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A perfect maths program would solve any problem This is impossible |
A perfect maths program would be able to solve any problem that it was given. This is not just science fiction, it is impossible. It is not difficult to prove that the size of all mathematical knowledge is uncountably infinite. It is therefore not possible for a computer program to know all of mathematics. Furthermore, a machine can always be given a problem that it knows nothing about. Some of these problems could take arbitrarily long to solve. |
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