Speaking about symmetry, look out our window, and you may see a cardinal attacking its reflection in the window. The cardinal is the only bird we have who often does this. If it has a nest nearby, the cardinal thinks there is another cardinal trying to invade its territory. It never realizes it is attacking its own reflection. Cardinals don't know much about mirror symmetry!

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all.

The sudden hunch, the creative leap of mind that "sees" in a flash how to solve a problem in a simple way, is something quite different from general intelligence.

One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers.