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

3.96  ·  Rating Details ·  79 Ratings  ·  13 Reviews
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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DJ
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
Gwern
Jan 21, 2014 Gwern rated it really liked it  ·  review of another edition
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
...more
Yaser Sulaiman
Sitting on the toilet one morning, it suddenly hit me: a Sudoku puzzle is a graph coloring problem in disguise. Such out-of-the-blue moments of mathematical inspiration, which usually come after struggling with a hard problem for days and then engaging in a different activity, are among the topics that Jacques Hadamard explored in this interesting small book.

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
Leeia Forrester
Jul 24, 2012 Leeia Forrester rated it really liked it  ·  review of another edition
I can appreciate that the author's almost tangential and scattered research of mathematical epiphanies allows me the option to learn many different hypotheses. I can latch onto the theories of many scientists in an attempt to understand and practice the acquisition of mathematical invention and discovery. This is a great blend of psychology and mathematics.
Václav Balcar
Uz si to nepamatuju do detailů, ale doporučil mi to Hedrlin a bylo to prvni čtení o matematice. kde se otevřeně píše o myšlení. Zajímalo by mě, jaké druhy motivací a postojů měly matematici kolem Poincareho a Hadamarda.
Frank
In it's early days, artificial intelligence naively sought to model human reasoning using combinatorial syllogism engines. This went nowhere: No one knew how to constrain the growth in discovery space within workable limits.

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.
Vuka :3
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!
Mark Gently
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.
Shraddha
Dec 11, 2014 Shraddha rated it really liked it
Reminds me of How to solve it and A mathematician's apology, different in content but similar in style.
Maruthi
Feb 19, 2012 Maruthi rated it it was amazing
The mostly inventions happen in the sub conscious space rather than in the conscious space.
Scott Kleinpeter
Fascinating. Like a character study of mathematical creativity.
Dylan
Oct 20, 2011 Dylan rated it liked it  ·  review of another edition
Shelves: 2011
a bit dated, but still has a lot of interesting stuff.
Erickson
Mar 02, 2016 Erickson rated it really liked it  ·  review of another edition
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.
More about Jacques Hadamard...

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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.” 0 likes
“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.” 0 likes
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