Poincare, Henri - Discovering the final fuchsian functions
Type of spiritual experience
A description of the experience
An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard
Poincare knew that his initial fuchsian functions constituted only a special case; the question was to investigate the most general ones. In this he was stopped by most serious difficulties, which a persistent conscious effort allowed him to define more adequately, but not at first, to overcome.
Then again, the solution appeared to him as unexpectedly as unpreparedly as in the other two instances, whilst he was serving his time in the army. And he adds:
‘Most striking at first is this appearance of sudden illumination, a manifest sign of long unconscious prior work. The role of the subconscious in mathematical invention appears to be incontestable’