Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow. - Richard Hamming

Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.

To see the obvious it often takes an outsider, or else someone like me who is thoughtful and wonders what he is doing and why it is all necessary. Even when told, the old timers will persist in the ways they learned, probably out of pride for their past and an unwillingness to admit there are better ways than those they were using for so long.

This is a book about thinking. One cannot talk about thinking in the abstract, at least not usefully. But one can talk about thinking about digital filters, and by studying how great scientists thought about digital filters, one learns, however gradually, to think like a great scientist.