- 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 atHarvard University .Life
Born in
New York, New York ,United States Mazur attended theBronx High School of Science andMIT , although he did not graduate from the latter on account of failing a then-presentROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. fromPrinceton University in 1959, becoming a Junior Fellow atHarvard 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 theVeblen Prize in geometry and theCole Prize in number theory from theAmerican Mathematical Society .Work
His early work was in
geometric topology . In a clever, elementary fashion, he proved thegeneralized Schoenflies conjecture (his complete proof required an additional result byMarston Morse ), around the same time asMorton Brown . Both Brown and Mazur received theVeblen Prize for this achievement. He also discovered theMazur manifold and theMazur swindle .Coming under the influence of
Alexander Grothendieck 's approach toalgebraic geometry , he moved into areas ofdiophantine geometry at the suggestion of H. J. Pringle.Mazur's torsion theorem , which gives a complete list of the possible torsion subgroups ofelliptic curve s 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 certainmodular curve s. This proof was carried in his seminal paper "Modular curves and the Eisenstein ideal". The ideas of this paper and Mazur's notion ofGalois deformation s, were among the key ingredients inAndrew Wiles 's ultimately successful attack onFermat'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]
*
Wikimedia Foundation. 2010.
