Mazur, Barry
Overview
Works:  90 works in 335 publications in 5 languages and 6,465 library holdings 

Genres:  History Conference papers and proceedings Educational films Filmed lectures 
Roles:  Author, Editor, Speaker, Author of introduction, Contributor, Other 
Classifications:  QA3, 512 
Publication Timeline
.
Most widely held works by
Barry Mazur
Imagining numbers : (particularly the square root of minus fifteen) by
Barry Mazur(
Book
)
19 editions published between 2003 and 2013 in English and Spanish and held by 799 WorldCat member libraries worldwide
A tour of the creative side of mathematics describes the first use of imaginary numbers in sixteenthcentury Italy and the subsequent twohundredyear effort to perfect the process, citing the words of key Renaissance thinkers
19 editions published between 2003 and 2013 in English and Spanish and held by 799 WorldCat member libraries worldwide
A tour of the creative side of mathematics describes the first use of imaginary numbers in sixteenthcentury Italy and the subsequent twohundredyear effort to perfect the process, citing the words of key Renaissance thinkers
Smoothings of piecewise linear manifolds by
Morris W Hirsch(
Book
)
13 editions published between 1974 and 2016 in English and held by 470 WorldCat member libraries worldwide
The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure
13 editions published between 1974 and 2016 in English and held by 470 WorldCat member libraries worldwide
The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure
Etale homotopy by
Michael Artin(
Book
)
27 editions published between 1968 and 2007 in 4 languages and held by 465 WorldCat member libraries worldwide
27 editions published between 1968 and 2007 in 4 languages and held by 465 WorldCat member libraries worldwide
Arithmetic moduli of elliptic curves by
Nicholas M Katz(
Book
)
14 editions published between 1984 and 2016 in English and Undetermined and held by 454 WorldCat member libraries worldwide
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by EichlerShimura, Igusa, and DeligneRapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld
14 editions published between 1984 and 2016 in English and Undetermined and held by 454 WorldCat member libraries worldwide
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by EichlerShimura, Igusa, and DeligneRapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld
Universal extensions and one dimensional crystalline cohomology by
Barry Mazur(
Book
)
25 editions published between 1974 and 2008 in 3 languages and held by 414 WorldCat member libraries worldwide
25 editions published between 1974 and 2008 in 3 languages and held by 414 WorldCat member libraries worldwide
Circles disturbed : the interplay of mathematics and narrative by
Apostolos K Doxiadēs(
Book
)
14 editions published in 2012 in English and held by 309 WorldCat member libraries worldwide
"Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier"Don't disturb my circles"Words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worldsstories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of 'myths of origins' in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more."Jacket
14 editions published in 2012 in English and held by 309 WorldCat member libraries worldwide
"Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier"Don't disturb my circles"Words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worldsstories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of 'myths of origins' in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more."Jacket
Padic monodromy and the Birch and SwinnertonDyer conjecture : a Workshop on padic Monodromy and the Birch and SwinnertonDyer
Conjecture, August 1216, 1991, Boston University by Conference on padic Monodromy and the Birch and SwinnertonDyer Conjecture(
Book
)
20 editions published in 1994 in English and held by 255 WorldCat member libraries worldwide
"Recent years have witnessed significant breakthroughs in the theory of padic Galois representations and padic periods of algebraic varieties. This book contains papers presented at the Workshop on pAdic Monodromy and the Birch and SwinnertonDyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between padic Hodge theory, analogues of the conjecture of Birch and SwinnertonDyer, padic uniformization theory, padic differential equations, and deformations of Gaels representations. Much of the workshop was devoted to exploring how the special values of (padic and "classical") Lfunctions and their derivatives are relevant to arithmetic issues, as envisioned in "BirchSwinnertonDyertype conjectures", "Main Conjectures", and "Beilinsontype conjectures" a la Greenberg and Coates."BOOK JACKET
20 editions published in 1994 in English and held by 255 WorldCat member libraries worldwide
"Recent years have witnessed significant breakthroughs in the theory of padic Galois representations and padic periods of algebraic varieties. This book contains papers presented at the Workshop on pAdic Monodromy and the Birch and SwinnertonDyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between padic Hodge theory, analogues of the conjecture of Birch and SwinnertonDyer, padic uniformization theory, padic differential equations, and deformations of Gaels representations. Much of the workshop was devoted to exploring how the special values of (padic and "classical") Lfunctions and their derivatives are relevant to arithmetic issues, as envisioned in "BirchSwinnertonDyertype conjectures", "Main Conjectures", and "Beilinsontype conjectures" a la Greenberg and Coates."BOOK JACKET
Filtrations on the homology of algebraic varieties by
E. M Friedlander(
Book
)
12 editions published in 1994 in English and held by 242 WorldCat member libraries worldwide
12 editions published in 1994 in English and held by 242 WorldCat member libraries worldwide
Kolyvagin systems by
Barry Mazur(
Book
)
9 editions published in 2004 in English and held by 231 WorldCat member libraries worldwide
Introduction Local cohomology groups Global cohomology groups and Selmer structures Kolyvagin systems Kolyvagin systems over principal artinian rings Kolyvagin systems over integral domains Examples Appendix A. Proof of Theorem 3.2.4 Appendix B. Proof of Theorem 4.3.3, by Benjamin Howard Bibliography
9 editions published in 2004 in English and held by 231 WorldCat member libraries worldwide
Introduction Local cohomology groups Global cohomology groups and Selmer structures Kolyvagin systems Kolyvagin systems over principal artinian rings Kolyvagin systems over integral domains Examples Appendix A. Proof of Theorem 3.2.4 Appendix B. Proof of Theorem 4.3.3, by Benjamin Howard Bibliography
Prime numbers and the Riemann hypothesis by
Barry Mazur(
Book
)
14 editions published between 2015 and 2016 in English and held by 167 WorldCat member libraries worldwide
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the socalled Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis
14 editions published between 2015 and 2016 in English and held by 167 WorldCat member libraries worldwide
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the socalled Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis
Differential topology from the point of view of simple homotopy theory by
Barry Mazur(
Book
)
12 editions published between 1963 and 1964 in 3 languages and held by 89 WorldCat member libraries worldwide
12 editions published between 1963 and 1964 in 3 languages and held by 89 WorldCat member libraries worldwide
The definition of equivalence of combinatorial imbeddings by
Barry Mazur(
Book
)
8 editions published in 1959 in English and held by 71 WorldCat member libraries worldwide
8 editions published in 1959 in English and held by 71 WorldCat member libraries worldwide
Ces nombres qui n'existent pas by
Barry Mazur(
Book
)
4 editions published between 2004 and 2005 in French and held by 70 WorldCat member libraries worldwide
L'auteur fait un parallèle entre l'atmosphère imaginative propre à la poésie et l'imagination à l'oeuvre en mathématiques. Il s'appuie sur l'exemple des nombres imaginaires (les nombres complexes, comme la racine carrée de nombres négatifs) pour nous faire vivre le voyage imaginaire qui a conduit les mathématiciens de la Renaissance italienne à envisager ces nombres
4 editions published between 2004 and 2005 in French and held by 70 WorldCat member libraries worldwide
L'auteur fait un parallèle entre l'atmosphère imaginative propre à la poésie et l'imagination à l'oeuvre en mathématiques. Il s'appuie sur l'exemple des nombres imaginaires (les nombres complexes, comme la racine carrée de nombres négatifs) pour nous faire vivre le voyage imaginaire qui a conduit les mathématiciens de la Renaissance italienne à envisager ces nombres
Fermat's last theorem by
Kenneth Ribet(
Visual
)
6 editions published between 1995 and 2008 in English and held by 50 WorldCat member libraries worldwide
In June 1993 Andrew Wiles announced that he had proved Fermat's last theorem. The proof was finally completed in November 1994, when Wiles and Richard Taylor filled a technical gap that had arisen. In this lecture, Barry Mazur outlines the main ideas in this groundbreaking work. Mazur sets the context for the problem, then focuses on three concepts and the key role they play in Wiles' work: elliptoc curves, Galois representations, and modular forms. The lecture is preceded by an introduction by Mazur in March 1995, bringing the topic up to date
6 editions published between 1995 and 2008 in English and held by 50 WorldCat member libraries worldwide
In June 1993 Andrew Wiles announced that he had proved Fermat's last theorem. The proof was finally completed in November 1994, when Wiles and Richard Taylor filled a technical gap that had arisen. In this lecture, Barry Mazur outlines the main ideas in this groundbreaking work. Mazur sets the context for the problem, then focuses on three concepts and the key role they play in Wiles' work: elliptoc curves, Galois representations, and modular forms. The lecture is preceded by an introduction by Mazur in March 1995, bringing the topic up to date
Topics in analytic number theory by
Serge Lang(
Book
)
3 editions published in 1961 in English and held by 46 WorldCat member libraries worldwide
3 editions published in 1961 in English and held by 46 WorldCat member libraries worldwide
Current developments in mathematics 1998 by
Barry Mazur(
Book
)
10 editions published between 1998 and 1999 in English and Undetermined and held by 33 WorldCat member libraries worldwide
10 editions published between 1998 and 1999 in English and Undetermined and held by 33 WorldCat member libraries worldwide
Collected papers by
Oscar Zariski(
Book
)
10 editions published in 1978 in English and held by 32 WorldCat member libraries worldwide
10 editions published in 1978 in English and held by 32 WorldCat member libraries worldwide
Current developments in mathematics 1999 by
Barry Mazur(
Book
)
9 editions published in 1999 in English and Undetermined and held by 28 WorldCat member libraries worldwide
9 editions published in 1999 in English and Undetermined and held by 28 WorldCat member libraries worldwide
Current developments in mathematics 2000(
Book
)
5 editions published between 2000 and 2001 in English and held by 23 WorldCat member libraries worldwide
5 editions published between 2000 and 2001 in English and held by 23 WorldCat member libraries worldwide
Colloquium on Elliptic Curves and Modular Forms by Colloquium on Elliptic Curves and Modular Forms(
)
1 edition published in 1997 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 0 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Doxiadēs, Apostolos K. 1953 Author Editor
 Artin, Michael Author Editor
 Messing, William
 Hirsch, Morris W. 1933 Author
 Katz, Nicholas M. 1943 Author
 Rubin, Karl
 Friedlander, E. M. (Eric M.) 1944 Author
 Stevens, Glenn 1953 Other Editor
 Stein, William A. 1974
 American Mathematical Society
Useful Links
Associated Subjects
Abelian varieties Algebraic cycles Algebraic topology Arithmetical algebraic geometry BirchSwinnertonDyer conjecture Combinatorial topology Communication in mathematics Curves, Elliptic Differential topology Fermat's last theorem Filters (Mathematics) Forms, Modular Functional analysis Functions Geometry, Algebraic Group schemes (Mathematics) Homology theory Homotopy theory Imagination Knot theory Lfunctions Lie algebras Logic, Symbolic and mathematical Manifolds (Mathematics) Mathematics MathematicsLanguage MathematicsPhilosophy Mirror symmetry Moduli theory Numbers, Complex Numbers, Prime Number theory padic analysis Piecewise linear topology Riemann hypothesis Riemannian manifolds Topology
Alternative Names
Barry Mazur Amerikaans wiskundige
Barry Mazur amerikansk matematikar
Barry Mazur amerikansk matematiker
Barry Mazur amerykański matematyk
Barry Mazur matematico statunitense
Barry Mazur mathématicien américain
Barry Mazur USamerikanischer Mathematiker
Mazur, B.
Mazur, B. 1937
Mazur, Barry
Mazur, Barry C. 1937
Mazur, Barry Charles
Mazur, Barry Charles 1937
Барри Мазур американский математик
בארי מזור
باري مازور
마주르, 배리
배리 메이저 미국의 수학자
バリー・メイザー
メイザー, バリー
巴里·馬聚爾
Languages
Covers