The unconscious machine

And yet, it’s not rest alone that made the idea arrive, but the oscillation of effort and rest. Poincaré continues:

These sudden inspirations...never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, where the way taken seems totally astray. These efforts have not be

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Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to be incontestable, and traces of it would be found in other cases where it is less evident. Often when one works at a hard question, nothing good is accomplished at ... See more