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

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.

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

The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes.

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.

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.