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?

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.

So you were a code-cracker?

I was.

Until you got fired?

Well, I did get fired. Yes.

How come?

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...

Oh, OK. I can see that would—

...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.

OK.

But it wasn't bad.

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?

Oh, Chern! Yeah, Chern was one of the great mathematicians of the century. I had known him when I was a graduate student, actually, at Berkeley. And I had some ideas, and I brought them to him and he liked them. And together, we did this work which you can easily see up there. There it is. And...

It led to you publishing a famous paper together. Can you explain at all what that work was?

No. I mean, I could explain it to somebody.

How about explaining this?

But not many. Not many people.

I think you told me it had something to do with spheres, so let's start here.

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." And today, those things in there called Chern-Simons invariants have spread through a lot of physics. And it's 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.

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?

God knows.

But there's a famous physicist named Wigner, and he wrote an essay on the unreasonable effectiveness of mathematics. So somehow, this mathematics, which is rooted in the real world in some sense—we learn to count, measure, 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. Minkowski had this geometry, and Einstein realized, "Hey! It's the very thing in which I can cast general relativity." So, you never know. And it is a mystery. It is a mystery.

So, here's a mathematical piece of ingenuity here. Come tell us about this.

Well, that's a ball—it's a sphere, and it has a lattice around it—you know, those squares sort of things. And what I'm going to show here was originally observed by 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 and 12 edges and six faces. And if you look at the difference—vertices minus edges plus faces—you get two. OK, 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. This comes out zero—vertices minus edges. It'll always come out zero. Every time you cover a torus with squares or triangles or anything like that, you're going to get zero when you take that thing. So, this is called the Euler characteristic. And it's what's called a topological invariant. That's pretty amazing. No matter how you do it, you're always 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.

And your own work took an idea like this and moved it into higher-dimensional theory, higher-dimensional objects, and found new invariances?

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.

OK, so that's at least given us a flavor of that amazing mind in there. Let's talk about Renaissance. Because you took that amazing mind and having been a code-cracker at the NSA, you started to become a code-cracker in the financial industry. I think you probably didn't buy efficient market theory. And somehow you found a way of creating these astonishing returns over two decades. I think, the way it's been explained to me, what's remarkable about what you did—it wasn't just the size of the returns, it was that you took them with surprisingly low volatility and risk, compared with other hedge funds. So how on earth did you do this, Jim?

I did it by assembling a wonderful group of people. When I started doing trading, I had gotten a little tired of mathematics. I was in my late 30s. I had a little money; I started trading and it went very well. I made quite a lot of money with pure luck. I mean, I think it was pure luck. It certainly wasn't mathematical modeling. But in looking at the data, after a while I realized, Hey, it looks like there's some structure here. And I hired a few mathematicians, and we started making some models—just the kind of thing we did back at IDA. You design an algorithm, you test it out on a computer. Does it work? Doesn't it work? And so on.

Can we take a look at this? Because here's a typical graph of some commodity or whatever. I mean, I look at that and I say, "That's just a random, up-and-down walk—maybe a slight upward trend over that whole period of time." How on earth could you trade looking at that, and see something that wasn't just random?

It turns out in the old days—this is kind of a graph from the old days, commodities or currencies had a tendency to trend. Not necessarily the very light trend you see here, but trending in periods. And if you decided, OK, I'm going to predict today, by the average move in the past 20 days—maybe that would be a good prediction, and I'd make some money. And in fact, years ago, such a system would work—not beautifully, but it would work. So you'd make money, you'd lose money, you'd make money. But this is a year's worth of days, and you'd make a little money during that period. It's a very vestigial system.

So you would test a bunch of lengths of trends in time and see whether, for example, a 10-day trend or a 15-day trend was predictive of what happened next.

Sure, you would try all those things and see what worked best. But the trend-following would have been great in the '60s, and it was sort of OK in the '70s. By the '80s, it wasn't.

Because everyone could see that. So, how did you stay ahead of the pack?

We stayed ahead of the pack by finding other approaches—shorter-term approaches to some extent. But the real thing was to gather a tremendous amount of data—and we had to get it by hand in the early days. We went down to the Federal Reserve and copied interest rate histories and stuff like that, because it didn't exist on computers. We got a lot of data. And very smart people—that was the key. I didn't really know how to hire people to do fundamental trading. I had hired a few—some made money, some didn't make money. I couldn't make a business out of that. But I did know how to hire scientists, because I have some taste in that department. And...so, that's what we did. And gradually these models got better and better, and better and better.

You're credited with doing something remarkable at Renaissance, which is building this culture, this group of people, who weren't just hired guns who could be lured away by money. Their motivation was doing exciting mathematics and science.

Well, I'd hoped that might be true. But some of it was money.

They made a lot of money.

I can't say that no one came because of the money. I think a lot of them came because of the money. But they also came because it would be fun.

What role did machine learning play in all this?

Well, in a certain sense, what we did was machine learning. You look at a lot of data, and you try to simulate different predictive schemes until you get better and better at it. It doesn't necessarily feed back on itself the way we did things. But it worked.

So these different predictive schemes can be really quite wild and unexpected. I mean, you looked at everything, right? You looked at the weather, length of dresses, political opinion.

Yes, length of dresses we didn't try.

What sort of things?

Well, everything. Everything is grist for the mill—except hem lengths. Weather, annual reports, quarterly reports, historic data itself, volumes, you name it. Whatever there is. We take in terabytes of data a day, and store it away and massage it and get it ready for analysis. You're looking for anomalies. You're looking for—like you said, the efficient market hypothesis is not correct.

But any one anomaly might be just a random thing. So, is the secret here to just look at multiple strange anomalies, and see when they align?

Well, any one anomaly might be a random thing; however, if you have enough data, you can tell that it's not. So you can see an anomaly that's persistent for a sufficiently long time—the probability of it being random is not high. But these things fade after a while; anomalies can get washed out. So you have to keep on top of the business.

A lot of people look at the hedge fund industry now and are sort of...shocked by it, by how much wealth is created there, and how much talent is going into it. Do you have any worries about that industry, and perhaps the financial industry in general? Kind of being on a runaway train that's—I don't know—helping increase inequality? How would you champion what's happening in the hedge fund industry?

Well, actually I think in the last three or four years, hedge funds have not done especially well. We've done dandy, but the hedge fund industry as a whole has not done so wonderfully. The stock market has been on a roll, going up as everybody knows, and price-earnings ratios have grown. So an awful lot of the wealth that's been created in the last—let's say, five or six years—has not been created by hedge funds. So people would ask me, "What's a hedge fund?" And I'd say, "One and 20." Which means—now it's two and 20—it's two percent fixed fee and 20 percent of profits. Hedge funds are all different kinds of creatures.

Rumor has it you charge slightly higher fees than that.

We had charged the highest fees in the world at one time. Five and 44, that's what we charge.

Five and 44. So five percent flat, 44 percent of upside. You still made your investors spectacular amounts of money.

We made good returns, yes. People got very mad: "How can you charge such high fees?" I said, "OK, you can withdraw." But "How can I get more?" was what people were... But at a certain point, as I think I told you, we bought out all the investors because there's a capacity to the fund.

But should we worry about the hedge fund industry attracting too much of the world's great mathematical and other talent to work on that, as opposed to the many other problems in the world?

Well, it's not just mathematical. We hire astronomers and physicists and things like that. I don't think we should worry about it too much. It's still a pretty small industry. And in fact, bringing science into the investing world has improved that world. It's reduced volatility. It's increased liquidity. Spreads are narrower because people are trading that kind of stuff. So I'm not too worried about Einstein going off and starting a hedge fund.

Now, you're at a phase in your life now where you're actually investing, though, at the other end of the supply chain—you're actually boosting mathematics across America. This is your wife, Marilyn. And you're working on philanthropic issues together. Tell me about that.

Well, Marilyn started—there she is up there, my beautiful wife—she started the foundation about 20 years ago. I think '94. I claim it was '93, she says it was '94, but it was one of those two years. We started the foundation, just as a convenient way to give charity. She kept the books, and so on. We did not have a vision at that time, but gradually a vision emerged—which was to focus on math and science, to focus on basic research. And that's what we've done. And six years ago or so, I left Renaissance and went to work at the foundation. So that's what we do.

And so Math for America here is basically investing in math teachers around the country, giving them some extra income, giving them support and coaching, and really trying to make that more effective and make that a calling to which teachers can aspire.

Yeah—instead of beating up the bad teachers, which has created morale problems all through the educational community, in particular in math and science, we focus on celebrating the good ones and giving them status. Yeah, we give them extra money, 15,000 dollars a year. We have 800 math and science teachers in New York City in public schools today, as part of a core. There's a great morale among them. They're staying in the field. Next year, it'll be 1,000 and that'll be 10 percent of the math and science teachers in New York public schools.

Jim, here's another project that you've supported philanthropically: Research into origins of life, I guess. What are we looking at here?

Well, I'll save that for a second. And then I'll tell you what you're looking at. So, origins of life is a fascinating question. How did we get here? Well, there are two questions: One is, what is the route from geology to biology—how did we get here? And the other question is, what did we start with? What material, if any, did we have to work with on this route? Those are two very, very interesting questions. The first question is a tortuous path from geology up to RNA or something like that—how did that all work? And the other, what do we have to work with? Well, more than we think. So what's pictured there is a star in formation. Now, every year in our Milky Way, which has 100 billion stars, about two new stars are created. Don't ask me how, but they're created. And it takes them about a million years to settle out. So, in steady state, there are about two million stars in formation at any time. That one is somewhere along this settling-down period. And there's all this crap sort of circling around it, dust and stuff. And it'll form probably a solar system, or whatever it forms. But here's the thing—in this dust that surrounds a forming star have been found, now, significant organic molecules. Molecules not just like methane, but formaldehyde and cyanide—things that are the building blocks—the seeds, if you will—of life. So, that may be typical. And it may be typical that planets around the universe start off with some of these basic building blocks. Now does that mean there's going to be life all around? Maybe. But it's a question of how tortuous this path is from those frail beginnings, those seeds, all the way to life. And most of those seeds will fall on fallow planets.

So for you, personally, finding an answer to this question of where we came from, of how did this thing happen, that is something you would love to see.

I would love to see, and like to know—if that path is tortuous enough, and so improbable, that no matter what you start with, we could be a singularity. But on the other hand, given all this organic dust that's floating around, we could have lots of friends out there. It'd be great to know.

Jim, a couple of years ago, I got the chance to speak with Elon Musk, and I asked him the secret of his success, and he said taking physics seriously was it. Listening to you, what I hear you saying is taking math seriously, that has infused your whole life. It's made you an absolute fortune, and now it's allowing you to invest in the futures of thousands and thousands of kids across America and elsewhere. Could it be that science actually works? That math actually works?

Well, math certainly works. Math certainly works. But this has been fun. Working with Marilyn and giving it away has been very enjoyable.

I just find it—it's an inspirational thought to me that by taking knowledge seriously, so much more can come from it. So thank you for your amazing life, and for coming here to TED. Thank you. Jim Simons!