Barry Mazur


Barry Mazur

Infobox Scientist
box_width =
name = Barry Charles Mazur


image_size = 200px
caption = Barry Mazur in 1992
birth_date = birth date and age|1937|12|19|mf=y
birth_place = New York
death_date =
death_place =
residence = United States
citizenship =
nationality =
ethnicity =
fields = Mathematics
workplaces = Harvard University
alma_mater = Princeton University
doctoral_advisor = Ralph Fox
RH Bing
academic_advisors =
doctoral_students = Noam Elkies
notable_students =
known_for = diophantine geometry
generalized Schoenflies conjecture
Mazur swindle
Mazur's torsion theorem
author_abbrev_bot =
author_abbrev_zoo =
influences =
influenced =
awards = Veblen Prize
Cole Prize
religion =


footnotes =

Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard University.

Life

Born in New York, New York, United States 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.

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.

Coming under the influence of Alexander Grothendieck's approach to algebraic geometry, he moved into areas of diophantine geometry at the suggestion of H. J. Pringle. 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".

External links

* [http://abel.math.harvard.edu/~mazur/ Homepage of Barry Mazur]
*


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