Mathematics in general is fundamentally the science of self-evident things.

Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.