Proof is an idol before whom the pure mathematician tortures himself.
(The Nature of the Physical World, 1928, chapter 15)
In the short form above in which it is usually quoted, that statement must have offered consolation to thousands of scientists — and even applied mathematicians — lost in the wilderness of analysis or number theory. As usual, though, the wider context repays a little attention:
We [Eddington was writing as a scientist with a religious faith] cannot pretend to offer proofs. Proof is an idol before whom the pure mathematician tortures himself. In physics we are generally content to sacrifice before the lesser shrine of Plausibility. And even the pure mathematician — that stern logician — reluctantly allows himself some prejudgements; he is never quite convinced that the scheme of mathematics is flawless, and mathematical logic has undergone revolutions as profound as the revolutions of physical theory. We are all alike stumblingly pursuing an ideal beyond our reach.
You can decide for yourself whether, in the nearly eighty years since that was written, mathematics has come to look any more flawless, or physics any more plausible.