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.

Point set topology is a disease from which the human race will soon recover.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

But for harmony beautiful to contemplate, science would not be worth following.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

To invent is to discern, to choose.