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!

Modern science should indeed arouse in all of us a humility before the immensity of the unexplored and a tolerance for crazy hypotheses.

All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.

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.

It is part of the pholosophic dullness of our time that there are millions of rational monsters walking about on their hind legs, observing the world through pairs of flexible little lenses, periodically supplying themselves with energy by pushing organic substances through holes in their faces, who see nothing fabulous whatever about themselves.

The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician.

The violence and double-talk in the Alice books probably does no harm to children, but the novels should not be allowed to circulate indiscriminately among adults who are undergoing analysis.