The public does not need to be convinced that there is something in mathematics.

Mathematics is not a contemplative but a creative subject.

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

The mathematician is in much more direct contact with reality. ... [Whereas] the physicist's reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.