Mathematics is the science which draws necessary conclusions.

Memoir read before the National Academy of Sciences in Washington, 1870.

[after proving Euler's formula *e ^{π i}* = -1 in a lecture]

Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it is the truth.

Quoted in E Kasner and J Newman