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

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.

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 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.

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.

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