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Newman’s lecture course at Cambridge
Turing’s own career provides a good example of the cleft between logic and mathematics.
When he submitted his paper ‘On computable numbers’ to the London Mathematical Society
in 1936 the journal could not referee it properly because Max Newman was the only other
expert in Britain and he had been involved in its preparation (Fig. 40.1).^11 Nevertheless, they
seem to have accepted it on Newman’s word.^12 But this detail prompts historical questions that
have not so far been explored. Why was this logical subject matter so little known in Britain?
Why was Newman, a mathematician, a specialist in it? Answers to these questions are sug-
gested below.^13
A crucial event, Newman’s lectures to Turing, occurred in the mid-1930s, when he taught a
new final-year course on ‘Foundations of mathematics’ for the Mathematical Tripos. The tripos
examination questions he set show that he had handled all the topics in logic and metamath-
ematics mentioned in the opening section of this chapter, and also the intuitionist mathematics
and logic of L. E. J. Brouwer. Turing, newly graduated from the tripos, sat in on the course in
1935 and learnt about decision problems and Gödel numbering from one of the few Britons
who was familiar with them.^14 There seems to be no documentation about contact between
Turing and Newman following the lecture course, but presumably the two met on a regular
basis during 1935 and 1936 as Turing prepared his paper on computability.
A sense of isolation hangs over Newman’s lecture course. Launched in the academic year
1933–34, Newman ran the course for only two more years before it was closed down, possibly
because of disaffection among dons as well as students. In 1937 Hardy opined to Newman:^15
figure 40.1 Max Newman.
Reproduced with permission of the Master and Fellows
of St John’s College, Cambridge.