There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

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

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.

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

Theory attracts practice as the magnet attracts iron.

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 the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.