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

Alan Turing

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Alan Turing
Age: 41 †
Born: 1912
Born: June 23
Died: 1954
Died: June 7
Artificial Intelligence Researcher
Computer Scientist
Cryptographer
Logician
Marathon Runner
Mathematician
Statistician
University Teacher
Warrington Lodge Medical and Surgery Home for Ladies
Alan M. Turing
Alan Mathieson Turing
Turing
Alan Mathison Turing
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Mathematical
Ontology
Certainty
Facilities
Combination
Ingenuity
Logic
Facility
Exercise
Regarded
Call
Reasoning
Rather
Uncertainty
Two
Intuition

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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
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The original question, 'Can machines think?' I believe to be too meaningless to deserve discussion.
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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.
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We may hope that machines will eventually compete with men in all purely intellectual fields.
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Mathematical reasoning may be regarded.
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We are not interested in the fact that the brain has the consistency of cold porridge.
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Sometimes it is the people no one imagines anything of who do the things that no one can imagine.
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When we want to sink a convoy, we send out an observation plane first... Of course, to observe is not its real duty, we already know exactly where the convoy is. Its real duty is to be observed...Then, when we come round and sink them, the Germans will not find it suspicious.
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It 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.
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The Exclusion Principle is laid down purely for the benefit of the electrons themselves, who might be corrupted (and become dragons or demons) if allowed to associate too freely.
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In attempting to construct such (artificially intelligent) machines we should not be irreverently usurping His (God's) power of creating souls, any more than we are in the procreation of children,” Turing had advised. “Rather we are, in either case, instruments of His will providing mansions for the souls that He creates.
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