2026 Barry Mazur: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	59	590	497	300	235	200	14188

Research.com Recognitions

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

Overview

Barry Mazur is affiliated with Harvard University in the United States and works primarily within the field of mathematics. Their research spans various subfields, including geometry and topology, algebra and number theory, mathematical physics, computational theory and mathematics, and electrical and electronic engineering.

The main topics covered in their work include:

Algebraic Geometry and Number Theory
Analytic Number Theory Research
Homotopy and Cohomology in Algebraic Topology
Mathematics and Applications
Commutative Algebra and Its Applications
Graph Theory and CDMA Systems
Advanced Differential Equations and Dynamical Systems

Recent publications exemplify the diversity of their research interests. Selected papers include:

"Arithmetic Conjectures Suggested by the Statistical Behavior of Modular Symbols," 2021, Experimental Mathematics
"Existential definability and diophantine stability," 2023, Journal of Number Theory
"Defining ℤ using unit groups," 2024, Acta Arithmetica
"Uniformity of rational points: an up-date and corrections," 2022, Tunisian Journal of Mathematics
"Existential definability and diophantine stability," 2022, arXiv (Cornell University)

Mazur frequently collaborates with several other researchers. Notable coauthors include:

Karl Rubin
Alexandra Shlapentokh
Jennifer S. Balakrishnan
Lucia Caporaso
Joe Harris

Their work is often published in esteemed venues such as:

arXiv (Cornell University)
Journal of Number Theory
The Mathematical Intelligencer
Notices of the American Mathematical Society
Experimental Mathematics

Barry Mazur has received several recognitions during their career, including:

Fellow of the American Mathematical Society, 2013
US President's National Medal of Science, 2011, presented by President Barack H. Obama for contributions spanning differential topology, number theory, and arithmetic algebraic geometry
Steele Prize for Seminal Contribution to Research, 2000
Fellow of John Simon Guggenheim Memorial Foundation, 1983
Member of the National Academy of Sciences, 1982
Frank Nelson Cole Prize in Number Theory, 1982
Fellow of the American Academy of Arts and Sciences, 1978
Fellow of Alfred P. Sloan Foundation, 1962

Best Publications

Modular curves and the Eisenstein ideal

Barry Mazur

1455
Citations
Arithmetic moduli of elliptic curves

Nicholas M. Katz;Barry Mazur

1026
Citations
Rational Isogenies of Prime Degree

B. Mazur

979
Citations
On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.

B. Mazur;J. Tate;J. Teitelbaum

668
Citations
Class fields of abelian extensions of Q.

B. Mazur;A. Wiles

648
Citations
Rational Points of Abelian Varieties with Values in Towers of Number Fields.

Barry Mazur

611
Citations
On Periodic Points

M. Artin;B. Mazur

479
Citations
Arithmetic of Weil Curves.

B. Mazur;P. Swinnerton-Dyer

431
Citations
Deforming Galois Representations

B. Mazur

428
Citations
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

Nicholas M. Katz;Barry Mazur

424
Citations
Universal Extensions and One Dimensional Crystalline Cohomology

Barry Mazur;William Messing

258
Citations
Mathematics: Frontiers and Perspectives

Harsh V. Pittie;V. Arnold;M. Atiyah;P. Lax

248
Citations
A Note on Some Contractible 4-Manifolds

Barry Mazur

231
Citations
Uniformity of rational points

Lucia Caporaso;Joe Harris;Barry Mazur

219
Citations
Formal groups arising from algebraic varieties

M. Artin;B. Mazur

215
Citations
On $p$-adic analytic families of Galois representations

B. Mazur;A. Wiles

204
Citations
An Introduction to the Deformation Theory of Galois Representations

Barry Mazur

198
Citations
The topology of rational points

Barry Mazur

183
Citations
The square-free sieve and the rank of elliptic curves

F. Gouvêa;B. Mazur

173
Citations
Frobenius and the Hodge filtration

B. Mazur

168
Citations
-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture

Barry Mazur;Glenn Stevens

28
Citations

Frequent Co-Authors

Nicholas M. Katz Princeton University

John Tate Harvard University

Joe Harris Harvard University

Michael Artin MIT

John B. Friedlander University of Toronto

Henryk Iwaniec Rutgers, The State University of New Jersey

David Mumford Brown University

Friedrich Hirzebruch Max Planck Institute for Mathematics

Eric M. Friedlander University of Southern California

David Eisenbud University of California, Berkeley

External Links

Wikipedia of Barry Mazur Personal website of Barry Mazur

If you think any of the details on this page are incorrect, let us know.

Related Online Degrees & Career Pathways

For students pursuing Mathematics in the USA, exploring related online degrees can expand career prospects. Many programs now offer flexibility, including transfer credits for online MBA programs, which help students leverage previous coursework to accelerate their studies.

Data-driven fields are increasingly popular, making a masters data analytics degree a valuable option for math graduates. This specialization enhances skill sets for careers in business intelligence, finance, and technology sectors.

Not all advanced degrees require rigorous admissions processes. Some of the easiest MBA programs provide a practical pathway for those wanting to combine managerial skills with their mathematical background. These programs cater to working professionals aiming for career growth without intense entry barriers.

Similarly, the easiest online MBA programs to get into offer a convenient option for distance learners seeking to upgrade their qualifications. Choosing these programs can be especially beneficial for students balancing work, study, and life commitments.

By understanding these linked pathways and the availability of flexible, accessible online programs, math students can strategically plan their education and career advancement.