Sneha Girap (Editor)

Barry Mazur

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit
Nationality
  
American

Name
  
Barry Mazur

Institutions
  
Role
  
Mathematician

Alma mater
  
Fields
  

Barry Mazur Quotes by Barry Mazur Like Success

Born
  
December 19, 1937 (age 86) New York City, New York (
1937-12-19
)

Doctoral students
  
Nigel BostonNoam ElkiesJordan EllenbergDavid GossMichael HarrisDaniel KaneMichael McQuillanVictor S. MillerPaul Vojta

Known for
  
diophantine geometrygeneralized Schoenflies conjectureMazur swindleMazur's torsion theorem

Education
  
Princeton University (1959), The Bronx High School of Science

Books
  
Imagining Numbers, Kolyvagin systems, Universal Extensions and One, Topics in Analytic Number T, Filtrations on the Homolog

Similar People
  
Karl Rubin, Nick Katz, Michael Artin, Ken Ribet, John Tate

Doctoral advisor
  
Ralph FoxR. H. Bing

Barry mazur logic elliptic curves and diophantine stability


Barry Charles Mazur (; born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.

Contents

Barry Mazur wwwmathharvardedumazurimagesmazur2jpg

Dr barry mazur the beauty in numbers


Life

Barry Mazur Barry Mazur 2011 National Medal of Science YouTube

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 the Gerhard Gade University Professor and a Senior Fellow at Harvard.

Work

Barry Mazur Barry Mazur Wikipedia

His early work was in geometric topology. In an 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.

Barry Mazur Sage Open Source Mathematics Software November 2015

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.

Barry Mazur TOP 6 QUOTES BY BARRY MAZUR AZ Quotes

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 Wiles's proof of Fermat's Last Theorem. Mazur and Wiles had earlier worked together on the main conjecture of Iwasawa theory.

Barry Mazur Barry Mazur and William Stein interview FifteenEightyFour

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 and Circles Disturbed, a collection of essays on mathematics and narrative that he edited with writer Apostolos Doxiadis.

Awards and honors

In 1982 he was elected a member of the National Academy of Sciences, and in 2012 he became a fellow of the American Mathematical Society.

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. In early 2013, he was presented with one of the 2011 National Medals of Science by President Barack Obama.

Books

  • Mazur, Barry; Stein, William (2016). Prime numbers and the Riemann hypothesis. New York, NY: Cambridge University Press. ISBN 9781107499430. 
  • Mazur, Barry; Jean-Pierre, Serre, eds. (2016). Collected works of John Tate : parts i and ii. American Mathematical Society. ISBN 0821890913. 
  • Mazur, Barry (2003). Imagining numbers : (particularly the square root of minus fifteen). New York: Farrar Straus Giroux. ISBN 0312421877. MR 1950850. 
  • Katz, Nicholas M.; Mazur, Barry (1985). Arithmetic moduli of elliptic curves. Annals of Mathematics Studies, 108. Princeton University Press. ISBN 0-691-08349-5. MR 0772569. 
  • References

    Barry Mazur Wikipedia