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

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

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.

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.

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.

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