AChaoticEnd? 239
There is no independent realm of mathematics, independent of intuition and life: the struggle over the foundations [of
mathematics] that now rages is in reality a racial conflict: ‘Political rootedness gives thinking its style!’
Since German mathematics is rooted in blood and soil, the state ought to and must support and cultivate it...
(‘New Mathematics’, by ‘P.S.’, cited in Segal 2003, p. 267)
It would appear that the Nazi command—who had a high regard for rationalism when it came
to organizing train time-tables—were too ideologically confused to make adequate use of the
mathematicians whom they had left, except in special favoured fields like aeronautics^1 and, with
a brief but deadly effect, rocketry. Reduced though they were, they could have participated more
fully in the war effort, ranging as they did from dissidents to patriotic conservatives to committed
Nazis; an effort was made to enlist their skills in the later part of the war, but by then it was
too late.^2
Germany’s loss was to a quite outstanding extent America’s gain, most particularly Princeton’s.
Overcoming fears, which were strong at Harvard, that they would end up with an excess of Jews,
Princeton used money from Rockefeller to build up a research department. Even more fortunately,
a gift from a New Jersey department store owning family, the Bambergers, endowed the Institute
for Advanced Study to which Einstein went.
Kurt Gödel, the Viennese wunderkind of logic, came in 1933, and Hermann Weyl, the reigning star of German
mathematics, followed Einstein a year later...Practically overnight, Princeton had become the new Göttingen.
(Nasar 1998, p. 54)
For once, the high-flown language reflects the reality. By 1936, solid Cambridge men like
G. H. Hardy and the young Alan Turing saw Princeton as a useful place to spend a year. [It has more
or less retained its dominant position ever since, in the face of stiff competition from a dozen equally
deserving American universities.] And, at Princeton and elsewhere in the United States (and indeed
Britain), refugees from Hitler were willing to take part in the war effort; and (in contrast to the Nazis)
the governments learned how to use them.
The most high-profile part of the story, the atom bomb project, is really a part of the history
of physics rather than of mathematics (see later for the difference); but mathematicians were
widely employed on it; often mentioned is von Neumann’s ‘conclusion that large bombs are better
detonated at a considerable altitude than on the ground’ (Macrae 1992, p. 209). Besides this
limited and spectacular application, many of the most distinguished of them were involved in what
could be seen as more routine work; planning resources, codebreaking, and ballistics. All of these,
which might seem a distraction from ‘real’ theorem-proving mathematics, led to the development
of new fields which were later promoted as the answer to the problems of peace (i.e. government
and business) as well as war. Norbert Wiener, in the United States, contributed the field which he
was to name ‘cybernetics’, the science of control, while his counterparts in Britain (Blackett and
others) devised the equally ambitious science of operational research. Again, Allied commanders
showed much less resistance to the use of such abstractions than did the Nazis.
There had to be some pattern that the methodical Germans were using to plant their mines along the convoy routes to
Britain. Johnny [von Neumann] was asked to work out mathematically what these patterns might be, and how best to
counter them. (Macrae 1992, p. 207)
- Here the practical Göring had some influence.
- The best-known example, the brilliant Nazi mathematician Teichmüller, was conscripted and died on the Russian front in 1943.
It seems unlikely that this would have happened in Britain or the United States.