Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
Alan TuringWe can only see a short distance ahead, but we can see plenty there that needs to be done.
Alan TuringBell Labs Cafeteria, New York, 1943: 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."
Alan TuringThere is, however, one feature that I would like to suggest should be incorporated in the machines, and that is a 'random element.' Each machine should be supplied with a tape bearing a random series of figures, e.g., 0 and 1 in equal quantities, and this series of figures should be used in the choices made by the machine. This would result in the behaviour of the machine not being by any means completely determined by the experiences to which it was subjected, and would have some valuable uses when one was experimenting with it.
Alan Turing