2013 - Fellow of the American Mathematical Society
2011 - US President's National Medal of Science "For original and landmark contributions to differential topology, number theory, and arithmetic algebraic geometry, where, among other applications, his work was foundational to Wiles proof of Fermats Last Theorem, and for his dedication to communicating subtle mathematical ideas to the broader public.", President Barack H. Obama in the East Room of the White House on February 1, 2013.
2000 - Steele Prize for Seminal Contribution to Research
1983 - Fellow of John Simon Guggenheim Memorial Foundation
1982 - Member of the National Academy of Sciences
1982 - Frank Nelson Cole Prize in Number Theory
1978 - Fellow of the American Academy of Arts and Sciences
1962 - Fellow of Alfred P. Sloan Foundation
His primary scientific interests are in Algebra, Pure mathematics, Combinatorics, Discrete mathematics and Elliptic curve. His research in the fields of Algebraic variety, Fundamental theorem of Galois theory and Galois extension overlaps with other disciplines such as Diophantine geometry. While working in this field, Barry Mazur studies both Pure mathematics and Heegner point.
His study in the fields of Homomorphism under the domain of Combinatorics overlaps with other disciplines such as Algebraic extension. His Discrete mathematics study incorporates themes from Winding number and Abelian group. His research ties Algebraic number field and Elliptic curve together.
Barry Mazur mainly focuses on Pure mathematics, Combinatorics, Elliptic curve, Discrete mathematics and Algebraic number field. His research integrates issues of Moduli and Algebra in his study of Pure mathematics. In most of his Combinatorics studies, his work intersects topics such as Class number.
His Elliptic curve study integrates concerns from other disciplines, such as Quadratic equation, Arithmetic and Rank. His biological study spans a wide range of topics, including Abelian group, Rational point and Conjecture. He has researched Galois module in several fields, including Galois group and Galois extension.
Combinatorics, Pure mathematics, Algebraic number field, Elliptic curve and Spectrum are his primary areas of study. His Combinatorics research integrates issues from Order and Spin-½. In the subject of general Pure mathematics, his work in Cohomology is often linked to Trigonometric substitution, thereby combining diverse domains of study.
His Algebraic number field study is concerned with the field of Discrete mathematics as a whole. His Elliptic curve study also includes
Barry Mazur spends much of his time researching Pure mathematics, Elliptic curve, Combinatorics, Conjecture and Quadratic equation. His Pure mathematics study frequently links to adjacent areas such as Rational point. As a part of the same scientific family, Barry Mazur mostly works in the field of Elliptic curve, focusing on Algebraic number field and, on occasion, Character, Isomorphism, Integer and Elliptic rational functions.
His work deals with themes such as Mathematical proof and Argument, which intersect with Combinatorics. His Conjecture research is multidisciplinary, incorporating elements of Term, Class number, Order and Generalization. The various areas that Barry Mazur examines in his Quadratic equation study include Absolute Galois group, Markov process, Markov model and Distribution.
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Modular curves and the Eisenstein ideal
Publications Mathématiques de l'IHÉS (1977)
Arithmetic moduli of elliptic curves
Nicholas M. Katz;Barry Mazur.
Rational Isogenies of Prime Degree
Inventiones Mathematicae (1978)
On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.
B. Mazur;J. Tate;J. Teitelbaum.
Inventiones Mathematicae (1986)
Class fields of abelian extensions of Q.
B. Mazur;A. Wiles.
Inventiones Mathematicae (1984)
Rational Points of Abelian Varieties with Values in Towers of Number Fields.
Inventiones Mathematicae (1972)
On Periodic Points
M. Artin;B. Mazur.
Annals of Mathematics (1965)
Arithmetic of Weil Curves.
B. Mazur;P. Swinnerton-Dyer.
Inventiones Mathematicae (1974)
Deforming Galois Representations
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108
Nicholas M. Katz;Barry Mazur.
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