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.

God does arithmetic.

To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

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

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 have done my duty; let others do theirs.

Few, but ripe.

The complete solution of the problem of the parallel lines must perhaps be sought elsewhere than in the nature of the straight line and plane.

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

The infinite is only a manner of speaking.

It is always better to postpone publication until one is absolutely certain, for once something is printed it can never be recalled.

I am never satisfied until I have said as much as possible in a few words.

Theorems are like ripe fruit: they fall when they are ready.

It is not the knowledge, but the act of learning, that grants the greatest enjoyment.

The magic of numbers has fascinated me from my earliest youth.

I have sometimes thought that perhaps the way to make mathematics more attractive would be to emphasize its human aspect.

The path to the summit is not climbed by flying.

I have often been struck by the way in which a new mathematical discovery, apparently quite remote from any practical application, has later proved to be of the greatest utility.