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

By far the most important consequence of the conceptual revolution brought about in physics by relativity and quantum theory lies not in such details as that meter sticks shorten when they move or that simultaneous position and momentum have no meaning, but in the insight that we had not been using our minds properly and that it is important to find out how to do so.

The operational approach demands that we make our reports and do our thinking in the freshest terms of which we are capable, in which we strip off the sophistications of millenia of culture and report as directly as we can on what happens.

But ... the working scientist ... is not consciously following any prescribed course of action, but feels complete freedom to utilize any method or device whatever which in the particular situation before him seems likely to yield the correct answer. ... No one standing on the outside can predict what the individual scientist will do or what method he will follow.

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

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.

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