Coincidence is what you have left over when you apply a bad theory.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

There is no adequate defense, except stupidity, against the impact of a new idea.

If a specific question has meaning, it must be possible to find operations by which an answer may be given to it ... I believe that many of the questions asked about social and philosophical subjects will be found to be meaningless when examined from the point of view of operations.

The first business of a man of science is to proclaim the truth as he finds it, and let the world adjust itself as best it can to the new knowledge.

It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.

... the scientist would maintain that knowledge in of itself is wholly good, and that there should be and are methods of dealing with misuses of knowledge by the ruffian or the bully other than by suppressing the knowledge.