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

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

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

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.

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

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.

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