A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or ex… - Richard Hamming

Although textbooks (and professors) like to make definite statements indicating that they know what they are talking about, there is in fact a great deal of uncertainty and ambiguity in the world. ...we will not evade this question but rather explore (overexplore?) it. ...great progress is often made when what was long believed to be true is now seen to be perhaps not the whole truth. Thus the text often uses words... to cause you to think about the uncertainess and even the arbitrariness of much of our current conventions and definitions, to ponder about your acceptance of them.

"If you will only ask yourself, "Is what I am being told really true?," it is amazing how much you can find is, or borders on, being false, even in a well-developed field!"

The only generally agreed upon definition of mathematics is "Mathematics is what mathematicians do." [...] In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D.C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become.