I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.
Alfred North WhiteheadThere is no greater hindrance to the progress of thought than an attitude of irritated party-spirit.
Alfred North WhiteheadWe must not expect simple answers to far-reaching questions. However far our gaze penetrates, there are always heights beyond which block our vision.
Alfred North WhiteheadVigorous societies harbor a certain extravagance of objectives, so that men wander beyond the safe provision of personal gratifications.
Alfred North WhiteheadOur rate of progress is such that an individual human being, of ordinary length of life, will be called on to face novel situations which find no parallel in his past. The fixed person, for the fixed duties, who, in older societies was such a godsend, in the future will be a public danger.
Alfred North WhiteheadThe point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
Alfred North Whitehead