Carl Friedrich Gauss

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

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.

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.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.

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

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

...as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.

Theory attracts practice as the magnet attracts iron.

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

A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

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

Mathematics is the queen of the sciences.

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

In mathematics there are no true controversies.