I am always interested in simple/elegant/cool proofs of mathematical facts. I’m also interested to know their origins. Does anyone know who came up with the following rather elegant proof of ? It’s likely that the origins are lost in time but I thought I would ask anyway. Proof: I like this because of the use of 2-1=1. Another situation where the use of 1 gives a cool proof is the following from complex analysis. Does anyone know the origin of the proof? Theorem: If is complex Riemann integrable and is Riemann integrable, then . Proof: If the left-hand side is zero, then the statement is trivial. Hence, assume that the left-hand side is non-zero. Define the complex number by We have, Do you have any cool proofs? (With or without clever use of...