Archimedes actually did write about how he'd switch between physical and formal reasoning, and his account even survived to today (barely): http://en.wikipedia.

Archimedes actually did write about how he'd switch between physical and formal reasoning, and his account even survived to today (barely): http://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theorems http://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theore...