Need we add that mathematicians themselves are not infallible?

All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

All of mathematics is a tale about groups.

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.