The psychology of invention in the mathematical field

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1. jmountNov 2025
   For a introspective view of "aha" I really recommend the enjoyable Hadamard "The Psychology of Invention in the Mathematical Field."
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2. pramodbiligiriJun 2022
   I've heard it being called Focussed Mode and Diffuse Mode, as described here - https://fs.blog/focused-diffuse-thinking/

   Bret Victor links to this book called Psychology of Invention in the Mathematical Field, which talks a lot about this too - http://worrydream.com/refs/Hadamard%20-%20The%20psychology%2...

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3. jmountMay 2018
   If you find this sort of thinking interesting, definitely also check out "The Psychology of Invention in the Mathematical Field" by Jacques Hadamard.
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4. keithpeterApr 2018
   The Psychology of Invention in the Mathematical Field by Jacques Hadamard, himself a mathematician is not scientific but a good source of anecdotes and systematic attempts at introspection.

   I find that 'stepping away' from the details after immersion for a few days and allowing the pieces to re-align themselves does seem to pay benefits, even with the mundane and practical problems I need to solve. I agree with the grandparent post that alcohol is not the only de-focusing agent around.

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5. pierre_d528Nov 2017
   > "intimidating"

   Exactly.

   /speculation

   There is a point where one starts to see "behind" the symbols. It's a strange sensation, as if one could understand the ideas in a non-verbal way. The symbols become optional. Intimidation crawls back before curiosity at this point.

   An amazing book on the subject is:

     "Hadamard - The psychology of invention in the mathematical field"
   

   /speculation
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6. evanbJul 2017
   I broke up my list into cultural (that is, about the people, history, etc), popular (that is, not aimed at a student or an expert), and texts.

   CULTURAL

   Einstein - Essays in Humanism

   Frayn - Copenhagen

   Feynman - Surely You're Joking, Mr. Feynman!

   Feynman - What Do You Care What Other People Think?

   de Grasse Tyson - Death by Black Hole

   Hoffman - The Man Who Loved Only Numbers

   Kaiser - Drawing Theories Apart

   Kaiser - How the Hippied Saved Physics

   Macaulay - The Way Things Work

   Paulos - Innumeracy

   Sagan - Cosmos

   Sagan - Broca's Brain

   Sagan - The Demon-Haunted World

   Salam - Science in the Third World

   Seife - Zero

   Weisskopf - The Joy of Insight

   POPULAR

   Deutsch - The Beginning of Infinity (especially his explanation about fungibility in quantum mechanics)

   Feynman - The Meaning of It All

   Feynman - Lectures on Physics

   Feynman and Weinberg - Elementary Particles and the Laws of Physics

   Galison - Einstein's Clocks, Poincaré's Maps

   Gamow - One, Two, Three... Infinity

   Hadamard - Psychology of Invention in the Mathematical Field

   Hawking - A Brief History of Time

   Hofstadter - Gödel Escher Bach

   Heisenberg - Physics and Philosophy: The Revolution in Modern Science

   Polya - How to Solve It

   Schrödinger - What is Life?

   Susskind - The Theoretical Minimum

   Susskind - Quantum Mechanics

   Wallace - Everything And More

   Weinberg - The First Three Minutes

   Wiener - God & Golem, Inc.

   TEXTS

   Aaronson - Quantum Computing with Democritus (but I don't have a version with me in the acknowledgements https://books.google.com/books?id=jRGfhSoFx0oC&lpg=PR31&ots=... )

   Abelson and Sussman - SICP

   Abrikosov, Gorkov, and Dzyaloshinski - Methods of Quantum Field Theory in Statistical Physics

   Cohen-Tannoudji - Quantum Mechanics (1+2)

   Dirac - Lectures on Quantum Mechanics

   Eddington - Space, Time, and Gravitation

   Feynman - Feynman's Thesis

   Feynman and Hibbs - Quantum Mechanics and Path Integrals

   Fermi - Thermodynamics

   Gattringer & Lang - Quantum Chromodynamics on the Lattice

   Goldstein - Classical Mechanics (the old version, NOT with Poole and Safko)

   Griffiths - Introduction to Electrodynamics

   Griffiths - Introduction to Quantum Mechanics

   Jackson - Classical Electrodynamics (2nd edition---the last one entirely in CGS---is preferable)

   Kleppner and Kolenkow - An Introduction to Mechanics

   Landau and Lifshitz - any book in this series

   Nielsen and Chuang - Quantum Computation and Quantum Information

   Pauli - Selected Topics in Field Quantization

   Peskin & Schroeder - An Introduction to Quantum Field Theory

   Purcell - Electricity and Magnetism

   Ryden - Introduction to Cosmology

   Sakurai - Modern Quantum Mechanics (up to chapter 5, after which Sakurai dies and the editors put his notes together)

   Sussman and Wisdom - Structure and Interpretation of Classical Mechanics

   Sipser - Introduction to the Theory of Computation

   Thorne - Black Holes & Time Warps

   Thouless - The Quantum Mechanics of Many-Body Systems

   Weinberg - The Quantum Theory of Fields I, II, and III

   Zee - Quantum Field Theory in a Nutshell

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