The Mathematician's Mind: The Psychology of Invention in the Mathematical Field

Jacques Hadamard

Published by Princeton University Press 1997

The Mathematician's Mind

The Psychology of Invention in the Mathematical Field

Jacques Hadamard

Volume 18 in the series Princeton Science Library

https://doi.org/10.1515/9780691212906

Overview
Contents

About this book

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life.

The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

Author / Editor information

Jacques Hadamard (1865-1963), an internationally known mathematician, was born in Versailles and lectured at universities throughout the world, including Hravard, Princeton, Stanford, and Columbia Universities, and at the Institute for Advanced Study.

Topics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	vii
PREFACE TO THE PAPERBACK EDITION Publicly Available Download PDF	ix
FOREWORD Publicly Available Download PDF	xv
INTRODUCTION Publicly Available Download PDF	xvii
I. GENERAL VIEWS AND INQUIRIES Requires Authentication Unlicensed Licensed Download PDF	1
II. DISCUSSIONS ON UNCONSCIOUSNESS Requires Authentication Unlicensed Licensed Download PDF	21
III. THE UNCONSCIOUS AND DISCOVERY Requires Authentication Unlicensed Licensed Download PDF	29
IV. THE PREPARATION STAGE. LOGIC AND CHANCE Requires Authentication Unlicensed Licensed Download PDF	43
V. THE LATER CONSCIOUS WORK Requires Authentication Unlicensed Licensed Download PDF	56
VI. DISCOVERY AS A SYNTHESIS. THE HELP OF SIGNS Requires Authentication Unlicensed Licensed Download PDF	64
VII. DIFFERENT KINDS OF MATHEMATICAL MINDS Requires Authentication Unlicensed Licensed Download PDF	100
VIII. PARADOXICAL CASES OF INTUITION Requires Authentication Unlicensed Licensed Download PDF	116
IX. THE GENERAL DIRECTION OF RESEARCH Requires Authentication Unlicensed Licensed Download PDF	124
FINAL REMARKS Requires Authentication Unlicensed Licensed Download PDF	133
APPENDIX I Requires Authentication Unlicensed Licensed Download PDF	137
APPENDIX II Requires Authentication Unlicensed Licensed Download PDF	142