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

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

Mathematicians stand on each other's shoulders.

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

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.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.