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by Jacques Hadamard

Download The Mathematician's Mind fb2, epub

ISBN: 0691029318
Author: Jacques Hadamard
Language: English
Publisher: Princeton University Press; Reprint edition (September 30, 1996)
Pages: 166
Category: Mathematics
Subcategory: Science
Rating: 4.2
Votes: 631
Size Fb2: 1754 kb
Size ePub: 1978 kb
Size Djvu: 1913 kb
Other formats: mbr txt mobi docx


Jacques Hadamard An interesting read.

Jacques Hadamard An interesting read. A fascinating and informative book.

Jacques Hadamard, a prominent mathematician, wrote this psychology text over 50 years ago, after having done his best work 50 years prior. Although in some ways dated, both in content and in writing style, the book provides an interesting examination of the role of the conscious and subconscious in solving a problem, particularly the process of incubation and (seemingly) sudden inspiration.

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.

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. 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.

Jacques Salomon Hadamard ForMemRS (French: ; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations

Jacques Salomon Hadamard ForMemRS (French: ; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations. The son of a teacher, Amédée Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the Lycée Charlemagne and Lycée Louis-le-Grand, where his father taught.

The Mathematician's Mind 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 thinkres of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein.

I've been meaning to discuss the book The Psychology of Mathematical Invention in the Mathematical Field, by Jacques Hadamard. It was inspired by a lecture of Poincare to the French Psychological Society entitled "Mathematical Creation"

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. Country of Publication.

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.

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he. .

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Jacques Hadamard : a universal mathematician. Books for People with Print Disabilities. Trent University Library Donation. Internet Archive Books.

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.

Comments:

Chi
Despite the age of this book the collections of stories from inventive geniuses about how "insight" sprang upon them out of the blue is highly convincing. This is the book that outlined the stages of insight including preparation, incubation, insight, etc. Doubt still exists regarding the operation of the subconscious mind but all the examples offered here lower the doubt in my own mind and I think we must recognize that which seems to be really happening..
Mullador
This is a short study of how creative thought works. Hadamard, a world-class mathematician best known for his proof of the prime number theorem in 1896, wrote this in the 40's, basing it on correspondence with many of the great living mathematicians of his time. The actual questions he posed are preserved in an appendix.
Most of his respondents were mathematicians (and he limited his correspondence to the best minds in the field), but he did get information from several other fields, and cites data about physicists (a letter from Einstein forms another appendix), chemists, physiologists, metaphysicians, and so on. What he is trying to examine is a slippery subject, perhaps best explained by a quote. Here is a discussion of Sidgwick, an economist: "His reasonings on economic questions were almost always accompanied by images, and the images were often curiously arbitrary and sometimes almost undecipherably symbolic. For example, it took him a long time to discover that an odd symbolic image which accompanied the word 'value' was a faint, partial image of a man putting something on a scale."
Hadamard gives his own mental images that accompany his following through the steps of Euclid's famous proof of the infinitude of primes. I won't reproduce that here for space reasons, but the contrast with Sidgwick's--and with other reports of mental activity--is fascinating. Many other examples are given, from Mozart to Polya to Galton to Poincare. Hadamard makes it clear that language and thought are not the same thing, contrary to a commonly expressed view among linguists. He cites Max Muller's comments equating thought and language, and acknowledges that for Muller it may be so, but convincingly demonstrates, by quoting numerous other mathematicians, that it is not true for everyone. The further conclusion, that the process of creative thought, while following similar patterns in similar discipline, can vary dramatically, is as far as Hadamard can go with the data he has.
One other note: this book was originally titled "The Psychology of Invention in the Mathematical Field" and is available under that title from Amazon, published by Dover Books. It's not immediately clear from the Amazon page that this is so. The Dover edition is substantially cheaper.
A fascinating and informative book.
Survivors
Not only is this book fascinating, it's the only one of it's kind. The book has also proved very useful to me in life. As a graduate student I used Poincaré's implicit `advice' (described in the book) in the following way. In electrodynamics we had a long problem sheet to hand in every two weeks. I started by writing down answers to all problems that I knew. Then, I thought about the next-easiest problem each day walking twice to and from the University (about 1 1/2 hours altogether). When the answer came I wrote it down and iterated the process. Before the end of two weeks most of the problems (from Jackson) had been solved. Poincari's advice is very good about giving the unconscious a chance to work. Phooey and double phooey on the silly, uncreative skinner-box types and other behaviorists who don't recognize the unconscious as the source of creativity!
Madis
The Mathematician's Mind is a study on how research mathematicians go about the business of advancing their field. Jacques Hadamard, a prominent mathematician, wrote this psychology text over 50 years ago, after having done his best work 50 years prior. Although in some ways dated, both in content and in writing style, the book provides an interesting examination of the role of the conscious and subconscious in solving a problem, particularly the process of incubation and (seemingly) sudden inspiration. He brings up the roles intuition and logic play in the way various mathematicians go about their business. Hadamard also examines the influence of aesthetics in not just choosing a problem, but in solving it. He studies the choice of research direction, with the interesting comment that Hadamard himself avoided areas of research where there was already a great deal of activity.
The book is short enough that if the subject interests you, it is worth your time.
The text is also published under the title "The Psychology of Invention in the Mathematical Field."

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