"The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable b…"

"The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configur…"

"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which…"

"Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-s…"

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

"There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system…"

"This is only a foretaste of what is to come, and only the shadow of what is going to be. We have to have some experie…"

"Science is a differential equation. Religion is a boundary condition."

"Let us now assume, for the sake of argument, that these machines are a genuine possibility, and look at the consequen…"

"We may compare a man in the process of computing a real number to a machine which is only capable of a finite number …"