I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.

To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.

It may be true that people who are merely mathematicians have certain specific shortcomings; however that is not the fault of mathematics, but is true of every exclusive occupation. Likewise a mere linguist, a mere jurist, a mere soldier, a mere merchant, and so forth. One could add such idle chatter that when a certain exclusive occupation is often connected with certain specific shortcomings, it is on the other hand always free of certain other shortcomings.

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.

That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.

In mathematics there are no true controversies.

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.