Jacques Hadamard was a well know French mathematician who undertook a monograph length exploration of "the psychology of invention in the mathematical field" (as the subtitle has it). The essay is particularly interesting because it combines introspection into his own working process with reports from a variety of other mathematicians to concoct a basic theory of how it feels to discover a new mathematical idea. The upshot is that most mathematician's seem to work with various visual, auditory or even motor (in the case of Einstein) images at a pre-verbal level. Hadamard takes these images to be conscious representatives of unconscious processes that get linked together as so many stepping stones that later guide linguistic or conventionally symbolic arguments. In short, there's nothing deductive about mathematical invention, which in Hadamard's view is not a substantially different process than what we might more readily associate with poetic invention. The conscious mind prepares the field with a long immersion into the subject. Then the mathematician sleeps on it, so to speak, and their unconscious tries out various combinations until a successful one bubbles to the surface in the form of concrete images. Finally, these images must be consciously and painstakingly translated back into a form that will stand up to the scrutiny of logical communication. I would reserve judgement on whether Hadamard's is an adequate description of all possible types of invention; surely the question has been studied in much greater depth in the 70 years since his publication. But it is a coherent and interesting one that definitely fits with my own experience of writing.
No comments:
Post a Comment