Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Machines take me by surprise with great frequency.

I'm afraid that the following syllogism may be used by some in the future. Turing believes machines think Turing lies with men Therefore machines do not think Yours in distress, Alan

We may hope that machines will eventually compete with men in all purely intellectual fields. But which are the best ones to start with? Many people think that a very abstract activity, like the playing of chess, would be best. It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English.

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.

If a machine is expected to be infallible, it cannot also be intelligent.

We may hope that machines will eventually compete with men in all purely intellectual fields.