The Mathematician's Mind: The Psychology of Invention in the Mathematical Field by Jacques Hadamard - ISBN 0486201074 - Princeton University Press 1945

Being interested in creativity and convinced that mathematics, as a discipline using abstraction to solve problems, does require such a skill, unlike the nearly automated techniques taught during school. Also previously discovered some of the work of Hadamard in the history of mathematics.

Draw a schema (using PmGraphViz or another solution) of the situation of the area in the studied domain before having read the book.

- Introduction
- distinction between discovery and invention (p.xi)
- "As my master, Hermite, told me: <<We are rather servants than master in Mathematics.>>" (p.xii)

- 1 General Views and Inquiries
- The Mathematics "Bump" (p3)
- Psychologists' Views on the Subject (p6)
- Mathematical Enquiries (p7)
- Some Criticisms (p9)
- Pointcarre's Statements (p11)
- Looking at One's Own Unconsciousness (p14)
- Instances in Other Fields (p15)
- enunciation a potential process starting by "incubation" then "illumination" following Graham Wallas' Art of Thought (p16)

- The Chance Hypothesis (p18)
- "explanation by
*pure*chance is equivalent to no explanation at all and to asserting that there are effects without causes" (p19)

- "explanation by

- 2 Discussions on Unconsciousness
- The Manifold Character of Unconsciousness (p23)
- see also Wikipedia:Manifold for the less metaphorical view

- Frindge-Consciousness (p24)
- Successive Layers in the Unconscious (p26)

- The Manifold Character of Unconsciousness (p23)
- 3 The Unconscious and Discovery
- Combination of Ideas (p29)
- "it is obvious that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas." (p29)
- footnote on the etymology of cogito as "to shake together"
- an intuitive principle that is coherent with evolutionary epistemology and the necessity to handle modularity

- "it is obvious that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas." (p29)
- The Following Steps (p30)
- "this first process, this building up of numerous combinations, is only the beginning of creation, even, as we should say, preliminary to it" (p30)

- To Invent is to Chose (p30)
- Paul Valéry's famous quote is also used in Gary Cziko and Donald Campbell work

- Coming Back to the Unconscious (p31)
- mention of "mathematical beauty" or "geometric elegance" probably close to Dijkstra sensibility on "mathematical elegance"
- "it is clear that no significant discovery or invention can take place without the
*will*of finding" (p31) - "that invention is choice, that this choice is imperatively governed by the sense of scientific beauty" (p31)

- Other Views on Incubation (p32)
- offering 2 chief hypothesis (p33)
- freshness or rest-hypothesis
- absence of interference or forgetting-hypothesis

- offering 2 chief hypothesis (p33)
- Discussion of These Ideas (p34)
- Other Views on Illuminations. An Intination Stage (p38)
- Further Theories on the Unconscious (p40)

- Combination of Ideas (p29)
- 4 The Preparation Stage. Logic and Chance
- Throughout Conscious Work (p43)
- Conscious Work as Preparatory (p45)
- Pointcarre's View on the Mode of Action of Preparatory Work (p46)
- Pointcarre's metaphor on ideas as combinations "liked the hooked atoms of Epicurus" sounds close to Seedea:Research.Research#CreativityIsPhysical view on "natural creativity" (information is physical, creativity is physical)

- Logic and Chance (p47)
- Personal Instances (p50)
- The Case of Pascal (p53)
- Attempts to Govern our Unconscious (p54)

- 5 The Later Conscious Work
- The Fourth Stage (p56)
- "preparation, incubation and illumination"
- "a rather mechanical part of the work [...] verification"

- A Statement by Paul Valery (p57)
- Numerical Calculators (p58)
- Appreciation of One's Own Work (p60)
- "every stage of the research, has to be, so to speak, articulated to the folowing one by a result in a precise form, which I should propoe to call a
*relay-result*" (p62)

- "every stage of the research, has to be, so to speak, articulated to the folowing one by a result in a precise form, which I should propoe to call a
- Incubation and Relay-results (p63)

- The Fourth Stage (p56)
- 6 Discovery as a Synthesis. The Help of Signs
- Synthesis in Discovery (p64)
- The Use of Signs (p66)
- Words and Wordless Thought (p66)
- Boileau's famous verses "
*Ce qui se conceoit bien s'enonce clairement,*" (p70)

Et les mots pour le dire arrivent aisement,

- Boileau's famous verses "
- Mental Pictures in Usual Thought (p71)
- Mental Pictures in Tense Thought (p73)
- Personal Observations (p75)
- "I have been told by some friends that I have a special way of looking when indulging in mathematical research. I hardly doubt that this especially accompanies the construction of the schema in question." (p78)
- see also Confirmation holism on Wikipedia, also known as Theory Laden or Theory Dependance
- a bias that seems to let some who developed their own model to "see what other can not see", yet begging for experimental confirmation

- "Quand on demande a Michel Foucault ce qu'un livre est pour lui, il repond: c'est une boite a outils. Proust.... disait que son livre etait comme des lunettes: voyez si elles vous conviennent, si vous percevez grace a elles ce que vous n'auriez pas pu saisir autrement; sinon laissez mon livre" page 73 of Mille Plateaux also published in La Guerre des Idees and Literary philosophers

- see also Confirmation holism on Wikipedia, also known as Theory Laden or Theory Dependance

- "I have been told by some friends that I have a special way of looking when indulging in mathematical research. I hardly doubt that this especially accompanies the construction of the schema in question." (p78)
- Respective Roles of Full Consciousness and Frindge-Consciousness (p80)
- see my notes on Cognitive research section of chapter 2 of Foundations in Evolutionary Cognitive Neuroscience

- Other Stages of Research (p81)
- Another Conception (p83)
- An Inquiry among Mathematicians (p83)
- Some Ideas of Descartes (p86)
- Other Thinkers (p89)
- Is Thought in words without inconvenience (p92)
- A Valuable Description (p96)
- Comparison with Another Question Concerning Imagery (p97)
- Can Imagery be Educated? (p98)
- "Such an auto-education of mental processes [Titchener ability to use auditory and visuals images] seems to me to be one of the most remarkable achievement in psychology." (p98-99)

- Using Relay-results (p99)
- General Remarks (p99)
- Addendum (p99)

- 7 Different Kinds of Mathematical Minds
- The Case of Common Sense (p100)
- Second Step: The Student in Mathematics (p103)
- Logic and Intuitive Minds: A Political Aspect of the Question (p106)
- Pointcarre's View of the Distinction (p108)
- Application of Our Previous Data (p112)
- (A) More or Less Depths in the Unconscious (p112)
- "It is quite natural to speak of an intuitive mind if the zone where ideas are combined is deeper, and of a logical if that zone is rather superficial." (p113)
- "If that zone is deeper, there will be more difficulty in bringing the result to the knowledge of consciousness and it is likely to happen for what is strictly necessary." (p113)

- (B) More or Less Narrowly Directed Thought (p114)
- (C) Different Auxiliary Representations (p114)
- Other Differences in Mathematical Minds (p115)

- 8 Paradoxical Cases of Intuition
- Fermat 1601-1661 (p116)
- Riemann 1826-1866 (p117)
- Galois 1811-1831 (p118)
- A Case in the Work of Pointcarre (p121)
- Historical Comparisons (p122)
- "we must admit that some part of the mental process develop so deeply in the unconscious, even important ones, remain hidden from our conscious self." (p122)

- 9 The General Direction of Research
- Two Conceptions of Invention (p124)
- "One could say that application's constant relation to theory is the same as that of the leaf to the tree : one supports the other, but the former feeds the latter." (p125)

- The Choice of Subjects (p126)
- "Then, how are we to select the subject of research? This delicate choice is one of the most important things in research; according to it we form, generally in a reliable manner, our judgement of the value of a scientist." (p126)

- Direction of Inventive Work and Desire of Originality (p131)

- Two Conceptions of Invention (p124)
- Final Remarks
- (p133)

- Appendix 1 An inquiry into the working methods of mathematicians
- (p137)

- Appendix 2 A testimonial from professor Einstein
- (p142)

- Appendix 3 The invention of infinitesimal calculus
- (p144)

- appreciating and enjoying beauty is also a training
- like training an evolutionary filter to remove and increase quality again and again.

- if reading is an act of not simply acquiring words but "executing" the thoughts of the author, how can one allows himself to meta-think without having competing executions during the reading?
- is there a most efficient way to handle that "battle for consciousness" of each executing series of thoughts

- instead of focusing on the quality of thoughts, one could think in term of "cognitive drag"
- see the consequently created CognitiveDrag page

- my reading notes on The Princeton Companion to Mathematics
- Internet Archive: Free Download of the book in multiple formats
- my notes on Origins of Genius by Dean Keith Simonton in which he refers to Hadarmard's work nearly 10 times
- Jacques Hadamard on creativity on Wikipedia
- overview of the book on Google Book
- mathmeth.com - Discipline in Thought Calculational Mathematics and Mathematical Methodology
- The science of thought by Friedrich Max Müller on Internet Archive
- The Scientific Method is A Complete Act of Thought including Wallas' formula
- How to Solve It by George Pólya, 1945 (Wikipedia)
- How to Solve It By Computer by R. G. Dromey, 1982 (Wikipedia)
- chapter 4 On the Role of Thought-Experiments in Mathematical Discovery by Eduard Glas in Models of Discovery and Creativity edited by Joke Meheus and Thomas Nickles, Springer 2009
- The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them by David Ruelle, Princeton University Press 2007
- reviews
- by Steve Hsu, MIT Technology Review 2009

Point A, B and C are debatable because of e, f and j.

(:new_vocabulary_start:) scantily a sieve (:new_vocabulary_end:)

Draw a schema (using PmGraphViz or another solution) of the situation of the area in the studied domain after having read the book. Link it to the pre-reading model and align the two to help easy comparison.

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