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.

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

Need we add that mathematicians themselves are not infallible?

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

Every good mathematician should also be a good chess player and vice versa.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.