Devlin's Angle

April 2006

How a wave led to a prize

This year's Mathematics Awareness Month - this month in fact - sees the MAM celebrate its 20th birthday, the annual festival having been first launched in 1986. With this years theme being Mathematics and Internet Security, it is perhaps fitting that it is also the 30th anniversary of the introduction by Whitfield Diffie and Martin Hellman of the idea of Public Key Cryptography. To find out more about MAM and what Diffie and Hellman did, click over to the Mathematics Awareness Month Website at www.mathaware.org, where you will find various articles describing the different ways that mathematics plays important roles in Internet Security.

The remainder of this month's column has nothing to do with either Mathematics Awareness Month or Internet security - at least as far as I know. But having found myself organizing the MAM national campaign this year, I couldn't resist giving it one final plug.

What I really want to talk about is the recent awarding of the Abel Prize to Swedish mathematician Lennart Carleson.

The idea for the prize, awarded annually by the Norwegian Academy of Science and Letters for work in mathematics, goes back to the start of the twentieth century. Observing that when Swedish scientist, industrialist, and philanthropist Alfred Nobel established the Nobel Prizes in 1895, he did not stipulate a prize for mathematics, the Norwegian government at the time decided to fill what they saw as an unfortunate gap and create an equivalent prize for mathematicians. They further decided that the prize should be named after the man who was arguably Norway's most famous mathematician of all time, Niels Henrik Abel, who had lived in the early part of the 19th century. Unfortunately, the breakup of the Swedish-Norwegian union in 1905 prevented the completion of the prize creation process, and it was not until 2003 that the Norwegian government finally made good on the century-old intention of their predecessors.

With this years award, the prize goes to a Scandinavian for the first time. Announcing the 2006 award on 23 March, Norwegian Academy President Ole Didrik Laerum cited Lennart "for his profound and seminal contribution to harmonic analysis and the theory of smooth dynamical systems." Lennart will receive his prize from Queen Sonja of Norway at a ceremony in Oslo on 23 May.

The result for which Lennart is most widely known is his completion of the work on wave analysis begun by Jean Baptiste Joseph Fourier (1768-1830) Fourier analysis, the basis of today's music synthesizers, iPod music players, and so forth. Fourier showed how to take the graph of a wave, such as a sound wave or heat radiation, and decompose it into an infinite sum of sine waves. Fourier's approach worked for all of the naturally occurring waves that people looked at, but would it work for all waves? Or were there some strange pathological waves that could not be expressed as an infinite sum of sine waves? That question remained open for many years until Carleson answered it in 1966, showing that the Fourier decomposition process does indeed work for all waves.

For most mathematicians, one result of that magnitude in a lifetime would be more than enough, but Carleson scored big a second time in 1991, when, together with his colleague Michael Benedicks, he gave a rigorous proof of an "order out of chaos" result that had been suggested by computer work but had long resisted definite proof - namely the existence of a so-called strange attractor for a certain widely studied dynamical system known as the Henon system.

For more details about Carleson's work and on the Abel Prize, see the Abel Prize website at www.abelprisen.no/en/

Oh, and one final thing. Please do not write to tell me that you once heard that the reason there is no Nobel Prize in Mathematics is that Nobel feared that the great Swedish mathematician Gosta Mittag-Leffler might win such a prize, and Nobel hated him for having an affair with his wife. This story is not true. It could not possibly be, since Nobel never married.


Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin (email: devlin@csli.stanford.edu) is the Executive Director of the Center for the Study of Language and Information at Stanford University and The Math Guy on NPR's Weekend Edition. Devlin's newest book, THE MATH INSTINCT: Why You're a Mathematical Genius (along with Lobsters, Birds, Cats, and Dogs) was published recently by Thunder's Mouth Press.