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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.
Yasushi Aoki
Well, I'll save that for a second.
->
JS: Well, I'll save that for a second.
JS: I think in the last
three of four years,
->
JS: I think in the last
three or four years,
Camille Martínez
Thank you, Yasush! The corrections have been made.
Camille Martínez
*Please note the following updates to the English subtitles as of 9/13/15:
14:43 - 14:45
JS: I think in the last
three OR four years,
19:04 - 19:05
JS: Well, I'll save that for a second. (speaker's initials were previously missing)
Margarida Ferreira
Please note error on line 6:47, which must be the following:
Vertices minus edges PLUS FACES come out to zero - (16-32+16=0)
Jim Simons speaks too fast...
Claudia Sander
6:46:53
Vertices minus edges comes out to be zero. -> Vertices minus edges plus faces comes out to be zero.
You can see it in the presentation and also calculating it.