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!

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

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!

If God creates a world of particles and waves, dancing in obedience to mathematical and physical laws, who are we to say that he cannot make use of those laws to cover the surface of a small planet with living creatures?

A god whose creation is so imperfect that he must be continually adjusting it to make it work properly seems to me a god of relatively low order, hardly worthy of any worship.

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.

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