Barry Mazur (born December 19, 1937) is a professor of mathematics at Harvard University. December 19 is the 353rd day of the year (354th in leap years) in the Gregorian calendar. ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ... Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ...

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. Midtown Manhattan, looking north from the Empire State Building, 2005 New York City (officially named the City of New York) is the most populous city in the state of New York and the entire United States. ... Princeton University is a coeducational private university located on an extensive campus in and around suburban Princeton, New Jersey. ... 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ... Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ... 1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ... President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ... The Cole Prize is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. ... AMS is a three-letter abbreviation with multiple meanings, as described below: American Meteorological Society Advanced Management Systems Aerospace Material Specification Accelerator mass spectrometry or accelerator mass spectrometer. ...

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. In mathematics, geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups. ... Alexander Grothendieck (Berlin, March 28, 1928) is one of the most important mathematicians of the 20th century. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... In algebraic geometry Mazurs torsion theorem, due to Barry Mazur, classifies the possible torsion subgroups of the group of rational points on an elliptic curve defined over the rational numbers. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ...

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 mathematics, the Eisenstein ideal is a certain ideal in the endomorphism ring of the Jacobian variety of a modular curve. ... In mathematics, in particular in the theory of modular forms, a Hecke operator is a certain kind of averaging operator that plays a significant role in the structure of vector spaces of modular forms (and more general automorphic representations). ... Sir Andrew John Wiles (born April 11, 1953) is a British mathematician living in the United States. ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats last theorem (edition of 1670). ... In number theory, Iwasawa theory is a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa as part of the theory of cyclotomic fields. ... In number theory , a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers. ...

In an expository paper, Number Theory as Gadfly, Mazur describes number theory as a field which Gadfly is a term for people who upset the status quo by posing upsetting or novel questions, or attempts to stimulate innovation by proving an irritant. ...

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. Mathematician Barry Mazur authored a book entitled Imagining Numbers: (particularly the square root of minus fifteen). ...

External link

• Homepage of Barry Mazur