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.
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.