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

I believe it to be of particular importance that the scientist have an articulate and adequate social philosophy, even more important than the average man should have a philosophy. For there are certain aspects of the relation between science and society that the scientist can appreciate better than anyone else, and if he does not insist on this significance no one else will, with the result that the relation of science to society will become warped, to the detriment of everybody.

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

... 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.

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

Science is what scientists do, and there are as many scientific methods as there are individual scientists.

In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.