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- Barry Mazur

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
54
Citations
12,377
169
World Ranking
611
National Ranking
318

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

- Algebra
- Mathematical analysis
- Pure mathematics

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.

- Modular curves and the Eisenstein ideal (806 citations)
- Arithmetic moduli of elliptic curves (622 citations)
- Rational Isogenies of Prime Degree (551 citations)

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.

- Pure mathematics (36.04%)
- Combinatorics (16.75%)
- Elliptic curve (14.72%)

- Combinatorics (16.75%)
- Pure mathematics (36.04%)
- Algebraic number field (13.71%)

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

- Absolute Galois group which is related to area like Twists of curves,
- Distribution which intersects with area such as Markov process. His Integer research is multidisciplinary, relying on both Isomorphism and Character, Algebra.

- Disparity in Selmer Ranks of Quadratic Twists of Elliptic Curves (37 citations)
- The spin of prime ideals (24 citations)
- Controlling Selmer groups in the higher core rank case (17 citations)

- Algebra
- Mathematical analysis
- Pure mathematics

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.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Modular curves and the Eisenstein ideal

Barry Mazur.

Publications Mathématiques de l'IHÉS **(1977)**

1340 Citations

Arithmetic moduli of elliptic curves

Nicholas M. Katz;Barry Mazur.

**(1985)**

990 Citations

Rational Isogenies of Prime Degree

B. Mazur.

Inventiones Mathematicae **(1978)**

893 Citations

On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.

B. Mazur;J. Tate;J. Teitelbaum.

Inventiones Mathematicae **(1986)**

632 Citations

Class fields of abelian extensions of Q.

B. Mazur;A. Wiles.

Inventiones Mathematicae **(1984)**

615 Citations

Rational Points of Abelian Varieties with Values in Towers of Number Fields.

Barry Mazur.

Inventiones Mathematicae **(1972)**

550 Citations

On Periodic Points

M. Artin;B. Mazur.

Annals of Mathematics **(1965)**

465 Citations

Arithmetic of Weil Curves.

B. Mazur;P. Swinnerton-Dyer.

Inventiones Mathematicae **(1974)**

412 Citations

Deforming Galois Representations

B. Mazur.

**(1989)**

394 Citations

Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

Nicholas M. Katz;Barry Mazur.

**(1985)**

383 Citations

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