@HenningMakholm If QED weren't ignoring you, you'd hear the following quote by JvN: "Young man, in mathematics you don't understand things. You just get used to them."
One story is that C proved it for finite sums, B extended it to integrals, and S generalized C's proof to cover general inner product spaces. In particular, Schwarz (I am going to switch to writing full names =)) gave the proof using the quadratic form (x - lambda y)^T (x - lambda y).
I used to know it as CSB too. For a long time, I didn't know what B meant. In my head, I expanded it to "Badger" just so that I had some pronunciation. =)