When we perceive any object of a familiar kind, much of what appears subjectively to be immediately given is really derived from past experience.

In the visible world, the Milky Way is a tiny fragment; within this fragment, the solar system is an infinitesimal speck, and of this speck our planet is a microscopic dot. On this dot, tiny lumps of impure carbon and water, of complicated structure, with somewhat unusual physical and chemical properties, crawl about for a few years, until they are dissolved again into the elements of which they are compounded.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Too little liberty brings stagnation, and too much brings chaos.

The degree of one's emotions varies inversely with one's knowledge of the facts - the less you know the hotter you get.

Mathematics rightly viewed possesses not only truth but supreme beauty.

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.