The nervous system and the automatic machine are fundamentally alike in that they are devices, which make decisions on the basis of decisions they made in the past.

What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.

Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.

Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst.

To live effectively is to live with adequate information.

There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.

The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.