  In Turing's presentation, intuition is in practice present in every part of a mathematician's thought, but when mathematical proof is formalised, intuition has an explicit manifestation in those steps where the mathematician sees the truth of a formally unprovable statement. Turing did not offer any suggestion as to what he considered the brain was physically doing in a moment of such ‘intuition’; indeed the word ‘brain’ did not appear in his writing in this era. This question is of interest because of the views of Penrose (1989, 1990, 1994, 1996) on just this issue: Penrose holds that the ability of the mind to see formally unprovable truths shows that there must be uncomputable physical operations in the brain. It should be noted that there is widespread disagreement about whether the human mind is really seeing the truth of a Gödel sentence; see for instance the discussion in (Penrose 1990) and the reviews following it. However Turing's writing at this period accepted without criticism the concept of intuitive recognition of the truth.