Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.

Codes are a puzzle. A game, just like any other game.

A very large part of space-time must be investigated, if reliable results are to be obtained.

A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.

Mathematical reasoning may be regarded.

I am not very impressed with theological arguments whatever they may be used to support. Such arguments have often been found unsatisfactory in the past. In the time of Galileo it was argued that the texts, 'And the sun stood still... and hasted not to go down about a whole day' (Joshua x. 13) and 'He laid the foundations of the earth, that it should not move at any time' (Psalm cv. 5) were an adequate refutation of the Copernican theory.