440 | 40 TURING’S mENTOR, mAX NEwmAN
though ‘Foundations’ is now a highly respectable subject, and everybody ought to know some-
thing about it, it is (like dancing or ‘groups’) slightly dangerous for a bright young mathematician!
Somehow Newman continued to set examination questions on foundations for five of the
six years that he remained at Cambridge before moving to Bletchley Park.^16 The questions for
1939 may have been set by Turing, who was invited—presumably in a spirit of resistance against
Hardy’s coolness—to give a lecture course on foundations in the Lent Term of 1939. He was
asked to repeat it in 1940, but by then he was at Bletchley Park.^17 Newman arrived there in the
summer of 1942, to join the fight against Tunny. During his wartime period he published three
technical papers in logic, one written jointly with Turing. Two, including the one written with
Turing, were on aspects of type theory, which was Russell’s solution of the paradoxes of logic
and set theory,^18 and one on the so-called ‘confluence’ problem (concerning the reduction of
terms).^19
Newman’s entry into logic
How did Newman become so involved with logic in the first place? Born Max Neumann in
London in 1897, to a German father and an English mother, he gained a scholarship in 1915 to
St John’s College, Cambridge, taking Part I of the Mathematical Tripos in the following year.^20 ,^21
During the First World War, Max’s father Herman was interned by the British; when released
he went back to Germany, never to return. In 1916, Max and his mother Sarah changed their
surname to ‘Newman’. A pacifist, Max served in the Army Pay Corps, returning to his college in
- He completed Part II of the tripos with distinction in 1921.
Against the odds, Newman spent much of the academic year 1922–23 at Vienna University.
He went with two other members of his college. One was the geneticist and psychiatrist Lionel
Penrose (father of the distinguished mathematician Roger Penrose), who seems to have
initiated the trip to Vienna; his family was wealthy enough to sustain it, especially as at that
inflationary time British money went a long way in Vienna. Penrose had been interested in
Russell’s mathematical logic as a schoolboy, and had studied traditional Aristotelian logic as an
undergraduate at Cambridge. He had also explored modern mathematical logic and it might
even have been Penrose who alerted his friend Newman to the subject. Penrose wanted to
meet Sigmund Freud, Karl Bühler, and other psychologists in Vienna. The third member of the
Cambridge party was Rolf Gardiner, an enthusiast for the Nazis, later active in organic farming
and folk dancing, and father of the conductor Sir John Eliot Gardiner. Gardiner’s younger sister
Margaret came along too. She would become an artist and companion to the biologist Desmond
Bernal. Margaret recalled ‘the still deeply impoverished town’ of Vienna, where Penrose and
Newman would walk side-by-side down the street playing a chess game in their heads.^22
Of Newman’s contacts with the Vienna mathematicians all that tangibly remains is a wel-
coming letter of July 1922 from Wilhelm Wirtinger.^23 ,24 Yet it seems clear that Newman’s expe-
rience of Viennese mathematics was decisive in changing the direction of his researches. His
principal mathematical interest was to become topology, which was not a speciality of British
mathematics. Some of Wirtinger’s own work in Vienna related to the topology of surfaces, and
in 1922 the University of Vienna recruited Kurt Reidemeister, who, like Newman himself, went
on to become a specialist in combinatorial topology. Most notably, Hans Hahn, later a leading