Barry Mazur
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Barry Mazur (born December 19, 1937) is a professor of mathematics at Harvard University.
Born in New York, New York, 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 University from 1961-64. He is currently the Gerhard Gade University Professor at Harvard University. In 1982 he was elected a member of the National Academy of Sciences. Mazur has received the Veblen Prize in geometry and the Cole Prize in number theory from the American Mathematical Society.
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.
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 seminar paper "Modular curves and the Eisenstein ideal". The ideas of this paper and Mazur's notion of Galois deformations, were among the keys 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.
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Categories: 1937 births | Living people | 20th century mathematicians | 21st century mathematicians | Number theorists | American mathematicians | Jewish mathematicians | Members and associates of the United States National Academy of Sciences | Princeton University alumni | Harvard University faculty | American mathematician stubs
