The ultimate goal of mathematics is to eliminate all need for intelligent thought.
Math is sometimes called the science of patterns.
Someone has said that all the great jugglers are dead.
Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'.
I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'.
AB=1/4((A+B)^2-(A-B)^2) is an amazing identity, and unfortunately, I have to remind my current students how to prove it.