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 not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

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.