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.

I can see no justification whatever for the attitude which refuses on purely a priori grounds to accept action at a distance ... Such an attitude bespeaks an unimaginativeness, a mental obtuseness and obstinacy.

The feeling of understanding is as private as the feeling of pain. The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. For this reason, science, when I push the analysis back as far as I can, must be private.

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 process that I want to call scientific is a process that involves the continual apprehension of meaning, the constant appraisal of significance accompanied by a running act of checking to be sure that I am doing what I want to do, and of judging correctness or incorrectness. This checking and judging and accepting, that together constitute understanding, are done by me and can be done for me by no one else. They are as private as my toothache, and without them science is dead.

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.