In other words, by noodling around, playing with the Method, he gets a feel for the territory. And that guides him to a watertight proof. This is such an honest account of what it’s like to do creative mathematics. Mathematicians don’t come up with the proofs first. First comes intuition. Rigor comes later. This essential role of intuition and imagination is often left out of high-school geometry courses, but it is essential to all creative mathematics. Archimedes
