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

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

The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity and split into diverse branches.

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

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...