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An Essay on the Psychology of Invention in the Mathematical Field Hardcover – November 4, 2008

by Jacques Hadamard (Author)

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An Essay on the Psychology of Invention in the Mathematical Field

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The Psychology of Invention in the Mathematical Field Paperback

Jacques Hadamard

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Hardcover: 164 pages
Publisher: Hadamard Press (November 4, 2008)
Language: English
ISBN-10: 1443730394
ISBN-13: 978-1443730396
Product Dimensions: 5.5 x 0.5 x 8.5 inches
Shipping Weight: 12.6 ounces (View shipping rates and policies)
Average Customer Review: 10 customer reviews
Amazon Best Sellers Rank: #4,758,233 in Books (See Top 100 in Books)
- #70814 in Books > Science & Math > Mathematics

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"Review of The Psychology of Invention in the Mathematical Field"

ByKevinon March 17, 2012

Format: PaperbackVerified Purchase

I found in this book important information on the power of the unconscious mind in the creation of new mathematics.

The author Jacques Hadamard's experience of suddenly getting a solution at the moment of waking from sleep and his testimony to the effectiveness of abandoning a problem and the resuming it later on aligns with my experience (on modest problems).

The inclusion of Henri Poincare's account of the sudden mathematical insight relating to fuchsian functions (that occurred to him just as he stepped on a bus) was evidence of the unconscious at work.

The book in effect discusses the four stages of thought (after Helmholtz and Poincare) of: Preparation (conscious work setting up the problem and trying to solve it); incubation (no conscious work on the problem) ; illumination (the fruits of incubation where an insight is received) and finally verification (consciously testing and verifying the insight).

The style of writing is a little hard to read but the contents repay the effort.

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Follow Poincare

ByDeniz Akyildizon April 26, 2017

Format: Paperback

This is a very nice book: Written by a first-rate mathematician about mathematical creation, following the steps of Poincare who described his own working methods in his famous lecture. Hadamard also surveyed mathematicians and physicists of the time to collect their experiences and the book also includes Einstein's letter to Hadamard on the topic.

The title is a bit misleading. Ignore the word "psychology" appears in the title, the book is filled with common sense and practical advice from a real scientist. It is written by a mathematician and it is apparent from every line of the text. Hadamard tries to survey some of the psychological theories of the time (even phrenology!), but thankfully, he sticks more with his own experiences and never fancies about things he didn't experience. It is also possible to see from this book that how experience (phenomena) is robust with respect to time and how psychological theories come and pass as theory is always a fragile construct compared to the collection of empirical facts.

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Understand the mind's inner creative workings

ByAmazon Customeron August 26, 2007

Format: Paperback

Well, the work is clearly outdated in many parts: that was inevitable. It is even a bit tedious, sometimes; and written in what sounded to me "a strange English"; after further reading I realized that it was not a translation, but it was Hadamard himself writing English...
The most interesting parts of the book are, obviously, the "case studies" presented by Hadamard (including, of course, himself). I found this parade of minds very interesting because it helped me to understand a bit more my own way of thinking and my own (little) creativity.
There is another most interesting point in this little book. Many mathematicians (perhaps all the true mathematicians) have a Platonic conception of an ideal world of numbers and mathematical concepts; in the course of their research they just "discover" these pre-existing, eternal truths. As a layman interested in many things, I have always agreed with this conception, but I have often wondered how and why such a Platonic view holds even today, against the recurrent blows of neopositivism and formalism, and so on.
Reading Penrose's books I saw some clues, but this book suggests a clear answer: true mathematicians really see glimpses of this ideal world.
One may argue that this could be just a way of our mind, so this ideal world is just an illusion cast by our mind (or I should say by the kind of mind which can develope into a mathematic mind). But there are many reasons to think that mathematics is a very real world which we can explore and discover. This is a very profound subject, involving the nature of our mind and that of the world around us, its being understandable, and the mysterious connections between the abstract world of pure mathematics and the physical world.

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A study of the mental workings of some great mathematicians

ByMike Christieon January 16, 2001

Format: Paperback

This is a short (136 page) 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 retitled "The Mathematician's Mind" and republished in the Princeton Science Library series; it's not immediately clear from the Amazon page that this is so. The Dover edition is substantially cheaper.
A fascinating and informative book.

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Most recent customer reviews

Easy, interesting read for those who like math

Great book for those who enjoy math. The insights into the way the mathematical mind works and the history behind math breakthroughs is very interesting.

Published on October 6, 2014 by Amazon Customer

Not helpful to understand the psychology of invention

It just talks about how great minds thought about their own thinking process and also about how the author thinks about psychology of invention.Read more

Published on February 22, 2013 by Abhi

the only book on the topic of doing mathematical research

I give it 5 stars because it is unique. I.e. although not perfect, there is to my knowledge no better book on the difficult and elusive topic of how to come up with new ideas and...Read more

Published on February 23, 2006 by twit

Creativity by the creative

Hadamard was one of the productive mathematicians of the late 19th and early/mid 20th century. Maybe his name isn't as broadly known as Gauss or many others.Read more

Published on June 8, 2004 by wiredweird

The Psychology of Math

The Psychology of Invention in the Mathematical Field is a study on how research mathematicians go about the business of advancing their field.Read more

Published on April 2, 2001 by Bukkene Bruse

First rate advice for science and math students

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.Read more

Published on January 25, 2000 by Professor Joseph L. McCauley

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