It is false to suggest that men must turn away from his desires in the interest of a higher duty. Men only responds to duty if he desires to do so. To understand men, you must understand their desires and the relative strength of those desires.

Beware the man of the single book

Although this may seem a paradox, all exact science is based on the idea of approximation. If a man tells you he knows a thing exactly, then you can be safe in inferring that you are speaking to an inexact man.

Most of the greatest evils that man has inflicted upon man have come through people feeling quite certain about something which, in fact, was false.

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

A good man will never suspect his friends of shady actions: this is part of his goodness. A good man will never be suspected by the public of using his goodness to screen villains: this is part of his utility

... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.