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

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

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

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

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

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.

Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.