Shower thoughts, flashes of insight, or eureka moments are not that uncommon, and the way a lot of creative thinking is done. This is probably a little outside the purview of history, but here is a general interest piece on the phenomenon. The gist of it is that distracting the conscious part of your mind lets the creative part work in the background, this results in the flash of insight appearing to come from nowhere.

It's a common detail in histories of scientists and artists. Albert Einstein first conceived of his theory of relativity while taking a break from his work and daydreaming. Newton famously got his inspiration for the theory of gravitation watching apples fall to the ground (but not actually getting hit in the head with one). Descartes developed coordinate geometry after getting an insight watching flies walk across his ceiling.

Artists experience this as well. Samuel Taylor Coleridge and Paul McCartney both had some of their most notable works come to them in dreams.

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