Visions of Infinity: The Great Mathematical Problems – Ian Stewart

Thoughts: Decent. A lot of it went over my head, but Stewart does an admirable job explaining complex topics clearly, so I understood more than I might have reading a lesser math communicator.

(The notes below are not a summary of the book, but rather raw notes - whatever I thought, at the time, might be worth remembering.)

Stewart, Ian. 2013. Visions of Infinity: The Great Mathematical Problems. Basic Books.

• 12-13: Henri Poincaré took a special interest in how mathematical insights come about. “His outline of the creative process distinguished three key stages: preparation, incubation, and illumination. Preparation consists of conscious logical efforts to pin the problem down, make it precise, and attacked by conventional methods. This stage Poincaré considered essential: it gets the subconscious going and provides raw materials for it to work with. Incubation takes place when you stop thinking about the problem and go off and do something else. The subconscious now starts combining ideas with each other, often quite wild ideas, until light starts to dawn. With luck, this leads to illumination: your subconscious taps you on the shoulder and the proverbial lightbulb goes off in your mind.” (cf. Graham Wallas’s model of creative breakthroughs)
• 30-31: Novel mentioned: Uncle Petros and Goldbach’s Conjecture by Apostolos Doxiadis. When it was released, Faber & Faber offered a million-dollar prize if a proof of the Goldbach Conjecture could be delivered within two years (i.e. it expired in April 2002).