- Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
- Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.
- A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.
- Science is a differential equation. Religion is a boundary condition.
- The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.
- 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.
- 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.
- We can only see a short distance ahead, but we can see plenty there that needs to be done.
- His high-pitched voice already stood out above the general murmur of well-behaved junior executives grooming themselves for promotion within the Bell corporation. Then he was suddenly heard to say: 'No, I'm not interested in developing a powerful brain. All I'm after is just a mediocre brain, something like the President of the American Telephone and Telegraph Company.'