The Mathematician's Mind

The Psychology of Invention in the Mathematical Field

Jacques Hadamard, P. N. Johnson-Laird

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English

Princeton University Press
02 January 1997

Cognition & cognitive psychology; Philosophy of mathematics

Series: Princeton Science Library

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 Levi-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.

By: Jacques Hadamard
Preface by: P. N. Johnson-Laird
Imprint: Princeton University Press
Country of Publication: United States
Edition: Revised edition
Volume: 18
Dimensions: Height: 203mm, Width: 127mm, Spine: 13mm
Weight: 170g
ISBN: 9780691029313
ISBN 10: 0691029318
Series: Princeton Science Library
Pages: 168
Publication Date: 02 January 1997
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Paperback
Publisher's Status: Active

Preface to the Paperback EditionForewordIntroductionIGeneral Views and Inquiries1IIDiscussions on Unconsciousness21IIIThe Unconscious and Discovery29IVThe Preparation Stage. Logic and Chance43VThe Later Conscious Work56VIDiscovery as a Synthesis. The Help of Signs64VIIDifferent Kinds of Mathematical Minds100VIIIParadoxical Cases of Intuition116IXThe General Direction of Research124Final Remarks133App. I137App. II142

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.