The all round genius, mathematician, physicist, engineer and philosopher, Henri Poincaré (1854 – 1912), wrote with scientific precision about how creative intelligence works: “I left Caen, where I was then living, to go on a geologic excursion [and…] the changes of travel made me forget my mathematical work.

“Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.

“On my return to Caen, for conscience’ sake, I verified the result at my leisure. Then I turned my attention to the study of some arithmetical questions apparently without much success and without a suspicion of any connection with my preceding researches.

“Disgusted with my failure, I went to spend a few days at the seaside. One morning, walking on the bluff, the idea came to me – with just the same characteristics of brevity, suddenness and immediate certainty – that the arithmetic transformations of indeterminate ternary quadratic forms were identical with those of non-Euclidean geometry.

“Returned to Caen, I meditated on this result and deduced the consequences…  I made a systematic attack upon them and carried all the outworks, one after another. There was one however that still held out, whose fall would involve that of the whole place. But all my efforts only served at first the better to show me the difficulty, which was indeed something. All this work was perfectly conscious.

“Thereupon I left for Mont-Valerian, where I was to go through my military service; so I was very differently occupied. One day, going along the street, the solution of the difficulty which had stopped me suddenly appeared to me… So I wrote out my final memoir at a single stroke and without difficulty.”

Poincaré concludes that:
1. Creation involves a period of conscious work, followed by a period of unconscious work.
2. Conscious work becomes necessary again after the unconscious work, to put it on a firm footing.
3. Creation, even in the highly analytical world of abstract mathematics, can never be purely mechanical. “It is not purely automatic; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed. In a word, is not the subliminal self superior to the conscious self?”
4. What the unconscious presents to the conscious mind is not a full and complete argument or proof, but rather “point of departure” from which the conscious mind can work out the argument in detail. The conscious mind is capable of the strict discipline and logical thinking, of which the unconscious is incapable.

From “The Foundations of Science” by Henri Poincaré, (Paris 1908), translated from French by G.B. Halstead. Illustration ‘Wordle Word Art: Einstein & Poincare’, from longstreet.typepad.com