In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

How is error possible in mathematics?

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Chance ... must be something more than the name we give to our ignorance.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.