Examines the impact of mathematics on our social life and on our perceptions of reality, knowledge, and time, ranging from ancient Egyptian land surveys to Descartes' work

Descartes' Dream: The World According to Mathematics

Davis, Philip J.

Hersh, Reuben

Computers & Technology

Harcourt

What Is Mathematics, Really?

Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, 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. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, with society, and with history. It fits with liberal anti-elitism 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 ramifications. Written by the co-author of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirty-five years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science.

What is Mathematics, Really?

Science & Math

Mathematics

Oxford University Press

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, 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. 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. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Politics & Social Sciences

Philosophy

What Is Mathematics Really

JONATHAN CAPE.

Examines the impact of mathematics on our social life and on our perceptions of reality, knowledge, and time

Houghton, mifflin, harcourt

"A passionate plea against the use of formal mathematical reasoning as a method for solving mankind's problems. . . . An antidote to the Cartesian view that mathematical and scientific knowledge will suffice to solve the central problems of human existence." — The New York Times "These cogitations can and should be read by every literate person." — Science Books and Films "A warning against being seduced or intimidated by mathematics into accepting bad science, bad policies, and bad personal decisions." — Philadelphia Inquirer Rationalist philosopher and mathematician René Descartes visualized a world unified by mathematics, in which all intellectual issues could be resolved rationally by local computation. This series of provocative essays takes a modern look at the seventeenth-century thinker's dream, examining the physical and intellectual influences of mathematics on society, particularly in light of technological advances. These essays survey the conditions of civilization that elicit the application of mathematic principles; the effectiveness of these applications; situations in which the applications are beneficial, dangerous, or irrelevant; and how applied mathematics constrain lives and transform perceptions of reality. Highly suitable for browsing, the essays require different levels of mathematical knowledge that range from popular to professional. Philip J. Davisis Professor Emeritus, Division of Applied Mathematics, Brown University. Reuben Hershis Professor Emeritus, University of New Mexico, Albuquerque.

Descartes' Dream: The World According to Mathematics (Dover Books on Mathematics)

Dover Publications

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than 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 John-Steiner 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 imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math.
 This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

John-Steiner, Vera

Princeton University Press

Reprint. Originally published: Boston: Birkh'auser, 1981.

The Mathematical Experience

Birkhauser

Winner of the 1983 National Book Award!
"…a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition)
Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.
The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisotto@csun.edu) upon request.

The Mathematical Experience, Study Edition (Modern Birkhäuser Classics)

Marchisotto, Elena Anne

History & Philosophy

See the best price to sell, buy, or rent books by Hersh, Reuben. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Hersh, Reuben

See the best price to sell, buy, or rent books by Hersh, Reuben. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Descartes' Dream: The World According to Mathematics

What is Mathematics, Really?

What Is Mathematics, Really?

What Is Mathematics Really

Descartes' Dream: The World According to Mathematics

Descartes' Dream: The World According to Mathematics (Dover Books on Mathematics)

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

The Mathematical Experience

The Mathematical Experience, Study Edition (Modern Birkhäuser Classics)