Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

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.

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

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

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

To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much more of my time than I like. Meanwhile I hope that the second time this expenditure of time will be much less, otherwise I would never be able to reconcile myself to it, even practical (astronomical) work must give far more satisfaction than if one brings up to B a couple more mediocre heads which otherwise would have stopped at A.