Conclusion 261
Is the development of algorithms (the word comes by a circuitous route from the name
al-Khw ̄arizm ̄i, chapter 5) to trace targets in underground bunkers^1 an indicator of how
mathematics, and you, readers, as mathematicians, relate to today’s ‘struggle’?
This book is long enough already; and to raise serious questions about mathematics’ present is
really a question for another book. Still, in the fashionable language of course objectives, it could be
useful to consider what you have learned. It’s not usual today to see history as a source of ‘lessons’,
and mathematicians rarely think that by understanding the past they might avoid repeating its
mistakes. Still less do they appeal to the court of history, or, like politicians, claim that it will
absolve them. We have seen mathematicians — Archimedes, Qin Jiushao, Galileo, Alan Turing —
getting involved in ‘history’, making political choices which may have had little to do with their
mathematical tastes. Do we judge them? We ourselves, having acquired their necessary skills, will
inevitably go out into the world and (like anyone else) become immersed in history, if of a different
sort. It may indeed be that we seek to be among the recipients of a large grant from the US Army.
Mathematics is traditionally seen as a peculiar kind of human activity. Hard, pure, exact
and faultless it is divorced from the day-to-day concerns of ordinary people, and has little or
nothing to say about their real-life problems. And yet it is a cliché by now that various applica-
tions of mathematics from computing to coding to accountancy pervade the world today. They
are not pure, they are not always even reliable^2. The student attracted by the traditional
image of mathematics might wish rather to be studying one of the seven ‘Millennium Problems’
(www.claymath.org/millennium/). Although not all to be classed as pure research — they include
problems in hydrodynamics and quantum field theory — they are all goals for the academically
ambitious, lead to a prize of $1,000,000 each and could allow a mathematician to escape the job
market and enjoy a life of leisure. A simple sum shows that few of this book’s readers can hope to
attain this goal.
For most of the world, a shrinking market and increased globalization constrain choices, though
they may provide unexpected windfalls. The advice to train as a software developer, which
the American Mathematical Society was tendering to graduates ten years ago, rings hollow as
illustrated with human detail inBusinessWeekin March 2004:
As Stephen and Deepa emerge this summer from graduate school – one in Pittsburgh, the other in Bombay – they’ll find
that their decisions of a half-decade ago placed their dreams on a collision course. The Internet links that were being
pieced together at the turn of the century now provide broadband connections between multinational companies
and brainy programmers the world over. For Deepa and tens of thousands of other Indian students, the globalization
of technology offers the promise of power and riches in a blossoming local tech industry. But for Stephen and his
classmates in the U.S., the sudden need to compete with workers across the world ushers in an era of uncertainty. Will
good jobs be waiting for them when they graduate? ‘I might have been better served getting an MBA,’ Stephen says.
Worse, Deepa is likely in turn to find herself losing her job as the software companies find yet
cheaper sources. Not only is mathematics, as we suggested above, less different from other human
activities than its idealized, originally Greek model might lead us to suppose. Mathematicians
as a caste are less sharply marked off by their unique abilities from others. The corporations
which employ them may ask in addition for a range of skills from Powerpoint presentations to a
- Having cited this as an application of mathematics to military uses, and so automatically undesirable, we should in fairness
note that the UN in October 2004 recommended its application as preferable to the Israeli Army’s wholesale demolition of houses in
Gaza where there might (in their opinion) be a bunker. - The failure of a US Patriot missile in 1991 leading to the loss of 28 lives, which was due to accumulated ‘rounding errors’ is
often cited.