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

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

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

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.

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.

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.