CHAPTER 40

Turing’s mentor,

Max Newman

ivor grattan-guinness

T

he interaction between mathematicians and mathematical logicians has always been

much slighter than one might imagine. This chapter examines the case of Turing’s

mentor, Maxwell Hermann Alexander Newman (1897–1984). The young Turing

attended a course of lectures on logical matters that Newman gave at Cambridge University

in 1935. After briefly discussing examples of the very limited contact between mathemati-

cians and logicians in the period 1850–1930, I describe the rather surprising origins and

development of Newman’s own interest in logic.

The cleft between logic and mathematics

One might expect that the importance to many mathematicians of means of proving theorems,

and their desire in many contexts to improve the level of rigour of proofs, would motivate them

to examine and refine the logic that they were using. However, inattention to logic has long

been common among mathematicians.

A very important source of the cleft between mathematics and logic during the 19th century

was the founding, from the late 1810s onwards, of the ‘mathematical analysis’ of real variables,

grounded on a theory of limits, by the French mathematician Augustin-Louis Cauchy. He

and his followers extolled rigour—most especially, careful definitions of major concepts and

detailed proofs of theorems. From the 1850s onwards, this project was enriched by the German

mathematician Karl Weierstrass and his many followers, who introduced (for example) multi-

ple limit theory, definitions of irrational numbers, and an increasing use of symbols, and then

from the early 1870s by Georg Cantor with his set theory. However, absent from all these devel-

opments was explicit attention to any kind of logic.

This silence continued among the many set theorists who participated in the inaugura-

tion of measure theory, functional analysis, and integral equations.^1 The mathematicians