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.

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

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

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

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.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.