Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and… - Doron Zeilberger

Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.

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.