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.

CA: You were a code-cracker.

JS: I was.

CA: Until you got fired.

JS: Well, I did get fired. Yes.

CA: How come?

JS: 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 ...

CA: Oh, OK. I can see that would --

JS: ... 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.

CA: OK.

JS: But it wasn't bad.

CA: 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?

JS: Oh, [Shiing-Shen] Chern.

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.

CA: It led to you publishing a famous paper together.

Can you explain at all what that work was?

JS: No.

(Laughter)

JS: I mean, I could explain it to somebody.

(Laughter)

CA: How about explaining this?

JS: But not many. Not many people.

CA: I think you told me it had something to do with spheres,

so let's start here.

JS: 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.

CA: 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?

JS: God knows.

(Laughter)

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, 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.

CA: So, here's a mathematical piece of ingenuity.

Tell us about this.

JS: 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.

That paper up there had its roots in this.

So, here's this thing:

it has eight vertices, 12 edges, 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.

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 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.

CA: And your own work took an idea like this and moved it

into higher-dimensional theory,

higher-dimensional objects, and found new invariances?

JS: 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.

CA: 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.

Somehow you found a way of creating astonishing returns over two decades.

The way it's been explained to me,

what's remarkable about what you did wasn't just the size of the returns,

it's that you took them with surprisingly low volatility and risk,

compared with other hedge funds.

So how on earth did you do this, Jim?

JS: 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:

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 [Institute for Defense Analyses].

You design an algorithm, you test it out on a computer.

Does it work? Doesn't it work? And so on.

CA: Can we take a look at this?

Because here's a typical graph of some commodity.

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?

JS: 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.

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.

CA: 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.

JS: Sure, you would try all those things and see what worked best.

Trend-following would have been great in the '60s,

and it was sort of OK in the '70s.

By the '80s, it wasn't.

CA: Because everyone could see that.

So, how did you stay ahead of the pack?

JS: We stayed ahead of the pack by finding other approaches --

shorter-term approaches to some extent.

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.

So, that's what we did.

And gradually these models got better and better,

and better and better.

CA: 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.

JS: Well, I'd hoped that might be true.

But some of it was money.

CA: They made a lot of money.

JS: 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.

CA: What role did machine learning play in all this?

JS: In a certain sense, what we did was machine learning.