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[P]
Jean-Pierre Serre awarded the first Abel Prize

By flo in Science
Tue Apr 08, 2003 at 03:14:48 AM EST
Tags: News (all tags)
News

The Norwegian Academy of Science and Letters has awarded the first ever Abel Prize to Jean-Pierre Serre of the Collège de France, Paris,

"for playing a key role in shaping the modern form of many parts of mathematics, including topology, algebraic geometry and number theory."
The prize is named after the brilliant Norwegian mathematician Niels Henrik Abel (1802-1829). A memorial fund was established in his name in 2002, and one of its purposes is to award a prize for outstanding work in the field of mathematics. The prize is worth NOK 6 million (about USD 800,000).


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 Archimedes, 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.

Jean-Pierre Serre

Jean-Pierre 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!

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Poll
Who do you think will win the 2004 Abel Prize?
o Andrew Wiles 15%
o Alain Connes 5%
o John H. Conway 9%
o John Tate 3%
o Yuri Manin 1%
o Pierre Deligne 1%
o other, see comment below 5%
o Who the hell are all these people? 56%

Votes: 53
Results | Other Polls

Related Links
o Google
o Abel Prize
o should not be confused
o Gösta Mittag-Leffler
o Fields Medals
o Archimedes
o awarded
o Andrew Wiles
o announced
o Niels Henrik Abel
o Jean-Pierr e Serre
o Amir D. Aczel
o Simon Singh
o Also by flo


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Jean-Pierre Serre awarded the first Abel Prize | 43 comments (24 topical, 19 editorial, 0 hidden)
This prize has no tradition or appeal (nt) (1.18 / 11) (#4)
by A Proud American on Mon Apr 07, 2003 at 01:23:13 PM EST



____________________________
The weak are killed and eaten...


Even Traditions have to start sometime... (5.00 / 7) (#31)
by Hobbes on Tue Apr 08, 2003 at 02:25:59 AM EST

And besides, you're just grumpy because a Frenchman is being awarded the prize.

:P

++++++
As bad as I am, I'm proud of the fact that I'm worse than I seem.
[ Parent ]

math suxx (1.00 / 17) (#10)
by tkatchev on Mon Apr 07, 2003 at 03:44:33 PM EST

ente

   -- Signed, Lev Andropoff, cosmonaut.

without maths k5 could not ever have existed! (none / 0) (#41)
by manmanman on Thu Apr 10, 2003 at 05:32:23 AM EST


Computer scientist, Montpellier, south of France.
[ Parent ]
What is the purpose of the prize? (4.00 / 2) (#11)
by gzt on Mon Apr 07, 2003 at 05:35:19 PM EST

Is it to reward lifetime achievement? Specific accomplishments? General greatness?

Lifetime achievement, mostly (5.00 / 2) (#14)
by flo on Mon Apr 07, 2003 at 10:14:25 PM EST

I have amended my article. Thanks.
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
Hmm (2.00 / 1) (#12)
by tetsuwan on Mon Apr 07, 2003 at 06:54:58 PM EST

Aren't there two guys in Japan that are really prominent in algebraic geometry as well? Now, of course math isn't just about algebraic geometry, but I heard from a Hungarian post-doc that these fellows are very bright.

There are many other brilliant mathematicians (5.00 / 4) (#13)
by flo on Mon Apr 07, 2003 at 10:13:01 PM EST

And the two Japanese you're thinking of are probably Mori and Hironaka (they both won Fields Medals for work in Algebraic Geometry). And there are others there, too. But this isn't the point. Algebraic Geometry is only one of the many fields to which Serre has contributed. For example, as far as I can tell, he was the first to consider an algebraic variety as a certain topological space equipped with a structure sheaf, which was the starting point for Grothendieck's definition of a scheme, on which all of modern Algebraic Geometry is based. He also introduced coherent and quasi-cohererent sheaves of modules. In fact, sheaves are very much Serre's speciality. For example, he won the Fields Medal in 1954 (at the age of 28) partly for reformulating complex analysis in terms of sheaves (and for his work on the homotopy groups of spheres).
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
Why I am glad I do not have to be a mathemetician: (none / 0) (#23)
by TheOnlyCoolTim on Mon Apr 07, 2003 at 11:50:39 PM EST

"coherent and quasi-cohererent sheaves of modules"

"homotopy groups of spheres"

I think I will stick to trying to be an engineer where you only need to know a little math...

Tim
"We are trapped in the belly of this horrible machine, and the machine is bleeding to death."
[ Parent ]

Why I'm glad I'm not an engineer (5.00 / 4) (#24)
by flo on Mon Apr 07, 2003 at 11:57:49 PM EST

Mathematicians can choose problems to work on which are fun. We are not constrained by usefulness of our work. Although there certainly are problems which are both fun and useful, there are far more things which are fun and useless.
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
On the other hand: (5.00 / 1) (#25)
by TheOnlyCoolTim on Tue Apr 08, 2003 at 12:00:23 AM EST

I prefer designing/building something concrete (as in real, although it could also be made out of concrete if I unexpectedly end up in civil engineering) rather than abstractions. Different strokes for different folks.

Tim
"We are trapped in the belly of this horrible machine, and the machine is bleeding to death."
[ Parent ]

modern maths is wide enough for both of you (4.50 / 4) (#26)
by martingale on Tue Apr 08, 2003 at 12:38:26 AM EST

It's actually no longer true that mathematics tends to be impractical or irrelevant to real-world concerns.

Last century was probably the exception in the modern era. Before the twentieth century, a lot of mathematics was indistinguishable from engineering and natural science. In particular, it was at the forefront of technology: astronomy for example was crucial for navigation around the world, and the only way to get anything useful out of it was to perform accurate calculations, which meant mathematical tricks and new theories. In truth, there just wasn't much difference between Physics and Mathematics before the twentieth century.

Then around the twentieth century Mathematics became much more abstract, in step with discoveries in Algebra. Computer Science probably became the first field which made any real use of number theory, and much of discrete mathematics. Hardy is famous for stating that he liked number theory because it was a branch of mathematics which couldn't be applied to war. Turing is famous for being part of the effort to change that.

So what I'm getting at is that with the advent of Computer Science, especially nowadays, a lot of mathematicians work on very concrete things (if you call software something concrete). The other big source of funding for the last fifty years, in the US at least, was the military. The ivory tower cliche is on the wane.

However, Serre's work is definitely part of that cliche, I'd say.

[ Parent ]

What I mean is (none / 0) (#29)
by TheOnlyCoolTim on Tue Apr 08, 2003 at 02:22:03 AM EST

At least in my perception Mathematics is the theory where I prefer the practice. I mean, can I hold a quasi-coherent sheave in my hand, or throw around a homotopy group of spheres? (Actually, for all I know about that stuff, maybe a homotopy group of spheres is the ball pit at McDonalds...) Software is sort of in between to me.

You still need a lot of maths in engineering, of course...

Tim
"We are trapped in the belly of this horrible machine, and the machine is bleeding to death."
[ Parent ]

some examples (5.00 / 2) (#34)
by martingale on Tue Apr 08, 2003 at 04:02:36 AM EST

Maybe I can give you some examples of concrete mathematical objects. Nothing too insightful, you probably won't be too impressed (but that's the point - it's ordinary).

1) A cryptographically signed license certificate. The bit that matters is usually just a bunch of really big numbers written as a base64 encoded string. Also, if you've bought software which needs an activation number, that little sticker with the number on the CD is pretty concrete.

2) If you've used the Gimp or Photoshop, you've come across various image enhancement filters. The enhancement is mostly done by cellular automata, and there's a branch of mathematics that deals with these directly. Actually, you don't need any software to perform the automata, if you have a pencil and paper. Either way, there's concrete evidence of an effect before and after the filter is applied to the image, and you can concretely apply the filter by changing each pixel in turn or pressing a button.

3) Compressed music formats. This involves different layers of purely mathematical formalism. There's the compression layer, where symbols are manipulated in terms of information theory, and there's the sound wave representation layer, which is a concrete Fourier series (or more likely, coefficients in some other function basis). But the MP3 file is just a concrete bunch of ones and zeros, which you could just as easily keep on (a very large stack of) paper.

Note I've given you only digital examples because that's where the mathematical objects are directly represented. You can practically hold them in your hand, and do whatever you want with them. Change a digit? No problem. You've just changed one of the frequencies in the music, or you've deactivated your version of XP. You can actually study all the properties of the object this way (but it's tedious ;-).

With analog examples such as in physics or engineering, the mathematical layer is much more an approximate representation, so isn't something you can "hold in your hand".

[ Parent ]

Ivory tower and all that (none / 0) (#43)
by flo on Fri Apr 25, 2003 at 09:27:41 AM EST

However, Serre's work is definitely part of that cliche, I'd say.

Actually, Serre's work on curves over finite fields is very relevant to coding theory - the science of making efficient error correcting codes. (He managed to improve the Hasse-Weil bound).
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
I was thinking of suggested 2004 prize cadidates (none / 0) (#30)
by tetsuwan on Tue Apr 08, 2003 at 02:23:05 AM EST



[ Parent ]
mathematical folklore (5.00 / 3) (#22)
by martingale on Mon Apr 07, 2003 at 11:19:20 PM EST

A classic book which, while not very accurate historically, is nevertheless a great source for stories such as the Mittag-Leffler one you alluded to, is Bell's "Men Of Mathematics". Fun to read for professionals and nonprofessionals alike.

Blatant name-dropping. (4.00 / 1) (#35)
by Akshay on Tue Apr 08, 2003 at 08:20:30 AM EST

My research-sup's great uncle was Niels Hendrik Abel. He has that plastered all over his office, including a huge banner he brought back from Abel's birth centenary celebrations.

Which reminds me. Time to get back on the research project.

M. Gromov (5.00 / 1) (#36)
by hading on Tue Apr 08, 2003 at 08:54:14 AM EST

I can dream, eh?  Sometimes he seems very underappreciated, but someday he'll get his due.

I.M. Gelfand would seem to be another excellent choice, especially given that we seem to be looking back at an entire lifetime of achievement.

Really there are just too many possibilities to make a reasonable guess.  Most Fields medalists are going to at least be in the running with others like the above two joining them.

Nor would I be surprised if there's a bit of politicking to assure that through the years the various branches of math receive a fairly equal representation.

age (none / 0) (#37)
by loudici on Tue Apr 08, 2003 at 03:30:38 PM EST

choosing serre seems to show they want to reward the acomplishment of a lifetime. gromov is still a bit young for that. they most probably will want to honor older heros while they are still around.
gnothi seauton
[ Parent ]
true enough (none / 0) (#38)
by hading on Tue Apr 08, 2003 at 04:31:06 PM EST

That's why I threw in Gelfand. :-)

I mostly brought up Gromov as a counter-balance against Wiles and Connes (who are similarly not yet very old) in the author's poll.  While he has the unfortunate position of not having won the Fields (as Connes has) nor having solved a very famous problem (as Wiles), IMHO his body of work stands up to theirs.

[ Parent ]

I was thinking of putting Gromov in the poll (5.00 / 1) (#39)
by flo on Tue Apr 08, 2003 at 11:26:07 PM EST

but there aren't many spaces there. My personal money is on John Tate, though. Gelfand isn't such a bad idea. I expect Gromov will get the prize eventually, but it's quite likely that the next few awards will be for the old masters.

Grothendieck should also have been in the poll.
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
Lower case 'a' for abelian (5.00 / 2) (#40)
by the on Wed Apr 09, 2003 at 08:18:41 PM EST

This isn't a nitpick.

When a mathematical construction is named after you you are famous in the mathematics world.

When it is named after you and the first letter of your name is lower case: then you're really famous - though you might lose your trade mark if you had one.

--
The Definite Article

Dangerous things those radicals... (none / 0) (#42)
by Alex Buchanan on Mon Apr 14, 2003 at 07:04:09 PM EST

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)...
Not to mention Galois Theory, named after another bright young thing who died at the tender age of 21 (if memory serves). Makes me kind of glad that I wasn't too hot at algebra. :o)

Jean-Pierre Serre awarded the first Abel Prize | 43 comments (24 topical, 19 editorial, 0 hidden)
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