102 A History ofMathematics
in Western Europe has gone through a variety of transformations. In the early Middle Ages, from
the eleventh to thirteenth centuries, it was highly regarded, for the good reason that the level of
achievement was visibly more sophisticated. Those works which were found most comprehensible
or useful were translated from Arabic into Latin as were the contemporaneous translations of
the Greek classics into Arabic. By the Renaissance (say by 1550) for complex reasons, there had
been a change of view, even though the West had not overall achieved the Islamic world’s level of
achievement, much less overtaken it.^1 The practice of translation from Arabic was less frequent,
while the publication of original Greek texts and their translation, again into Latin, made possible
a claim that the Moderns were the direct inheritors of the Ancients. Even though, as far as algebra
and the number system were concerned, this was clearly untrue, it was a useful myth in constituting
a Renaissance world-view which built on the classics as a source of legitimacy.
We shall see later how much the work of Viète, Stevin, Descartes, and their contemporaries owed
to Islamic precursors; what is important for the moment is that it was not normal to acknowledge
the debt. It is not excessively oversimplifying to say that the broad outlines of the Eurocentric history,
which Joseph criticizes were laid down in the sixteenth century, and were the dominant version of
history until relatively recently. And yet a number of important, often striking Islamic works have
been published and studied in western Europe over the last 200 years. Their understanding, and
their incorporation into a general history remained the preserve of specialists with no impact on
the mainstream view. A better understanding of what Islamic mathematics was has had to wait for:- a political motivation—the demand for recognition from the Islamic world from the
1950s on^2 ; - unified research programmes, partly related to that politics, which rapidly deepened and
expanded the work of study and translation in the 1950s and 1960s.
We shall have more to say about what material is and is not available in Section 2. The important
change has been not so much an increasing accessibility of sources as an increasing consciousness
of the achievements of the Islamic mathematicians. Twenty years ago,^3 Roshdi Rashed, one of the
leading historical researchers, made much the same points as Joseph:
The same representation is encountered time and again: classical science, both in its modernity and historicity, appears
in the final count as the work of European humanity alone; furthermore, it is essentially the means by which this
branch of humanity is defined. In fact, only the scientific achievements of European humanity are the objects of
history. (Rashed 1994, p. 333)New texts, new research, and persuasive arguments by respected scholars have largely allowed
Islamic mathematics to take its legitimate place in the histories; and among scholars with any
serious academic credentials one will no longer find it neglected or downgraded. The main problems
in building up a proper picture are constituted first by the great gaps in our knowledge—which
are, of course, also there for the cultures of Greece and China—and second by the sheer diversity
of activity (arithmetic, algebra, classical geometry, astronomy, trigonometry, and much else) over- This case is argued by Rashed (1994, appendix 2). The general point is incontestable, although there is disagreement about the
detail. - Said’s influential book (1978), although quite unrelated to the sciences, played a key part in making academics more self-
conscious about how they treated things ‘Oriental’. - Rashed’s book dates from 1984, although its English translation is 10 years later.