Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
Alan TuringA man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.
Alan TuringIt seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers… They would be able to converse with each other to sharpen their wits. At some stage therefore, we should have to expect the machines to take control.
Alan Turing