I remember reading, maybe in a decades-ago issue of Scientific American, that geometry and physics professors sometimes hear from cranks. These are arrogant people, working in isolation, who earnestly believe they have discovered something important. Typical examples might be trisecting an angle with a compass and straightedge in a finite number of steps or unifying physics. I have not understood the details of those examples personally, but there is a basic, recurring disconnect between the position of the crank – “The establishment has tried and failed; they do not understand” – and the position of the establishment – “We understand thoroughly; this task is proven to be impossible.”
