A History of Mathematics From Mesopotamia to Modernity

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has its serious historians. Where are the comparable works on the development of chaos theory,
category theory, and financial mathematics? Naturally there is a problem: many of the actors
are still alive, and the writer must usually be cautious about describing them. As in the previ-
ous chapter, the best sources are often biographies of mathematicians who are either dead (Alan
Turing, Hodges 1985, John von Neumann, Macrae 1992) or cooperative (John Nash, Nasar
1998, Smale, Batterson 2000). The best of these add valuable information on the wider scene—
Hodges on Cambridge, Nasar on Princeton, at key periods. Mathematicians are also given, in
their retirement, to producing autobiographies and reminiscences, of variable value. And indi-
vidual spectacular developments are covered in more or less journalistic accounts which attempt
to popularize and promote a view of what the writer finds exciting: Gleick (1987) on chaos,
Singh (1997) on Fermat’s Last Theorem, even perhaps Hofstadter’s over-the-top mathematical
rhapsody (1979).
Corry (2004) on abstraction and Dieudonné (1989) and James (1999) on topology, mentioned
in the last chapter, continue to be useful; and we shall draw on Segal’s interesting specialist account
(2003) of mathematics under the Third Reich. However, the full history of the period is still to
be told.
The previous chapter’s remarks about difficulty apply again, of course; even if one can follow
the popularizers of chaos theory with their coffee-table pictures, what can one do about Wiener
measure, étale cohomology, or topological quantum field theory? Faced with the mathematical
world of today, the popular consumer is naturally tempted to give up on the content and settle
for an experience of awestruck wonder: who are the people who carry on this strange, remote,
abstracted activity, and why do they do it? Accounts of how they operate always seem to miss
something.

Professor Mazur sipped his cappuccino and listened to Ribet’s idea. Then he stopped and stared at Ken in disbelief.

‘But don’t you see? You’ve already done it! All you have to do is add some gamma-zero of (M) structure and just run

through your argument and it works’. (Singh 1997, p. 221)

Is it, then, just a question of getting access to Barry Mazur’s brand of cappuccino? In Singh’s portrait

of Wiles, we have the mathematician as secretive solitary obsessive—set against the background

of a research community which has the opposite values, exchanging ideas over coffee. In Sylvia

Nasar’s book on Nash, and still more in the ‘spectacularly dumb’ (Taylor 2001) Russell Crowe

film version of it, we have the mathematician as paranoid–schizoid, a genius haunted by demons.

Most recently, if perhaps least seriously, Mark Haddon (2003) contributes a new element by

presenting the mathematical genius as a sufferer from Asperger’s Syndrome, physically unable to

construct human relationships, numbering his chapters by primes. The ‘mathematician-problem’

has become another object for consumption, a way of selling books, TV programmes, films, etc.

In the old (1960s) situationist language of Guy Debord, the activity of mathematicians, especially

at its most arcane and difficult level, has become part of the ‘Spectacle’, and so removed from

historical thought.

With the destruction of history, contemporary events themselves retreat into a remote and fabulous realm of

unverifiable stories, uncheckable statistics, unlikely explanations and untenable reasoning. (Debord 1990)

It will be an uphill struggle for this chapter to do any better, but it is our aim to try.