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Chris Anderson: You were something of
a mathematical phenom.

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You had already taught
at Harvard and MIT at a young age.

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And then the NSA came calling.

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What was that about?

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Jim Simons: Well the NSA --
that's the National Security Agency --

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they didn't exactly come calling.

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They had an operation at Princeton
where they hired mathematicians

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to attack secret codes
and stuff like that.

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And I knew that existed.
And they had a very good policy

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And they had a very good policy
because you could do half your time

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at your own mathematics

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and at least half your time
working on their stuff.

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And they paid a lot.
So that was an irresistible pull.

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So, I went there.

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CA: So you were a code-cracker.

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JS: I was.

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CA: Until you got fired.

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JS: Well, I did get fired. Yes.

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CA: How come?

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JS: Well, how come?

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I got fired because,
well the Vietnam War was on,

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and the boss of bosses in my organization
was a big fan of the war

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and wrote a New York Times article,
a magazine section cover story,

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about how we're going
to win in Vietnam and so on.

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And I didn't like that war,
I thought it was stupid

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and I wrote a letter to the Times,
which they published, saying

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not everyone who works for Maxwell Taylor,
if anyone remembers that name,

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agrees with his views.

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And I gave my own views.

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

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JS: Which were different from General Taylor's.

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But in the end nobody said anything.

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But then, I was 29 years old at this time
and some kid came around

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and said he was a stringer 
from Newsweek magazine

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and he wanted to interview me
and ask what I was doing about my views.

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And I told him, I said, 
"I'm doing mostly mathematics now,

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and when the war is over
then I'll do mostly their stuff."

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Then I did the only 
intelligent thing I'd done that day --

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I told my local boss
that I gave that interview.

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And he said, "What'd you say?"

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And I told him what I said.

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And then he said, "I've got to call Taylor."

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He calls Taylor; that took 10 minutes.

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I was fired five minutes after that.

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But it wasn't bad.

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CA: It wasn't bad, because
you went on to Stony Brook

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and stepped up your mathematical career.

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You started working
with this man here. Who is this?

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JS: Oh, [Shiing-Shen] Chern.

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Chern was one of the great 
mathematicians of the century.

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I had known him when
I was a graduate student at Berkeley.

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And I had some ideas,

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and I brought them to him
and he liked them.

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Together, we did this work 
which you can easily see up there.

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There it is.

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

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Can you explain at all what that work was?

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JS: No.

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(Laughter)

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

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CA: How about explaining this?

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(Laughter)

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JS: But not many.
Not many people.

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

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so let's start here.

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JS: Well, it did. But I'll say about that work --

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it did have something to do with that,
but before we get to that --

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that work was good mathematics.

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I was very happy with it; so was Chern.

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It even started a little subfield
that's now flourishing.

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But, more interestingly,
it happened to apply to physics,

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something we knew nothing about --
at least I knew nothing about physics,

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and I don't think Chern
knew a heck of a lot.

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And about 10 years
after the paper came out,

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a guy named Ed Witten in Princeton
started applying it to string theory

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and people in Russia started applying it
to what's called "condensed matter."

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Today, those things in there
called Chern-Simons invariants

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have spread through a lot of physics.

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And it was amazing.

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We didn't know any physics.

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It never occurred to me
that it would be applied to physics.

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But that's the thing about mathematics --
you never know where it's going to go.

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CA: This is so incredible.

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So, we've been talking about
how evolution shapes human minds

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that may or may not perceive the truth.

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Somehow, you come up
with a mathematical theory,

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not knowing any physics,

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discover two decades later
that it's being applied

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to profoundly describe
he actual physical world.

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How can that happen?

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JS: God knows.

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(Laughter)

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But there's a famous physicist
named [Eugene] Wigner,

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and he wrote an essay on the
unreasonable effectiveness of mathematics.

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Somehow, this mathematics,

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which is rooted in the real world
in some sense -- we learn to count,

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measure, everyone would do that --
and then it flourishes on its own.

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But so often it comes back
to save the day.

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General relativity is an example.

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[Hermann] Minkowski had this geometry,
and Einstein realized,

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"Hey, it's the very thing 
in which I can cast General Relativity."

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So, you never know. It is a mystery.

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It is a mystery.

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

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Tell us about this.

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JS: Well, that's a ball -- it's a sphere,
and it has a lattice around it --

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you know, those squares.

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What I'm going to show here was 
originally observed by [Leonhard] Euler,

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the great mathematician, in the 1700's.

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And it gradually grew to be 
a very important field in mathematics:

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algebraic topology, geometry.

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That paper up there had its roots in this.

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So, here's this thing:

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it has eight vertices,
12 edges, six faces.

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And if you look at the difference --

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vertices minus edges plus faces --
you get two.

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OK, well, two? That's a good number.

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Here's a different way of doing it --
these are triangles covering --

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this has 12 vertices and 30 edges
and 20 faces, 20 tiles.

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And vertices minus edges
plus faces still equals two.

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And in fact you could
do this any which way,

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cover this thing with all kinds
of polygons and triangles

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and mix them up.

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And you take vertices minus edges
plus faces -- you'll get two.

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Here's a different shape.
This is a torus, the surface of a donut,

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16 vertices covered by these rectangles,

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

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It'll always come out 0.

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Every time you cover a torus
with squares or triangles

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

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So, this is called
the Euler characteristic.

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And it's what's called
a topological invariant.