The mathematician who cracked Wall Street

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

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: So 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're going
to win in Vietnam and so on.

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 said,
"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 calls Taylor; that took 10 minutes.

I was fired five minutes after that.

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.

CA: How about explaining this?

(Laughter)

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 subfield
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
he 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 1700's.

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, the surface of a donut,

16 vertices covered by these rectangles,

32 edges, 16 faces,
vertices minus edges comes out 0.

It'll always come out 0.

Every time you cover a torus
with squares or triangles

or anything like that,
you're going to get 0.

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'll 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 invariants?

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
as 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 -- there's 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.