  A certain mathematician M, considering some hypothesis H, conclusion C and
text P, can arrive at one of the following judgments: (1) P does not convince M
of the fact that since H, it follows that C; (2) P is the proof that since H,
it follows that C (judgment of the type "Proved"). Is it possible to replace
such a mathematician with an arbitrary Turing machine? The paper provides a
proof that the answer to the question is negative under the two following
conditions: (1) M is faultless, namely his judgment "Proved" always implies
that since H, it actually follows that C; (2) M recognizes a certain P' as the
correct proof of the fact that for certain H' and C', if H', then C' (where P',
H', and C' are stated in the paper).
