Cauchy-Schwarz proof sample

This proof of the Cauchy-Schwarz Inequality is used to start a discussion about proof elegance. The class compares this proof with the proof of the Cauchy-Schwarz inequality given in Proofs from the Book by Aigner and Ziegler. The class discusses which proof one would discover first and how it’s a good idea, after having proved something, to think about rewriting it. This writing sample was developed by Mohammed Abouzaid and Peter Speh.