A Nobel Prize for Mathematics?
As is well known, the Nobel Prizes are awarded annually in the fields of Physics, Chemistry, Medicine and Physiology, Literature, and Peace. (Since 1968, the "Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel" is also awarded, but this should not be confused with a real Nobel Prize). But
there is no Nobel Prize in Mathematics. The predominant theory for this omission is that Alfred Nobel did not
want the Swedish mathematician
Gösta Mittag-Leffler to receive the prize (some claim he had had an affair with
Nobel's wife). This theory sounds quite dramatic and is often quoted, but is disputed by
other sources, such as in the article "Why is there no Nobel Prize in Mathematics?", by
Lars Gårding and Lars Hörmander, Mathematical Intelligencer vol 7
(1985), pp 73-74 (sorry, no online version available). The explanation in that article
is that Nobel was simply a practical person (he invented dynamite, remember?), and did
not consider Mathematics useful enough to be attributed a prize.
The Fields Medal
In 1924, at the International Congress of Mathematicians (ICM) in Toronto, the creation
of a prize in Mathematics was proposed which would be awarded to two outstanding young
mathematicians at every ICM, which is held every four years. Money left over from the
conference was used to establish a fund for this prize, named in honor of Professor J.
C. Fields, a Canadian mathematician who was secretary of the 1924 Congress. This is
slightly ironic, as Fields himself had insisted that the medal should not be named after
any person or country. The Fields Medals, first awarded to
Lars Ahlfors and Jesse Douglas in 1936, is a gold medal bearing the image of
the greatest mathematician of antiquity. In 1966 it was agreed that the medal could be
awarded to up to four people at each ICM.
The most recent Fields Medals were again
awarded to only two people, Laurent Lafforgue and Vladimir Voevodsky, at the 2002 ICM in Beijing.
Most people today consider the Fields Medal to be the Mathematicians' equivalent of the
Nobel Prize, but there are some significant differences. Firstly, the Fields Medal is
only awarded every four years, to at most four people, giving an average of less than
one medalist per year. In contrast, most Nobel Prizes are shared by three people each
year. The second difference is that the Fields Medal is intended to encourage further
work, and, as Mathematics is a young man's game, this means that it is never awarded to
somebody older than forty. For example, Andrew
Wiles, who proved Fermat's Last Theorem, did not receive it. The reason is that his
proof of Fermat's Last Theorem was only complete by the end of 1994, so his first chance
at winning the Fields Medal was only at the 1998 ICM in Berlin, by which time he was
already 45 years old. He was awarded the ICM Silver Plaque instead, a unique prize which
was created specifically for him, and has not been awarded since.
The Abel Prize
Then, in 2001, the Norwegian government
announced the creation of the Abel Prize, named after the brilliant Norwegian
mathematician Niels Henrik
Abel (1802-1829), in commemoration of the 200th anniversary of his birth.
Abel, one of the shining lights of 19th century mathematics, died tragically
of Tuberculosis at the age of only 26. He is best known for his proof that the general
quintic equation cannot be solved by radicals (work which lead to the modern field of Group Theory), and for his work on elliptic functions.
Today, a number of important mathematical concepts bear his name, such as Abelian
groups, Abelian varieties, Abelian integrals and Abelian functions. The Abel Prize had already been proposed in 1902, but the idea was abandoned when the union between the kingdoms of Sweden and Norway was disbanded. The Abel Prize, now finally a reality, will be awarded annually to one person, based on lifetime achievement. Time will tell whether the Abel Prize or the Fields Medal will ultimately become accepted as "the" Nobel Prize in Mathematics.
Serre, born on 15 September 1926 in Bages, France, has been selected as the winner
of the 2003 (and first ever) Abel Prize. Serre has made fundamental contributions to
various fields of Mathematics, and has long been considered one of the leading
mathematicians of our time. The award came as no surprise. Serre has also won a number
of other important prizes, including the Prix Gaston Julia (1970), the Balzan Prize
(1985), the Steele Prize (1995) and the Wolf Prize (2000). Most notably, however, he
also won the Fields Medal in 1954, being the youngest recipient ever, and still before
some of his most important work.
The award citation mentions his work in Topology, Algebraic Geometry and Number Theory,
but he has also done important work in Complex Analysis, Commutative Algebra and Group
Theory, and probably also in other fields I am not aware of. As just one example, he
played a major role in paving the way for Wiles's proof of Fermat's Last Theorem. A very
large number of Mathematicians have contributed to the mathematics underlying this
fantastic exploit, but there are five people who's role is usually highlighted. They
are, in pseudo-chronological order: Gerhard Frey, Jean-Pierre Serre, Ken Ribet, Richard
Taylor and Andrew Wiles himself. There are a large number of sources on Fermat's Last
Theorem (google it yourself), including the popular books by
Amir D. Aczel, and
Simon Singh. I would like to point out, however, that Singh's book, though
beautifully written and hugely successful, does little justice to the role played by
Serre (or Frey, for that matter). Of course, this is not Serre's most
important contribution to modern Mathematics.
Serre is also a master expositor and has written a number of books which have since
become classics. His lectures are always inspirational and extremely clear, and the
lecture halls are usually crowded by students and professional mathematicians alike. I
have had the pleasure of listening to him speak on several occasions, and have been
amazed every time. Now, at the age of 76, he is still going strong and is as sharp as ever.
I saw this demonstrated most recently at a talk in Paris at the end of last year, when
he gave a colloquium on finite groups. At the end of the talk somebody in the audience
asked a rather interesting question (is every finite simple group a quotient of
SL(2,Z)?). He reasoned out the answer aloud (SL(2,Z) has two generators,
hence so does every quotient, then he recalled some finite simple group - I don't
remember which - that needs at least three generators, so the answer is no). This took
him five seconds.
Félicitations, Monsieur Serre!