Programming is much much harder than doing mathematics. - Doron Zeilberger

Regardless of whether or not God exists, God has no place in mathematics, at least in my book.

When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.

The best way to learn a topic is by teaching it. Similarly the best way to understand a new proof is by writing an expository article about it.