"The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. ...According to my definition, a number is computable if its decimal can be written down by a machine. ...I show that certain large classes of numbers are computable. They include, for instance, the real parts of alls, the real parts of the zeros of the Bessel functions, the numbers π, e, etc. The computable numbers do not, however, include all definable numbers. ...onclusions are reached which are superficially similar to those of Gödel. ...t is shown ...that the Hilbertian can have no solution. In a recent paper... reaches similar conclusions..."

“原文：Sometimes it is the people who no one imagines anything of , that do the things that no one can imagine.”

“Can machines think?"... The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man , a woman , and an interrogator who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B... We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?”

“Machines take me by surprise with great frequency.”

“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.”

“Some of the symbols written down will form the sequence of figures which is the decimal of the real number... being computed. The others are just rough notes to "assist the memory ". ...nly ...these rough notes ...will be liable to erasure.”

“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.”