By AI Staff

Barry Mazur currently holds the title of Gerhard Gade University Professor at Harvard University, where he has worked as a professor since 1962. Prior to his long tenure at Harvard, Mazur held post-doctoral fellowships at Harvard and the Institute for Advanced Study. Mazur earned his PhD in Mathematics at Princeton University; though he attended MIT as an undergraduate, he did not complete a bachelor’s degree.

Mazur boasts a long career of discoveries and advancements in geometry, arithmetic, and number theory. In fact, he has several discoveries and proofs named after him, including the Mazur swindle, the Mazur manifold, and Mazur’s torsion theorem. Mazur is particularly famous for the latter, which was used by Andrew Wiles in his groundbreaking proof of Fermat’s Last Theorem.

Notable works from Mazur include Imagining Numbers and Prime Numbers and the Riemann Hypothesis.

For his work, Mazur has received awards and honors including membership with the American Philosophical Society, the Steele Prize, the Cole Prize, and the Veblen prize from the American Mathematical Society, as well as fellowship, and the Chauvenet Prize from the Mathematical Association of America.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Barry Charles Mazur is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology.

- Modular curves and the eisenstein ideal
- Arithmetic moduli of elliptic curves
- Rational isogenies of prime degree
- Class fields of abelian extensions of Q
- Onp-adic analogues of the conjectures of Birch and Swinnerton-Dyer
- Rational points of abelian varieties with values in towers of number fields
- On Periodic Points
- Deforming Galois Representations
- Arithmetic of Weil curves
- Arithmetic Moduli of Elliptic Curves. (AM-108)
- -Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture
- Universal Extensions and One Dimensional Crystalline Cohomology
- Uniformity of rational points
- Mathematics: Frontiers and Perspectives
- On $p$-adic analytic families of Galois representations
- An Introduction to the Deformation Theory of Galois Representations
- Frobenius and the Hodge filtration
- A Note on Some Contractible 4-Manifolds
- Formal groups arising from algebraic varieties
- Filtrations on the Homology of Algebraic Varieties
- The Topology of Rational Points
- Notes on étale cohomology of number fields
- Ranks of twists of elliptic curves and Hilbert’s tenth problem
- This is the Story.
- The square-free sieve and the rank of elliptic curves
- Refined conjectures of the “Birch and Swinnerton-Dyer type”
- Frobenius and the Hodge Filtration (estimates)
- Arithmetic on curves
- Rational points on modular curves
- Smoothings of piecewise linear manifolds
- Algebraic Numbers By
- Visualizing Elements in the Shafarevich—Tate Group
- Questions of Decidability and Undecidability in Number Theory
- On the arithmetic of special values ofL functions
- Canonical Height Pairings via Biextensions
- Families of modular eigenforms
- Galois Representations in Arithmetic Algebraic Geometry: The Eigencurve
- On embeddings of spheres
- Finding Large Selmer Rank via an Arithmetic Theory of Local Constants
- Modular curves and arithmetic
- The $p$-adic sigma function
- Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
- On the van Kampen theorem
- Hypersurfaces of low degree
- Computation of p-Adic Heights and Log Convergence
- Number theory as gadfly
- Finding meaning in error terms
- Two-dimensional representations in the arithmetic of modular curves
- Rational torsion of prime order in elliptic curves over number fields
- Evolutions, symbolic squares, and Fitting ideals.
- On embeddings of spheres
- Stable equivalence of differentiable manifolds
- Local euler characteristics
- Nearly ordinary Galois deformations over arbitrary number fields
- On the Passage From Local to Global in Number Theory
- Relative Neighborhoods and the Theorems of Smale
- Relative modular symbols and Rankin-Selberg convolutions
- Average Ranks of Elliptic Curves: Tension between Data and Conjecture
- Selmer Ranks of Quadratic Twists of Elliptic Curves
- Rational connectivity and sections of families over curves
- Differential topology from the point of view of simple homotopy theory and further remarks
- Twisting Commutative Algebraic Groups
- An "infinite fern" in the universal deformation space of Galois representations
- How Many Rational Points Can a Curve Have
- On the density of modular representations
- Analogies Between Function Fields and Number Fields
- Galois Representations in Arithmetic Algebraic Geometry: Open problems regarding rational points on curves and varieties
- The Method of Infinite Repetition in Pure Topology: I
- Explicit Universal Deformations of Galois Representations
- Proof and other Dilemmas: When is One Thing Equal to Some Other Thing?
- Speculations about the topology of rational points: an update
- Perturbations, Deformations, and Variations (and "Near-Misses") in Geometry, Physics, and Number Theory
- Points of order 13 on elliptic curves
- On the characteristic power series of the U operator
- Elliptic curves and class field theory
- Correspondence homomorphisms for singular varieties
- How can we construct abelian Galois extensions of basic number elds
- Refined class number formulas for Gm
- CONJECTURE
- Refined class number formulas and Kolyvagin systems
- Refined class number formulas for Gm
- Prime Numbers and the Riemann Hypothesis
- Controlling Selmer groups in the higher core rank case
- The spin of prime ideals
- Abelian Varieties and the Mordell-Lang Conjecture
- Visualizing elements of order three in the Shafarevich–Tate group
- The definition of equivalence of combinatorial imbeddings
- Growth of Selmer rank in nonabelian extensions of number fields
- Organizing the arithmetic of elliptic curves
- Studying the Growth of Mordell-Weil
- Local Flat Duality
- A Markov model for Selmer ranks in families of twists
- Diophantine stability
- Two-dimensional $p$-adic Galois representations unramified away from $p$
- Mathematical Platonism and its Opposites
- Refined class number formulas for $\mathbb{G}_m$
- Symmetric homology spheres
- Topology of curves and surfaces, and special topics in the theory of algebraic varieties
- Arithmetic conjectures suggested by the statistical behavior of modular symbols
- FINDING LARGE SELMER GROUPS
- Questions about Powers of Numbers
- Current developments in mathematics, 2003
- Is it Plausible?
- "Imagining Numbers" (Particularly the Square Root of Minus Fifteen)@@@"Abel's Proof": An Essay on the Sources and Meaning of Mathematical Unsolvability@@@"The Riemann Hypothesis": The Greatest Unsolved Problem in Mathematics
- Arithmetic Questions Related to Rationally Connected Varieties
- Open problems: Descending cohomology, geometrically
- Universal extensions and crystals
- Searching for $p$-adic eigenfunctions
- Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80
- Mathematics: Controlling our errors
- Homotopy of Varieties in the Etale Topology
- How Many Primes are There
- A Note on a Classical Theorem of Blichfeldt
- Combinatorial equivalence versus topological equivalence
- Review: André Weil, Ernst Edward Kummer, Collected Papers
- Jumps in Mordell-Weil Rank and Arithmetic Surjectivity
- Pairings in the Arithmetic of Elliptic Curves
- The Method of Infinite Repetition in Pure Topology: II. Stable Applications
- Rational families of 17-torsion points of elliptic curves over number fields
- Galois deformations and Hecke curves
- RATIONAL CURVES AND POINTS ON K3 SURFACES By FEDOR BOGOMOLOV and YURI TSCHINKEL
- Selmer companion curves
- Erratum to: The spin of prime ideals
- p-Aàic Analytic Number Theory of Elliptic Curves and Abelian Varieties over Q
- A brief introduction to the work of Haruzo Hida
- On the structure of certain semi-groups of spherical knot classes
- The Education of T.C. Mits: What modern mathematics means to you
- Reading bombelli
- Corrections to my paper, “Symmetric homology spheres”
- Pure and Applied Mathematics
- CCD Survey for Short Period Variables and sdB/O Stars in 47 TUC
- A celebration of the mathematical work of Glenn Stevens
- Fermat's last theorem : AMS-CMS-MAA joint invited address
- Ramsey Geometric and p-adic Modular Forms of Half-Integral Weight
- Contemporary Mathematics Introduction to Kolyvagin systems
- SMOOTHINGS OF PIECEWISE LINEAR MANIFOLDS II: CLASSIFICATION
- 1954 – 2014
- Current Developments in Mathematics 1998
- Primes, Knots and Po
- Corrections to {\it Uniformity of rational points} and further comments
- Math in the Time of Plague
- On mathematics, imagination & the beauty of numbers
- Some comments on elliptic curves over general number fields and Brill-Noether modular varieties
- Alexandre Grothendieck, 1928–2014, Part 2
- About the cover: Diophantus’s Arithmetica
- What is Riemann's Hypothesis?
- A course in Analytic Number Theory Taught
- Zariski's Topological and Other Early Papers
- The Verdier functor
- The Consolation of Math in Plague Time
- Explicit constructions of universal extensions
- Spectra and Trigonometric Sums
- Building π(X) from the Spectrum
- Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS
- A Sneak Preview of Part III
- UNIFORM BOUNDS FOR STABLY INTEGRAL POINTS ON ELLIPTIC CURVES
- Square Root Error and Random Walks
- What is a “Good Approximation”?
- Afterword to the article “Arithmetic on curves”
- To Our Readers of Part I
- Open problems : Descending cohomology , geometrically compiled by
- Slopes of Graphs That Have No Slopes
- PROBLEMS CONNECTING LOGIC AND NUMBER THEORY
- Prime Numbers Viewed from a Distance
- ELLIPTIC CURVES, SERRE’S CONJECTURE AND FERMAT’S LAST THEOREM
- Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES
- A question about quadratic points on X0(N)
- Memorial Article for John Tate
- The Mystery Moves to the Error Term
- AN INTRODUCTORY LECTURE ON EULER SYSTEMS
- Chapter 7. QUOTIENTS BY FINITE GROUPS
- Chapter 6. Visions, Dreams, and Mathematics
- The Word “Spectrum”
- Why is it plausible
- VERY ROUGH NOTES TO ACCOMPANY THE TALKS ABOUT THE METHOD OF CHABAUTY, COLEMAN, KIM
- The Staircase of Primes
- As Riemann Envisioned It
- Raoul Bott as we knew him
- Thinking about Grothendieck
- About Hermann Weyl’s “Ramifications, old and new, of the eigenvalue problem”
- Robert F. Coleman 1954–2014
- Explicit Local Class Field Theory
- To the Edge of the Map
- Computer Music Files and Prime Numbers
- A View of|Li(X)-π(X)|
- The theory and practice of international market research
- Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES
- Cohomological criteria for ♮-isomorphism
- Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION
- A glossary of the categories in which we shall work, and fibre resolutions
- Fourier Transforms: Second Visit
- Chapter 4. THE FORMALISM OF MODULI PROBLEMS
- L-functions and Arithmetic Conference Program 1 Monday , June 13 9 : 15-9 : 30 am
- Homotopy groups of completions
- The fundamental group
- Fourier Transform of Delta
- Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS
- Big fields that are not large
- How Many θi's are There?
- AVERAGE RANKS OF ELLIPTIC CURVES
- Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring
- Chapter 6. CYCLICITY
- Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS
- Tinkering with the Staircase of Primes
- Companion to Mathematics Proof 1 Algebraic Numbers By Barry Mazur
- Pro-objects in the homotopy category
- Companions to the Zeta Function
- Homomorphisms for Singular Varieties
- Thoughts About Numbers
- On Losing No Information
- From Primes to the Riemann Spectrum
- The Prime Number Theorem
- Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION
- Part I The Program for these lectures 1 Around Hilbert ’ s Tenth Problem
- “Named” Prime Numbers
- The average elliptic curve has few integral
- The Spectrum and the Staircase of Primes
- Biographical Memoirs: Andrew Gleason
- Notes on Utility
- NOTES ADDED IN PROOF
- P-adic monodromy and the Birch and Swinnerton-Dyer conjecture : a Workshop on p-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, August 12-16, 1991
- Further Questions About Primes
- Orthotopy and spherical knots
- The definition of equivalence of combinatorial imbeddings ; On the structure of certain semi-groups of spherical knot classes ; Orthotopy and spherical knots
- Topics in Analytic Number Theory
- Completions and fibrations
- Chapter 5. REGULARITY THEOREMS
- In celebration of John Coates’ 60th birthday
- BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 78 , Number 5 , September 1972 FROBENIUS AND THE HODGE FILTRATION BY
- Infinity: Beyond the Beyond the Beyond
- Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS
- B.: Evolutions, symbolic squares, and Fitting ideals
- Chapter 1. GENERALITIES ON “ A-STRUCTURES” AND “ A-GENERATORS”
- From the Riemann Spectrum to Primes
- Preface to the Present Volume
- Chapter 2. REVIEW OF ELLIPTIC CURVES
- Questions About Primes
- IV.1 Algebraic Numbers
- A “BASIC NOTIONS” LECTURE ABOUT SIGN INTUITIONS
- Hilbert's Tenth Problem and Elliptic Curves
- A Probabilistic First Guess
- Further Questions About the Riemann Spectrum
- What are Prime Numbers
- Elliptic Curves and Their Statistics Rough Notes for My Basic Notions Talk, Feb 28 2012 Part I. Densities
- This paper was presented at a colloquium entitled “ Elliptic Curves and Modular Forms , ” organized by
- A profiniteness theorem
- III · 1 – 3 Elliptic Curves and Class Field Theory

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Barry Mazur is most known for their academic work in the field of mathematics. They are also known for their academic work in the fields of philosophy, computer science, economics, physics, literature, psychology, biology, and chemistry.

Barry Mazur has made the following academic contributions:

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