Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".

If an opinion contrary to your own makes you angry, that is a sign that you are subconsciously aware of having no good reason for thinking as you do.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.

Why is propaganda so much more successful when it stirs up hatred than when it tries to stir up friendly feeling?

Intelligence, it might be said, has caused our troubles; but it is not unintelligence that will cure them. Only more and wiser intelligence can make a happier world

But if thought is to become the possession of many, not the privilege of the few, we must have done with fear. It is fear that holds men back - fear lest their cherished beliefs should prove delusions, fear lest the institutions by which they live should prove harmful, fear lest they themselves should prove less worthy of respect than they have supposed themselves to be.