Hersh, Reuben 1927
Overview
Works:  50 works in 392 publications in 8 languages and 12,640 library holdings 

Genres:  History Biography 
Roles:  Author, Editor, Other 
Classifications:  QA8.4, 510.1 
Publication Timeline
.
Most widely held works about
Reuben Hersh
 Hersh, Reuben : mathematical analysis( )
 Humanizing Mathematics and its Philosophy : Essays Celebrating the 90th Birthday of Reuben Hersh by Bharath Sriraman( )
Most widely held works by
Reuben Hersh
The mathematical experience by
Philip J Davis(
Book
)
119 editions published between 1980 and 2012 in 4 languages and held by 2,830 WorldCat member libraries worldwide
Traces the history of mathematics, offers profiles of major mathematicians and their discoveries, and looks at the philosophy of mathematics
119 editions published between 1980 and 2012 in 4 languages and held by 2,830 WorldCat member libraries worldwide
Traces the history of mathematics, offers profiles of major mathematicians and their discoveries, and looks at the philosophy of mathematics
Descartes' dream : the world according to mathematics by
Philip J Davis(
Book
)
48 editions published between 1984 and 2005 in English and held by 1,880 WorldCat member libraries worldwide
Discusses the impact that mathematics and computers have on our intellectual and emotional lives
48 editions published between 1984 and 2005 in English and held by 1,880 WorldCat member libraries worldwide
Discusses the impact that mathematics and computers have on our intellectual and emotional lives
What is mathematics, really? by
Reuben Hersh(
Book
)
41 editions published between 1990 and 2009 in 3 languages and held by 1,232 WorldCat member libraries worldwide
Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy  ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact  Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal antielitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political consequences
41 editions published between 1990 and 2009 in 3 languages and held by 1,232 WorldCat member libraries worldwide
Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy  ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact  Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal antielitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political consequences
Loving + hating mathematics : challenging the myths of mathematical life by
Reuben Hersh(
Book
)
14 editions published in 2011 in English and held by 865 WorldCat member libraries worldwide
"Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotionsand inspire more love and hatredthan mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera JohnSteiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonmentas well as of those rare individuals driven to insanity and even murder by an obsession with math."Overview
14 editions published in 2011 in English and held by 865 WorldCat member libraries worldwide
"Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotionsand inspire more love and hatredthan mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera JohnSteiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonmentas well as of those rare individuals driven to insanity and even murder by an obsession with math."Overview
18 unconventional essays on the nature of mathematics by
Reuben Hersh(
Book
)
23 editions published between 2005 and 2006 in English and held by 286 WorldCat member libraries worldwide
"This new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thoughtprovoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths."BOOK JACKET
23 editions published between 2005 and 2006 in English and held by 286 WorldCat member libraries worldwide
"This new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thoughtprovoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths."BOOK JACKET
Erfahrung Mathematik by
Philip J Davis(
Book
)
16 editions published between 1985 and 1996 in 3 languages and held by 224 WorldCat member libraries worldwide
Ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen  die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf {laquo}Aber Zahlen lügen nicht!{raquo} befinden wir uns in der Gesellschaft von Plato oder Lakatos
16 editions published between 1985 and 1996 in 3 languages and held by 224 WorldCat member libraries worldwide
Ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen  die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf {laquo}Aber Zahlen lügen nicht!{raquo} befinden wir uns in der Gesellschaft von Plato oder Lakatos
L'Univers mathématique by
Philip J Davis(
Book
)
7 editions published between 1985 and 1991 in French and held by 164 WorldCat member libraries worldwide
Un exposé très documenté, accessible au profane cultivé. Les principaux axes en sont la substance des mathématiques, leur histoire, leur philosophie, leur pédagogie et leurs multiples applications. La plupart des thèmes peuvent être lus indépendamment les uns des autres. Les auteurs sont tous deux docteurs en mathématiques
7 editions published between 1985 and 1991 in French and held by 164 WorldCat member libraries worldwide
Un exposé très documenté, accessible au profane cultivé. Les principaux axes en sont la substance des mathématiques, leur histoire, leur philosophie, leur pédagogie et leurs multiples applications. La plupart des thèmes peuvent être lus indépendamment les uns des autres. Les auteurs sont tous deux docteurs en mathématiques
The companion guide to The mathematical experience, study edition by
Philip J Davis(
Book
)
18 editions published in 1995 in English and held by 160 WorldCat member libraries worldwide
This guide is designed as a teaching tool, aimed at both teachers and student teachers. Its main purpose is to enhance the value of "The Mathematical Experience" as a textbook. It includes a sample syllabus, outlines for group work, sample exams and hints for grading essays
18 editions published in 1995 in English and held by 160 WorldCat member libraries worldwide
This guide is designed as a teaching tool, aimed at both teachers and student teachers. Its main purpose is to enhance the value of "The Mathematical Experience" as a textbook. It includes a sample syllabus, outlines for group work, sample exams and hints for grading essays
Experiencing mathematics : what do we do, when we do mathematics? by
Reuben Hersh(
Book
)
7 editions published in 2014 in English and held by 148 WorldCat member libraries worldwide
"Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincaré, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant 'analytic philosophy'. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis."Page 4 of cover
7 editions published in 2014 in English and held by 148 WorldCat member libraries worldwide
"Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincaré, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant 'analytic philosophy'. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis."Page 4 of cover
Peter Lax, mathematician : an illustrated memoir by
Reuben Hersh(
Book
)
10 editions published in 2015 in English and held by 139 WorldCat member libraries worldwide
"This book is a biography of one of the most famous and influential living mathematicians, Peter Lax. He is virtually unique as a preeminent leader in both pure and applied mathematics, fields which are often seen as competing and incompatible."Page 4 de la couverture
10 editions published in 2015 in English and held by 139 WorldCat member libraries worldwide
"This book is a biography of one of the most famous and influential living mathematicians, Peter Lax. He is virtually unique as a preeminent leader in both pure and applied mathematics, fields which are often seen as competing and incompatible."Page 4 de la couverture
L'Empire mathématique by
Philip J Davis(
Book
)
5 editions published in 1988 in French and held by 109 WorldCat member libraries worldwide
5 editions published in 1988 in French and held by 109 WorldCat member libraries worldwide
Descartes' Traum : über die Mathematisierung von Zeit und Raum  von denkenden Computern, Politik und Liebe by
Philip J Davis(
Book
)
9 editions published between 1988 and 2016 in German and held by 88 WorldCat member libraries worldwide
9 editions published between 1988 and 2016 in German and held by 88 WorldCat member libraries worldwide
Experiencia matemática by
Philip J Davis(
Book
)
7 editions published between 1985 and 1989 in Spanish and Portuguese and held by 35 WorldCat member libraries worldwide
7 editions published between 1985 and 1989 in Spanish and Portuguese and held by 35 WorldCat member libraries worldwide
El sueäno de Descartes el mundo segun las matematicas by
Philip J Davis(
Book
)
5 editions published between 1989 and 1994 in Spanish and Undetermined and held by 27 WorldCat member libraries worldwide
5 editions published between 1989 and 1994 in Spanish and Undetermined and held by 27 WorldCat member libraries worldwide
Matemáticas : una historia de amor y odio by
Reuben Hersh(
Book
)
5 editions published in 2012 in Spanish and English and held by 19 WorldCat member libraries worldwide
Las matemáticas tienen para muchos mala fama: frías, complicadas, ajenas a todo aquello que no sea "racional". Sin embargo, semejante historia no es real: las matemáticas tienen que ver, y mucho, con emociones y fuerzas sociales; esto es, con todo aquello que es primaria y genuinamente humano. Que es así, es algo que se muestra en este libro, en el que un matemático, Reuben Hersh, y una experta en lingüística y educación, Vera JohnSteiner, narran, con un estilo vivo y accesible, las vidas de distinguidos matemáticos, vidas en las que no faltaron amistades, amores, rivalidades, frustraciones, pasiones o momentos de éxtasis. A través de las páginas de este esclarecedor libro, comprobamos como las matemáticas representaron una inmensa ayuda para individuos durante tiempos de crisis, guerras e incluso prisión. Y aunque se combate la idea de que los matemáticos son, en general, personas excéntricas, que viven en un universo propio practicando de manera individual la disciplina que aman, no se deja de presentar por ello los, poco frecuentes, casos de matemáticos que enloquecieron debido a sus obsesiones científicas. Es esta una obra, en resumen, que ayuda a comprender cómo la más racional de las habilidades humanas es al mismo tiempo una de las más emocionales
5 editions published in 2012 in Spanish and English and held by 19 WorldCat member libraries worldwide
Las matemáticas tienen para muchos mala fama: frías, complicadas, ajenas a todo aquello que no sea "racional". Sin embargo, semejante historia no es real: las matemáticas tienen que ver, y mucho, con emociones y fuerzas sociales; esto es, con todo aquello que es primaria y genuinamente humano. Que es así, es algo que se muestra en este libro, en el que un matemático, Reuben Hersh, y una experta en lingüística y educación, Vera JohnSteiner, narran, con un estilo vivo y accesible, las vidas de distinguidos matemáticos, vidas en las que no faltaron amistades, amores, rivalidades, frustraciones, pasiones o momentos de éxtasis. A través de las páginas de este esclarecedor libro, comprobamos como las matemáticas representaron una inmensa ayuda para individuos durante tiempos de crisis, guerras e incluso prisión. Y aunque se combate la idea de que los matemáticos son, en general, personas excéntricas, que viven en un universo propio practicando de manera individual la disciplina que aman, no se deja de presentar por ello los, poco frecuentes, casos de matemáticos que enloquecieron debido a sus obsesiones científicas. Es esta una obra, en resumen, que ayuda a comprender cómo la más racional de las habilidades humanas es al mismo tiempo una de las más emocionales
Descartes' droom : een wiskundige visie op de wereld by
Philip J Davis(
Book
)
1 edition published in 1988 in Dutch and held by 17 WorldCat member libraries worldwide
Inventarisatie van de wiskundige invloed op de hedendaagse wetenschap en op het hedendaagse dagelijks leven
1 edition published in 1988 in Dutch and held by 17 WorldCat member libraries worldwide
Inventarisatie van de wiskundige invloed op de hedendaagse wetenschap en op het hedendaagse dagelijks leven
Il sogno di Cartesio : il mondo secondo la matematica by
Philip J Davis(
Book
)
2 editions published in 1988 in Italian and held by 15 WorldCat member libraries worldwide
2 editions published in 1988 in Italian and held by 15 WorldCat member libraries worldwide
L'esperienza matematica : da Talete al computer by
Philip J Davis(
Book
)
3 editions published in 1985 in Italian and held by 13 WorldCat member libraries worldwide
3 editions published in 1985 in Italian and held by 13 WorldCat member libraries worldwide
The Mathematical Experience, Study Edition by
Philip J Davis(
Book
)
8 editions published between 1995 and 2012 in English and held by 11 WorldCat member libraries worldwide
8 editions published between 1995 and 2012 in English and held by 11 WorldCat member libraries worldwide
Boundary conditions for equations of evolution by
Reuben Hersh(
Book
)
3 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
The term evolutionary equation is used to mean one for which the Cauchy problem is correct, such as, for example, hyperbolic or parabolic equations. Mixed initialboundary value problems for systems of differential equations with constant (real or complex) coefficients in a quarter space are considered. (Author)
3 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
The term evolutionary equation is used to mean one for which the Cauchy problem is correct, such as, for example, hyperbolic or parabolic equations. Mixed initialboundary value problems for systems of differential equations with constant (real or complex) coefficients in a quarter space are considered. (Author)
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Related Identities
 Davis, Philip J. 1923 Author
 JohnSteiner, Vera 1930 Author
 Marchisotto, Elena
 Lax, Peter D.
 Rota, GianCarlo Author of introduction
 Sriraman, Bharath Editor
 Descartes, René 15961650
 Zehnder, Jeannette
 Espanya Ministerio de Educación y Ciencia
 Adelaar, Patty
Useful Links
Associated Subjects
Canada Computers and civilization Descartes, René, Differential equations EducationPhilosophy Lax, Peter D Logic, Symbolic and mathematical Mathematicians MathematiciansPsychology Mathematics MathematicsEducation MathematicsPhilosophy MathematicsSocial aspects MathematicsStudy and teaching Philosophy SciencePhilosophy Scientists Social sciences United States
Alternative Names
Hersh, R. 1927
Hersh, Reuben
Reuben Hersh Amerikaans wiskundige
Reuben Hersh amerikansk matematikar
Reuben Hersh amerikansk matematiker
Reuben Hersh matemático estadounidense
Reuben Hersh matematico statunitense
Reuben Hersh mathématicien américain
Reuben Hersh USamerikanischer Mathematiker
허시, 로이벤
ヘルシュ, R
ルーベン・ハーシュ
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