We now come to the decisive step of mathematical abstraction: we forget about what the symbols stand for. ...[The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for. -- Hermann Weyl, The Mathematical Way of Thinking

It’s hard to grasp abstractions if you don’t understand what they’re abstracting away from. -- Nathan Weizenbaum

You can recognize truth by its beauty and simplicity. When you get it right, it is obvious that it is right. -- Richard Feynman

There are many ways to avoid success in life, but the most sure-fire just might be procrastination. -- Hara Estroff Marano.

I think it is wise, and only honest, to warn you that my goal is immodest. It is not my purpose to "transfer knowledge" to you that, subsequently, you can forget again. My purpose is no less than to effectuate in each of you a noticeable, irreversable change. I want you to gain, for the rest of your lives, the insight that beautiful proofs are not "found" by trial anf error but are the result of a consciously applied design discipline. I want you to raise your quality standards. I mean, if 10 years from now, when you are doing something quick and dirty, you suddenly visualize that I am looking over your shoulders and say to yourself "Dijkstra would not have liked this", well, that would be enough immortality for me. -- E. W. Dijkstra

What Paul does, and does very well, is to take ideas and concepts that are beautiful in the abstract, and brings them down to a real world level. That's a rare talent to find in writing these days. -- Jeff "hemos" Bates, Director, OSDN; Co-evolver, Slashdot

You may have to fight a battle more than once to win it. ~Margaret Thatcher

If you’re going through hell keep going. ~Winston Churchill

Courage is resistance to fear, mastery of fear - not absense of fear. ~Mark Twain

Everything has beauty, but not everyone can see. –Confucius