Mathematics is the queen of science, and arithmetic the queen of mathematics.

When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

Mathematics is concerned only with the enumeration and comparison of relations.