Progress imposes not only new possibilities for the future but new restrictions.

Progress imposes not only new possibilities for the future but new restrictions.

The Human Use of Human Beings.

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.

Ex-Prodigy: My Childhood and Youth.

There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.

Introduction to the Foundations of Mathematics.

Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.

In The American Mathematical Monthly, March 1994.

[Occam's Razor:]

Entities should not be multiplied unnecessarily.

Quodlibeta.

A monument to Newton! A monument to Shakespeare! Look up to Heaven, look into the Human Heart. Till the planets and the passions, the affections and the fixed stars are extinguished, their names cannot die.

unknown

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

Tractatus Logico Philosophicus, New York, 1922.

Mathematics is a logical method ... Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

Tractatus Logico Philosophicus, New York, 1922, p. 169.

There can never be surprises in logic.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

The riddle does not exist. If a question can be put at all, then it can also be answered.

Tractatus Logico Philosophicus, New York, 1922.