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An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard

The same character of suddenness and spontaneity …. has been recognised by psychologists as being present in every kind of invention ……………..On has attracted the attention of psychologist Paulhan [Psychologie de l’invention].  It is a celebrated letter of Mozart:

When I feel well and in good humour, or when I am taking a drive or walking after a good meal, or in the night when I cannot sleep, thoughts crowd into my mind as easily as you could wish.  Whence and how do they come?

I do not know and I have nothing to do with them.  Those which please me, I keep in my head and hum them; at least others have told me that I do so.  Once I have my theme, another melody comes, linking itself to the first one, in accordance with the needs of the composition as a whole; the counterpoint, the part of each instrument, and all these melodic fragments at last produce the entire work.  Then my soul is on fire with inspiration, if however nothing occurs to distract my attention. 

The work grows; I keep expanding it, conceiving it more and more clearly until I have the entire composition finished in my head though it may be long.  Then my mind seizes it as a glance of my eye a beautiful picture or a handsome youth.  It does not come to me successively, with its various parts worked out in detail, as they will be later on, but it is in its entirety that my imagination lets me hear it.

Now, how does it happen, that while I am at work, my compositions assume the form or the style which characterise Mozart and are not like anybody else’s?  Just as it happens that my nose is big and hooked, Mozart’s nose and not another man’s.  I do not aim at originality and I should be much at a loss to describe my style.  It is quite natural that people who really have something particular about them should be different from each other on the outside as well as on the inside.