Barry Mazur
Barry Charles Mazur | |
|---|---|
 Barry Mazur in 1992 | |
| Born | December 19, 1937 |
| Nationality |  United States |
| Alma mater | Princeton University |
| Known for | diophantine geometry generalized Schoenflies conjecture Mazur swindle Mazur's torsion theorem |
| Awards | Cole Prize (1982) Veblen Prize (1966) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Harvard University |
| Doctoral advisor | Ralph Fox R. H. Bing |
| Doctoral students | Nigel Boston Noam Elkies Jordan Ellenberg David Goss Michael Harris Daniel Kane Paul Vojta |
Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard.
Life
Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959, becoming a Junior Fellow at Harvard from 1961 to 1964. He is currently the Gerhard Gade University Professor and a Senior Fellow at Harvard. In 1982 he was elected a member of the National Academy of Sciences. Mazur has received the Veblen Prize in geometry, the Cole Prize in number theory, the Chauvenet Prize for exposition, and the Steele Prize for seminal contribution to research from the American Mathematical Society.
Work
His early work was in geometric topology. In a clever, elementary fashion, he proved the generalized Schoenflies conjecture (his complete proof required an additional result by Marston Morse), around the same time as Morton Brown. Both Brown and Mazur received the Veblen Prize for this achievement. He also discovered the Mazur manifold and the Mazur swindle.
His observations in the 1960s on analogies between primes and knots were taken up by others in the 1990s giving rise to the field of Arithmetic topology.
Coming under the influence of Alexander Grothendieck's approach to algebraic geometry, he moved into areas of diophantine geometry. Mazur's torsion theorem, which gives a complete list of the possible torsion subgroups of elliptic curves over the rational numbers, is a deep and important result in the arithmetic of elliptic curves. Mazur's first proof of this theorem depended upon a complete analysis of the rational points on certain modular curves. This proof was carried in his seminal paper "Modular curves and the Eisenstein ideal". The ideas of this paper and Mazur's notion of Galois deformations, were among the key ingredients in Andrew Wiles's ultimately successful attack on Fermat's last theorem. Mazur and Wiles had earlier worked together on the main conjecture of Iwasawa theory.
In an expository paper, Number Theory as Gadfly, Mazur describes number theory as a field which
- produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet... number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!
He expanded his thoughts in the 2003 book Imagining Numbers.