Don Zagier
Encyclopedia
Don Bernard Zagier is an American mathematician
whose main area of work is number theory
. He is currently one of the directors of the Max Planck Institute for Mathematics
in Bonn
, Germany
, and a professor at the Collège de France
in Paris
, France
.
He was born in Heidelberg
, Germany
. His mother was a psychiatrist, and his father was the dean of instruction at the American College of Switzerland
. His father held five different citizenships, and he spent his youth living in many different countries. After finishing high school and attending Winchester College
for a year, he studied for three years at M.I.T., completing his bachelor's and master's degrees and being named a Putnam Fellow in 1967 at the age of 16. He then wrote a doctoral dissertation on characteristic class
es under Friedrich Hirzebruch
at Bonn
, graduating at 21, and later collaborated with Hirzebruch in work on Hilbert modular surface
s.
One of his most famous results is a joint work with Benedict Gross
(the so-called Gross–Zagier formula). This formula relates the first derivative of the complex L-series
of an elliptic curve
evaluated at 1 to the height of a certain Heegner point
. This theorem has many applications including implying cases of the Birch and Swinnerton-Dyer conjecture
along with being a key ingredient to Dorian Goldfeld's solution of the class number problem.
He also is known for discovering a short and elementary proof of Fermat's theorem on sums of two squares.
Zagier won the Cole Prize in Number Theory
in 1987 and the von Staudt Prize in 2001.
The First 50 Million Prime Numbers
"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definitions and role as the building blocks of the natural numbers, the prime numbers belong to the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision."
The First 50 Million Prime Numbers
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
whose main area of work is number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He is currently one of the directors of the Max Planck Institute for Mathematics
Max-Planck-Institut für Mathematik
The Max-Planck-Institut für Mathematik is a mathematical research institute located in Bonn, Germany. It is named in honour of the German physicist Max Planck...
in Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, and a professor at the Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
.
He was born in Heidelberg
Heidelberg
-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. His mother was a psychiatrist, and his father was the dean of instruction at the American College of Switzerland
American College of Switzerland
The American College of Switzerland is a liberal arts college in Leysin, Switzerland in the canton of Vaud.The campus is housed in the modernized Victorian style Grand Hôtel de Leysin, built in 1892. A private train station on campus connects to all main lines and cities in Switzerland...
. His father held five different citizenships, and he spent his youth living in many different countries. After finishing high school and attending Winchester College
Winchester College
Winchester College is an independent school for boys in the British public school tradition, situated in Winchester, Hampshire, the former capital of England. It has existed in its present location for over 600 years and claims the longest unbroken history of any school in England...
for a year, he studied for three years at M.I.T., completing his bachelor's and master's degrees and being named a Putnam Fellow in 1967 at the age of 16. He then wrote a doctoral dissertation on characteristic class
Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle on a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted" — particularly, whether it possesses sections or not...
es under Friedrich Hirzebruch
Friedrich Hirzebruch
Friedrich Ernst Peter Hirzebruch is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.-Life:He was born in Hamm, Westphalia...
at Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
, graduating at 21, and later collaborated with Hirzebruch in work on Hilbert modular surface
Hilbert modular surface
In mathematics, a Hilbert modular surface is one of the surfaces obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group....
s.
One of his most famous results is a joint work with Benedict Gross
Benedict Gross
Benedict Hyman Gross is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College....
(the so-called Gross–Zagier formula). This formula relates the first derivative of the complex L-series
L-function
The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases...
of an elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
evaluated at 1 to the height of a certain Heegner point
Heegner point
In mathematics, a Heegner point is a point on a modular elliptic curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class...
. This theorem has many applications including implying cases of the Birch and Swinnerton-Dyer conjecture
Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
along with being a key ingredient to Dorian Goldfeld's solution of the class number problem.
He also is known for discovering a short and elementary proof of Fermat's theorem on sums of two squares.
Zagier won the Cole Prize in Number Theory
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
in 1987 and the von Staudt Prize in 2001.
Common quotations
"Upon looking at these numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation."The First 50 Million Prime Numbers
"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definitions and role as the building blocks of the natural numbers, the prime numbers belong to the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision."
The First 50 Million Prime Numbers
Selected publications
.- Zagier, D. "The First 50 Million Prime Numbers." Math. Intel. 0, 221–224, 1977.
External links
- Biography from the webpage of the Max Planck SocietyMax Planck SocietyThe Max Planck Society for the Advancement of Science is a formally independent non-governmental and non-profit association of German research institutes publicly funded by the federal and the 16 state governments of Germany....