Barry Mazur
Barry Mazur (born December 19, 1937) is a professor of Mathematics at Harvard University.
Born in New York, New York, Mazur received his Ph.D. from Princeton University in 1959 and was 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 AMS.
His early work was in geometric topology. Coming under the influence of Alexander Grothendieck's approach to algebraic geometry, he moved into areas of diophantine geometry. Mazur's torsion theorem is a basic result on elliptic curves.
He is noted also for the introduction of the Eisenstein ideal in Hecke algebras. This idea was one of the steps in Andrew Wiles's ultimately successful attack on Fermat's Last Theorem. Mazur and Wiles had earlier worked together in a major paper on the problems of Iwasawa theory over totally real fields.
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.