5. Islam, neglect and discovery
1. Introduction
It should be clear from the present chapter that the traditional view of the Arabs as mere custodians of Greek learning
and transmitters of knowledge is a partial and distorted one. (Joseph 1992, p. 344)
A number of medieval thinkers and scientists living under Islamic rule, by no means all of them ‘Moslems’ either
nominally or substantially, played a useful role of transmitting Greek, Hindu, and other pre-Islamic fruits of knowledge
to Westerners. They contributed to making Aristotle known in Christian Europe. But in doing this, they were but
transmitting what they themselves had received from non-Moslem sources. (Trifkovic 2002)
The history of Islamic mathematics is clearly a contested area, and recent history has if anything
sharpened the divisions. The view which Joseph described as ‘partial and distorted’ 13 years ago
lives on in some academic circles, as the quote from an admittedly right-wing anti-Islamic columnist
illustrates. It is perhaps natural that in the current context even questions about algebra in Baghdad
in the ninth century should be charged with political relevance, and voices on the fringe should
perpetuate old myths. As far as the mainstream of historians is concerned, the points made by
Joseph are almost universally conceded, as Katz’ recent respected textbook makes clear:
Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, system-
atized the study of algebra and began to consider the relationship between algebra and geometry, brought the rules
of combinatorics from India and reworked them into an abstract system, studied and made advances on the major
Greek geometrical treatises of Euclid, Archimedes and Apollonius, and made significant improvements in plane and
spherical trigonometry. (Katz 1998, p. 240)
The only quibble which could be made against this generous assessment is that Katz does not
mention the difficulties which previous scholars have had in getting such reasonable claims accep-
ted. The major obstacle has been the viewpoint, referred to by Joseph, which sees the Arabs as
transmitters rather than innovators. Why is this? We saw in the last chapter that Chinese math-
ematics, obviously outside the Western tradition, could be relegated to the sidelines as a mere
collection of isolated problems without coherence and without any idea of proof. With the math-
ematics which was developed in the Islamic world from the ninth to the fifteenth centuryce, the
problem is the opposite. The work could with some justice be seen as a part of ‘Western’ math-
ematics, looking back to the Greeks and forward to the European Renaissance, and the existence of
influences is not in dispute. However, because it was a specialist field of study and the original texts
were often inaccessible, it was possible to ‘forget’ the ways in which the Islamic writers transformed
mathematics and to claim (as Trifkovic does) that they did nothing but pass it on.
To undertake a proper discussion of the history as it is now understood, it is useful to look briefly at
the West, the Islamic world, and their changing interactions. (Historians have a problem about the
choice between ‘Arabic mathematics’ and ‘Islamic mathematics’. Neither is completely accurate for
the mathematics practiced in the Islamic world between, say, 800 and 1500ceSince a choice must
be made, we shall opt for the more inclusive ‘Islamic’.) The understanding of Islamic mathematics