## Devlin's Angle |

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.