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Questions of cultural superiority can muddle mathematical thinking

** Review of ***A History of Mathematics*

by Luke Hodgkin,

Times Higher Education Supplement, 29 September, 2006
Courses in the history of mathematics are a welcome addition to the
undergraduate maths curriculum. Part of their popularity lies in the
fact that students ``may find that a little history will serve them as
light relief from the rigours of algebra''. This attitude is
misconceived. The history of any theoretical subject is the story
of the emergence and development of ideas, and an understanding of these
ideas is crucial if the student is to appreciate their history.

In the first half of Luke Hodgkin's book, the focus is on mathematical
cultures. There are two chapters on Greek maths and one each relating to
Babylonian, Chinese and Islamic cultures. In the second half, attention
shifts to shorter historical periods or specific concepts: the scientific
revolution, calculus and non-Euclidean geometries. Each chapter starts
with an immensely useful discussion of the primary and secondary
literature.

The introduction is a lengthy apology for adding another book to a
crowded market. Although Hodgkin asserts that he ``does not set out to
argue a case'', he rightly has no time for those who adhere to an outdated
Eurocentrism. But I do not find the evidence he presents convincing.
One of his guides for the non-European roots of mathematics is
George Joseph's *The Crest of the Peacock*, reviews of which
have not inspired my confidence in its scholarly quality. But Hodgkin
dismisses such criticism as ``the fashionable nonsense school of
reviewing''. This allusion to a book by Alan Sokal and Jean Bricmont
suggests that Hodgkin thinks their well-argued critique of postmodern
and feminist abuse of science is initimately connected with ``current
anti-Islamic trends in the West''.

Hodgkin makes a convincing case for the importance of Islamic mathematics.
But the emphasis ought to be on tracing the mathematical thinking, not
on questions of cultural superiority.

Later chapters focus even more on priority disputes instead of
mathematical content. Concerning calculus, students would benefit from
learning how mathematical rigour and, say, the notion of limit
evolved. By contrast, the question, ``Did the Indians have a version
of Calculus in the Middle Ages?'' is - in the words of Gian-Carlo Rota -
one of palaeontology, not history.

H. Geiges