Gwern's Reviews > The Psychology of Invention in the Mathematical Field
The Psychology of Invention in the Mathematical Field
by Jacques Hadamard
by Jacques Hadamard
I took a gander at this for its possible relevance to an essay of mine on mathematical error - Hadamard's book is one of the classics in the area of mathematical discovery, mentioned along with Poincaré's lecture.
With due allowance for style and age, Hadamard ably describes and defends the basic model of 'work, incubation, illumination, verification', with reference to his own discoveries, his many famous acquaintances, Poincaré's lecture, and a very interesting survey of mathematicians. In fact, it's a little depressing that we don't seem to have gone much beyond that in the half-century since this was published back in 1945 or so. While at least we no longer need his defense of the unconscious as a meaningful part of cognition, much of the rest is depressingly familiar - for example, his acute observations on mental imagery & people who solely think in words, and mention of Francis Galton's survey (little-known outside of psychology), could be usefully read by many who commit the typical mind fallacy.
If Hadamard comes to no hard and fast conclusions, but merely raises many interesting points and criticizes a number of theories, we can hardly hold that against him, as we can do little better and so it becomes our failing, not his.
(I read the Internet Archive scan.)
With due allowance for style and age, Hadamard ably describes and defends the basic model of 'work, incubation, illumination, verification', with reference to his own discoveries, his many famous acquaintances, Poincaré's lecture, and a very interesting survey of mathematicians. In fact, it's a little depressing that we don't seem to have gone much beyond that in the half-century since this was published back in 1945 or so. While at least we no longer need his defense of the unconscious as a meaningful part of cognition, much of the rest is depressingly familiar - for example, his acute observations on mental imagery & people who solely think in words, and mention of Francis Galton's survey (little-known outside of psychology), could be usefully read by many who commit the typical mind fallacy.
If Hadamard comes to no hard and fast conclusions, but merely raises many interesting points and criticizes a number of theories, we can hardly hold that against him, as we can do little better and so it becomes our failing, not his.
(I read the Internet Archive scan.)
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| 01/20/2014 | marked as: | to-read | ||
| 01/20/2014 | marked as: | read | ||
