We must be sceptical even of our scepticism.

One must expect a war between U.S.A. and U.S.S.R. which will begin with the total destruction of London. I think the war will last 30 years, and leave a world without civilised people, from which everything will have to build afresh - a process taking (say) 500 years.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

Americans and Englishmen, when they become acquainted with the Balkans, feel an astonished contempt when they study the mutual enmities of Bulgarians and Serbs, of Hungarians and Rumanians. It is evident to them that these enmities are absurd and that the belief of each little nation in its own superiority has no objective basis. But most of them are quite unable to see that the national pride of a Great Power is essentially as unjustifiable as that of a little Balkan country.

I have lived in the pursuit of a vision, both personal and social. Personal: to care for what is noble, for what is beautiful, for what is gentle; to allow moments of insight to give wisdom at more mundane times. Social: to see in imagination the society that is to be created, where individuals grow freely, and where hate and greed and envy die because there is nothing to nourish them. These things I believe, and the world, for all its horrors, has left me unshaken.

The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.

It is one of the defects of modern higher education that it has become too much a training in the acquisition of certain kinds of skill, and too little an enlargement of the mind and heart by an impartial survey of the world.