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Frontmatter

The History of the Abel Prize and the Honorary Abel Prize

Frontmatter

The History of the Abel Prize

On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Government decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003.

Arild Stubhaug

2002—an Honorary Abel Prize to Atle Selberg

When the Abel Prize was established in 2002 it was decided to award an honorary prize to the renowned Norwegian mathematician Atle Selberg in recognition of his status as one of the world’s leading mathematicians. His contributions to mathematics are so deep and original that his name will always be an important part of the history of mathematics. His special field in mathematics was number theory in a broad sense.

Nils A. Baas

2003 Jean-Pierre Serre

Frontmatter

Jean-Pierre Serre: Mon premier demi-siècle au Collège de France

Jean-Pierre Serre was interviewed by Marc Kirsch at the occasion of his first fifty years at Collège de France. He talks about his inaugural lecture, and why it was never written up; he recalls his experience with Bourbaki; he gives his views on the development of mathematics, as well as on other issues. The text is bilingual French-English.

Marc Kirsch

Jean-Pierre Serre: An Overview of His Work

For more than five decades, the mathematical contributions of Jean-Pierre Serre have played an essential role in the development of several areas of mathematics. The present paper aims to provide an overview of his work. The selected references include his books, most of the papers collected in his

Œuvres

, as well as some of his more recent publications.

Pilar Bayer

List of Publications for Jean-Pierre Serre

2004 Sir Michael Atiyah and Isadore M. Singer

Frontmatter

Autobiography

I was born in London on 22

nd

April 1929, but in fact I lived most of my childhood in the Middle East. My father was Lebanese but he had an English education, culminating in three years at Oxford University where he met my mother, who came from a Scottish family. Both my parents were from middle class professional families, one grandfather being a minister of the church in Yorkshire and the other a doctor in Khartoum.

Michael Atiyah

Autobiography

My mother, Freda Rosemaity, and father, Simon Singer, were born in Poland. After World War I, they immigrated to Toronto, Canada where they met and were married. My father was a printer and my mother a seamstress. In the early 1920’s they moved to Detroit, Michigan. I was born there in 1924.

Isadore M. Singer

The Atiyah–Singer Index Theorem

The Abel Prize citation for Michael Atiyah and Isadore Singer reads: “The Atiyah–Singer index theorem is one of the great landmarks of twentieth-century mathematics, influencing profoundly many of the most important later developments in topology, differential geometry and quantum field theory”. This article is an attempt to describe the theorem, where it came from, its different manifestations and a collection of applications. It is clear from the citation that the theorem spans many areas. I have attempted to define in the text the most important concepts but inevitably a certain level of sophistication is needed to appreciate all of them. In the applications I have tried to indicate how one can use the theorem as a tool in a concrete fashion without necessarily retreating into the details of proof. This reflects my own appreciation of the theorem in its various forms as part of the user community. The vision and intuition that went into its proof is still a remarkable achievement and the Abel Prize is a true recognition of that fact.

Nigel Hitchin

List of Publications for Sir Michael Atiyah and Isadore M. Singer

2005 Peter D. Lax

Frontmatter

Autobiography

Like most mathematicians, I became fascinated with mathematics early, about age ten. I was fortunate that my uncle could explain matters that puzzled me, such as why minus times minus is plus—it follows from the laws of algebra.

Mathematics had a deep tradition in Hungary, going back to the epoch-making invention of non-Euclidean geometry by János Bolyai, an Hungarian genius in the early 19th century. To this day, the Hungarian mathematical community seeks out mathematically talented students through contests and a journal for high school students. Winners are then nurtured intensively. I was tutored by Rose Peter, an outstanding logician and pedagogue; her popular book on mathematics, “Playing with Infinity” is still the best introduction to the subject for the general public.

Peter D. Lax

A Survey of Peter D. Lax’s Contributions to Mathematics

We discuss Peter D. Lax’s contributions to mathematics over a period of more than 60 years.

Helge Holden, Peter Sarnak

List of Publications for Peter D. Lax

2006 Lennart Carleson

Frontmatter

Reflections on My Life as a Mathematician

My ancestors are all from the Swedish bourgeois society. Among them are rather prominent civil servants and officers in the army. My father was originally a civil engineer and he became executive director of a large steel mill. My adolescence was very privileged and as a Swede I was fortunate to escape from the sufferings of the Second World War. There was no academic tradition in my family but I grew up in an intellectually stimulating environment where political matters were the main topics. I went to the local schools and skipped one grade, so that I finished high school barely 17 years old. I had then started to read mathematics textbooks, for the first undergraduate level, but I was in no way determined to become a mathematician. Most of my reading during the three last years of high school was classical literature, and when I now think back to that period I am amazed at how much I managed to read. This was actually the only period of my life that I could find time for a general education.

Lennart Carleson

Carleson for Beginners

When I was just beginning as a research student, an older mathematical friend invited me to dine at Trinity. At dessert I was seated next to Littlewood, Hardy’s collaborator and a legendary figure in modern British analysis. With old fashioned politeness, Littlewood set himself out to entertain me. He talked about a recent comet and recalled how fifty years earlier he had viewed Halley’s comet in company with a Trinity fellow who had himself seen its previous visitation. He then spoke about Carleson’s recent proof of the convergence theorem, what a marvellous result it was, how surprising it was that it turned out that Lusin’s conjecture was true, how many people known to him had thought about the problem for a long time without success and how much he regretted being too old to take up the task of understanding the details of the proof.

Tom Körner

List of Publications for Lennart Carleson

2007 S.R. Srinivasa Varadhan

Frontmatter

Autobiography

According to my school records I was born on Jan 2, 1940, in the city of Madras, in the state of Madras in India, which was then a British colony. The city is now called Chennai and the state has become Tamil Nadu in the Republic of India.

My father was born in the last year of the nineteenth century, in 1899 and he married my mother in 1917, when he was eighteen and she was ten. I am an only child and my parents had been married for nearly twenty five years when I was born. Both my parents were the eldest siblings in rather large families and I have always received special attention from all my uncles, aunts, cousins, grandmothers and other assorted relatives. I was born so late that I did not really get to know either of my grandfathers.

S. R. Srinivasa Varadhan

A Personal Perspective on Raghu Varadhan’s Role in the Development of Stochastic Analysis

I know Raghu Varadhan professionally but not personally—that is to say we have attended some of the same conferences and Oberwolfach meetings, and even the odd meal while waiting for trains home. Still, it is obvious to me, and I am sure to anyone else who comes close, that he is a person of great humanity who generates warmth and humour whenever he is in the room. A few months after the award of Fields Medals to Werner, Okounkov and Tao in Madrid, Varadhan and I were both in a group of mathematicians talking about the event. I remember clearly Varadhan’s concise summary of the business as “A great day for the coin flippers”. It certainly was: all three used probability in their ground-breaking work and, for the first two, Stochastic Analysis has been a decisive part of their mathematical toolbox. We were all excited that stochastic ideas were having such a substantial effect across areas as far apart as conformal field theory, geometry and number theory. We were also delighted that these achievements were recognized. To me, Varadhan’s remark seemed to capture his modesty and humour rather well. Surely it was another excellent day for the coin flippers when Varadhan was awarded the Abel Prize.

Terry Lyons

List of Publications for S.R. Srinivasa Varadhan

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