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.

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.

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

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