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

Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.

His second motto: Thou, nature, art my goddess; to thy laws my services are bound.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

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.

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.

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