| Don Zagier | |
|---|---|
| Born | 29 June 1951 Heidelberg, Germany |
| Nationality | United States of America |
| Fields | Mathematics |
| Institutions | Max Planck Institute for Mathematics Collège de France |
| Alma mater | University of Bonn |
| Doctoral advisor | Friedrich Hirzebruch |
| Doctoral students | Winfried Kohnen Maxim Kontsevich |
| Known for | Gross–Zagier theorem Herglotz–Zagier function |
Don Bernard Zagier (born 29 June 1951) 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 classes under Friedrich Hirzebruch at Bonn, graduating at 21, and later collaborated with Hirzebruch in work on Hilbert modular surfaces.
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.[1][2]
Zagier won the Cole Prize in Number Theory in 1987[3] and the von Staudt Prize in 2001.[4]
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"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