If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.

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

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.

Life stands before me like an eternal spring with new and brilliant clothes.

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.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.