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.

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.

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

My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.

With a thousand joys I would accept a nonacademic job for which industriousness, accuracy, loyalty, and such are sufficient without specialized knowledge, and which would give a comfortable living and sufficient leisure, in order to sacrifice to my gods [mathematical research]. For example, I hope to get the editting of the census, the birth and death lists in local districts, not as a job, but for my pleasure and satisfaction.

Mathematics is the queen of the sciences.

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.