Archimedes’s books present perfect proofs, but they do not say how he reached the results. For centuries, mathematicians suspected he had a secret method. They were right, and the method was found in the most unlikely place. The letter to Eratosthenes Certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards, because their investigation by this method did not furnish an actual proof. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge. — Archimedes, The Method, letter to Eratosthenes