My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

It was long before I got at the maxim, that in reading an old mathematician you will not read his riddle unless you plough with his heifer; you must see with his light, if you want to know how much he saw.

The Astronomer's Drinking Song Astronomers! What can avail Those who calumniate us; Experiment can never fail With such an apparatus.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]

I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.

The moving power of mathematical invention is not reasoning but imagination.