Considerations

"But in the intuitive mind the principles are found in common use and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles and, in the next place, an accurate mind not to draw false deductions from known principles."
--Blaise Pascal, Pensees



"You don't see what you're seeing until you see it, but when you do see it, it lets you see many other things."
--Dr. William Thurston, mathematician, quoted in "An Elusive Proof and Its
Elusive Prover": NY Times, August 15, 2006