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

Thoughtful and articulate study of the origin of ideas. Role of the unconscious in invention; the medium of ideas — do they come to mind in words? in pictures? in mathematical terms? Much more. "It is essential for the mathematician, and the layman will find it good reading." —

*Library Journal*.Paperback, 168 pages

Published
October 20th 1996
by Princeton University Press
(first published 1949)

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## Community Reviews

(showing 1-30 of 344)

May 16, 2010
DJ
rated it
liked it
·
review of another edition

Recommends it for:
Henry Yuen

Shelves:
philosophy

I dove into this book excited to learn how the minds of great scientists churn but instead was reminded of the great danger that accompanies reading old science texts - lengthy discussions of crackpot theories (i.e. phrenology) and passionate defenses of well-accepted ideas (i.e. not all mental activity is conscious). Taken as a survey of late 19th/early 20th century thinking on creativity and thought, the book reveals how stubbornly we humans cling to the mech warrior hypothesis of behavior - t
...more

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 ...more

As P. N. Johnson-Laird notes in the preface of this edition, the book was prescient: when Hadamard set out to explore mathematical inventio ...more

Another class of attempts was based on strong reductionism; modelling neuron function.

It occurs to me in reading this book that I know of no attempts at the mid-level, i.e. modelling Hadamard's fringe consciousness, Poincaré's idea fragments, activated by association, etc.

Aug 02, 2013
Vuka :3
rated it
really liked it
·
review of another edition

Shelves:
mathematics,
mind

The rapid development of neuroscience and psychology in the last several decades makes some of the ideas in this book a bit outdated, although I don't think it renders them completely useless.

This book is a bold interdisciplinary move in trying to understand what goes on in the mind of mathematicians and other scientists engaging in mathematical thinking. I think it lacks something, but I'm not quite sure what... other than that, it's pretty good!

This book is a bold interdisciplinary move in trying to understand what goes on in the mind of mathematicians and other scientists engaging in mathematical thinking. I think it lacks something, but I'm not quite sure what... other than that, it's pretty good!

Jun 15, 2016
Mark Gently
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review of another edition

Shelves:
alex-tr,
tr-length-1

Mostly of historical interest. Appendix II contains an interesting letter from Einstein, in which he has some intriguing things to say about the nature of his own thought processes.

Feb 16, 2016
Scott Kleinpeter
rated it
it was amazing
·
review of another edition

Shelves:
systems,
reference-unfinished

Fascinating. Like a character study of mathematical creativity.

Mar 02, 2016
Erickson
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really liked it
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review of another edition

Shelves:
philosophy,
mathematics

For some reason didn't learn much.

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Jacques Salomon Hadamard was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.

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“Στη συνέχεια, ακολουθεί το στάδιο της επαλήθευσης και του «τελειώματος». Σ' αυτή την τελική φάση της εργασίας, μπορεί να χρησιμοποιήσω αλγεβρικά σύμβολα. Πολύ συχνά, όμως, δεν τα χρησιμοποιώ με το συνήθη και κανονικό τρόπο. Δεν σπαταλώ χρόνο για να γράψω τις εξισώσεις πλήρως, με ενδιαφέρει μόνο να δω, ούτως ειπείν, πώς μοιάζουν. Αυτές οι εξισώσεις, ή κάποιοι όροι τους, συχνά διατάσσονται σε μια παράξενη και αλλόκοτη σειρά όπως οι ηθοποιοί σε μια σκηνή και με αυτό τον τρόπο μου «μιλούν» ενόσω εξακολουθώ να τις μελετώ. Αν όμως διακόψω την εργασία μου και συνεχίσω την επόμενη μέρα, ό,τι έχω γράψει με αυτό τον τρόπο είναι «νεκρό» για μένα. Γενικά, το μόνο που μπορώ να κάνω είναι να πετάξω τα χαρτιά μου και να ξεκινήσω τα πάντα από την αρχή, εκτός αν έχω καταλήξει, την πρώτη μέρα, σ' έναν-δυο τύπους τους οποίους έχω επαληθεύσει πλήρως και μπορώ να τους χρησιμοποιήσω ως τύπους-κόμβους.”
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“Όσον αφορά το ερώτημα αν η ασυνείδητη νόηση είναι «ανώτερη» ή «κατώτερη» από τη συνειδητή, αρνούμαι να δεχθώ ότι έχει οποιοδήποτε νόημα. Θεωρώ ότι κανένα ερώτημα περί «ανωτερότητας» ή «κατωτερότητας» δεν είναι επιστημονικό. Όταν ιππεύετε ένα άλογο, είναι αυτό ανώτερο ή κατώτερό σας; Είναι δυνατότερο και ταχύτερο από εσάς, αλλά εσείς μπορείτε να το κατευθύνετε όπως θέλετε. Δεν ξέρω τι νόημα θα είχε να πούμε ότι το οξυγόνο είναι ανώτερο ή κατώτερο από το υδρογόνο. Ούτε το δεξί πόδι είναι ανώτερο ή κατώτερο από το αριστερό· και τα δύο συνεργάζονται για να περπατάμε. Αυτό κάνουν και το συνειδητό και ασυνείδητο, και τη συνεργασία αυτή θα εξετάσουμε στη συνέχεια.”
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