Fea-milnor-interview indd

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Interview with John Milnor

Martin Raussen and Christian Skau 

Raussen & Skau: Professor John Milnor, on behalf of 

the Norwegian and Danish Mathematical Societies, we 

would like to congratulate you for being selected as the 

Abel Prize Laureate in 2011.

Milnor: Thank you very much.

Student at Princeton University

R & S: What kindled your interest in mathematics and 

when did you discover that you had an extraordinary 

aptitude for mathematics?

Milnor: I can place that quite clearly. The first time 

that I developed a particular interest in mathematics 

was as a freshman at Princeton University. I had been 

rather socially maladjusted and did not have too many 

friends, but when I came to Princeton, I found myself 

very much at home in the atmosphere of the math-

ematics common room. People were chatting about 

mathematics, playing games, and one could come by 

at any time and just relax. I found the lectures very 

interesting. I felt more at home there than I ever had 

before and I have stayed with mathematics ever since.

R & S: You were named a Putnam Fellow as one of 

the top scorers of the Putnam competition in math-

ematics in 1949 and 1950. Did you like solving math-

ematics problems and puzzles?

Milnor: I think I always approached mathematics 

as interesting problems to be solved, so I certainly 

found that congenial.

R & S: Your first important paper was accepted al-

ready in 1949 and published in 1950 in the prestigious 

journal  Annals of Mathematics. You were only 18 

years of age at the time and this is rather exceptional. 

The title of the paper was “On the Total Curvature 

of Knots”. Could you tell us how you got the idea for 

that paper?

Milnor: I was taking a course in differential geom-

etry under Albert Tucker. We learned that Werner 

Fenchel, and later Karol Borsuk, had proved the 

following statement: the total curvature of a closed 

curve in space is always at least 2π, with equality 

only if the curve bounds a convex subset of some 

plane. Borsuk, a famous Polish topologist, had 

asked what one could say about total curvature if 

the curve was knotted? I thought about this for a 

few days and came up with a proof that the total 

curvature is always greater than 4π. (I think I did 

a poor job explaining the proof in the published 

paper, but one has to learn how to explain math-

ematics.) The Hungarian mathematician István 

Fáry had produced a similar proof at more or 

less the same time, but this was still a wonderful 

introduction to mathematics.

R & S:  That was quite an achievement! When 

you started your studies at Princeton in 1948, you 

met John Nash, three years your senior, who was 

a Ph.D. student. John Nash is well known through 

the book and movie A Beautiful Mind. Did you have 

any interaction with him? And how was it to be a 

Princeton student?

Milnor: As I said, I spent a great deal of time 

in the common room, and so did Nash. He was a 

very interesting character and full of ideas. He also 

used to wander in the corridors whistling things 

like Bach, which I had never really heard before—a 

strange way to be introduced to classical music! 

I saw quite a bit of him over those years and I 

also became interested in game theory, in which 

he was an important contributor. He was a very 

interesting person.

R & S: At Princeton, you played Kriegspiel, Go, 

and a game called Nash?

Milnor:  That is true. Kriegspiel is a game of 

chess in which the two players are back-to-back 

and do not see each other’s boards. There is a

referee who tells whether the moves are legal 

or not. It is very easy for the referee to make a 

mistake, and it often happened that we could 

not finish because he got confused. In that case 

we said that the referee won the game! It was a 

marvelous game.

The game of Go was also very popular there. My 

first professor, Ralph Fox, was an expert in Go. So 

I learned something of it from him and also from 

John W. Milnor is the recipient of the 2011 Abel Prize of the Norwegian Academy of Science and Letters. This in-

terview, conducted by Martin Raussen and Christian Skau, took place in Oslo in conjunction with the Abel Prize 

celebration on May 25, 2011, and originally appeared in the September 2011 issue of the Newsletter of the European 

Mathematical Society.

Martin Raussen is associate professor of mathematics at 

Aalborg University, Denmark. His email address is raussen@

math.aau.dk.

Christian Skau is professor of mathematics at the Norwegian 

University of Science and Technology, Trondheim, Norway. 

His email address is [e-mail].

DOI: http://dx.doi.org/10.1090/noti803

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