One geometry cannot be more true than another; it can only be more convenient.

Sociology is the science with the greatest number of methods and the least results.

In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.

Need we add that mathematicians themselves are not infallible?

Einstein does not remain attached to the classical principles, and when presented with a problem in physics he quickly envisages all of its possibilities. This leads immediately in his mind to the prediction of new phenomena which may one day be verified by experiment.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know