A History of Mathematics From Mesopotamia to Modernity

Islam,Neglect andDiscovery 125

of Mecca where the faithful should turn for prayer. As he says:

[L]et us point out the great need for ascertaining the direction of theqiblain order to hold the prayer which is the

pillar of Islam and also its pole. God, be He exalted, says: ‘So from wheresoever thou startest forth, turn thy face in

the direction of the Sacred Mosque, and wheresoever ye are, turn your face thither.’ (Qur’an, Sura 2:150). (Al-B ̄ir ̄un ̄i

1967, pp. 11–12)

The mathematicians may well have thought their knowledge essential; but mathematicians are not
always as important as they think, and George Sarton pointed out in 1933 that many medieval
mosques in North Africa and Spain have ‘incorrect’ alignments, despite the flourishing state of
mathematics in those countries.
This problem has recently been cleared up, it appears, in a detailed study of legal writings and of
the mosques themselves by Mónica Rius.^12 The answer is interesting for the light it throws on the
status of mathematics: in fact, Islamic lawyers pointed out that the complex mathematical methods
were (a) sometimes uncertain—particularly in the case of longitude—and (b) not accessible to the
mass of the faithful, as they should be. They therefore allowed recourse to simpler definitions,
which of course gave more ‘approximate’ directions for prayer. This is not to say that al-B ̄ir ̄un ̄i and
others were irrelevant; there must have been cases of mosques where the qiblawas determined
by mathematics. However, here, as elsewhere, its use could be contested and the idea that it was
‘imposed by religion’ certainly begins to seem simplistic.
This example can serve as a cautionary tale on the limits of the usefulness of mathematics, which
was certainly important enough in the world of medieval Islam. As we shall see, Marxists tend to
claim that mathematics is driven by the demands of society, and mathematicians, when it suits
them, claim that they are doing vital and useful work. However, if much of the organization of Islam
was favourable to science, there were certainly times and places when science could be dispensed
with, even treated with hostility.^13 To make a parallel, Descartes, Pascal, and Galileo were no less
good Christians than their predecessors. If they found that their religion could be harmonized with
a rational and practical scientific outlook, the cause is perhaps to be found in the ideological climate,
or what Marxists would call the relations of production. Accordingly, a particular difficulty in the
statement with which this section opens is that Rashed seems to be treating Islam, as religion and
philosophical outlook, as homogeneous in its positive effect on the sciences (at least during the
medieval period). It will be interesting to see how other specialist historians react.

Exercise 9.What would be necessary to know in order to determine the qibla? Given the necessary

information, how would you do it?

Appendix A. From al-Khw ̄arizm ̄i’s algebra

(From Fauvel and Gray 6.B.1)

A root is any quantity which is to be multiplied by itself, consisting of units, or numbers

ascending, or fractions descending.

A square is the whole amount of the root multiplied by itself.

12. La Alquibla en al-Andalus y al-Magrib al-Aqs.à, reviewed inIsis94 (2003, p. 371).


13. Again, Rashed produces good exmples to show that an anti-science outlook cannot be equated with religious ‘orthodoxy’, but
    there were trends within orthodoxy which were opposed to science.