times, which they published, saying not everyone who works for Maxwell Taylor, if anyone remembers that name, agrees with his views. And I gave my own views…
Chris Anderson: Oh, Okay I can see that would —
Jim Simons:… which were different from General Taylor’s. But in the end, nobody said anything. But then, I was 29 years old at this time, and some kid came around and said he was a stringer from Newsweek magazine and he wanted to interview me and ask what I was doing about my views. And I told him, “I’m doing mostly mathematics now, and when the war is over, then I’ll do mostly their stuff.” Then I did the only intelligent thing I’d done that day — I told my local boss that I gave that interview. And he said, “What’d you say?” And I told him what I said. And then he said, “I’ve got to call Taylor.” He called Taylor; that took 10 minutes. I was fired five minutes after that.
Chris Anderson: Okay.
Jim Simons: But it wasn’t bad.
Chris Anderson: It wasn’t bad, because you went on to Stony Brook and stepped up your mathematical career. You started working with this man here. Who is this?
Jim Simons: Oh, Chern. Shiing-Shen Chern was one of the great mathematicians of the century. I had known him when I was a graduate student at Berkeley. And I had some ideas, and I brought them to him and he liked them. Together, we did this work which you can easily see up there. There it is.
Chris Anderson: It led to you publishing a famous paper together. Can you explain at all what that work was?
Jim Simons: No. I mean, I could explain it to somebody.
Chris Anderson: How about explaining this?
Jim Simons: But not many. Not many people.
Chris Anderson: I think you told me it had something to do with spheres, so let’s start here.
Jim Simons: Well, it did, but I’ll say about that work — it did have something to do with that, but before we get to that — that work was good mathematics. I was very happy with it; so was Chern. It even started a little sub-field that’s now flourishing. But, more interestingly, it happened to apply to physics, something we knew nothing about — at least I knew nothing about physics, and I don’t think Chern knew a heck of a lot. And about 10 years after the paper came out, a guy named Ed Witten in Princeton started applying it to string theory and people in Russia started applying it to what’s called condensed matter. Today, those things in there called Chern-Simons invariants have spread through a lot of physics. And it was amazing. We didn’t know any physics. It never occurred to me that it would be applied to physics. But that’s the thing about mathematics — you never know where it’s going to go.
Chris Anderson: This is so incredible. So, we’ve been talking about how evolution shapes human minds that may or may not perceive the truth. Somehow, you come up with a mathematical theory, not knowing any physics, discover two decades later that it’s being applied to profoundly describe the actual physical world. How can that happen?
Jim Simons: God knows. But there’s a famous physicist named Eugene Wigner, and he wrote an essay on the unreasonable effectiveness of mathematics. Somehow, this mathematics, which is rooted in the real world in some sense — we learn to count, measure, that’s kind of everyone would do that — and then it flourishes on its own. But so often it comes back to save the day. General relativity is an example. Hermann Minkowski had this geometry, and Einstein realized, “Hey! It’s the very thing in which I can cast general relativity.” So, you never know. It is a mystery. It is a mystery.
Chris Anderson: So, here’s a mathematical piece of ingenuity. Tell us about this.
Jim Simons: Well, that’s a ball — it’s a sphere, and it has a lattice around it — you know, those squares. What I’m going to show here was originally observed by Leonhard Euler, the great mathematician, in the 1700s. And it gradually grew to be a very important field in mathematics: algebraic topology, geometry. And that paper up there had its roots in this. So, here’s this thing: it has eight vertices, 12 edges, and six faces. And if you look at the difference — vertices minus edges plus faces — you get two. Okay, well, two. That’s a good number. Here’s a different way of doing it — these are triangles covering — this has 12 vertices and 30 edges and 20 faces, 20 tiles. And vertices minus edges plus faces still equals two. And in fact, you could do this any which way — cover this thing with all kinds of polygons and triangles and mix them up. And you take vertices minus edges plus faces — you’ll get two.
Now here’s a different shape. This is a torus, or the surface of a doughnut: 16 vertices covered by these rectangles, 32 edges, 16 faces. Vertices minus edges comes out to be zero. It’ll always come out to zero. Every time you cover a torus with squares or triangles or anything like that, you’re going to get zero. So, this is called the Euler characteristic. And it’s what’s called a topological invariant. It’s pretty amazing. No matter how you do it, you’re always going to get the same answer. So that was the first sort of thrust, from the mid-1700s, into a subject which is now called algebraic topology.
Chris Anderson: And your own work took an idea like this and moved it into higher-dimensional theory, higher-dimensional objects, and found new invariances?
Jim Simons: Yes. Well, there were already higher-dimensional invariants: Pontryagin classes — actually, there were Chern classes. There were a bunch of these types of invariants. I was struggling to work on one of them and model it sort of combinatorially, instead of the way it was typically done, and that led to this work and we uncovered some new things. But if it wasn’t for Mr. Euler — who wrote almost 70 volumes of mathematics and had 13 children, who he apparently would dandle on his knee while he was writing — if it wasn’t for Mr. Euler, there wouldn’t perhaps be these invariants.