The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

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

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 am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.

Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

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