104 A History ofMathematics
(Khayyam 1931). This, however, is long out of print and far from easy to find. Again, there are
good extracts in Fauvel and Gray.- A more recent find is the startlingly innovative algebra textal-B ̄ahir fi-l jabr(‘The Shining
Treatise on Algebra’) of al-Samaw’al (twelfth century). This has been extensively discussed,
and good summaries of what is said in some key passages concerned with sums of series and
with polynomials are to be found both in Rashed (1994) and in Berggren (1986). However,
while there is a modern Arabic text dating from 1976 with introduction and some foot-
notes in French by Rashed, there is no translation, indeed there are no translated extracts.
And the edition itself, published in Damascus, is not likely to be stocked outside specialist
libraries. - Lastly, one of the most famous works, often referred to for its sophisticated calculations—
in particular the use of decimal fractions—is al-K ̄ash ̄i’sMift ̄ah.al-h.is ̄ab(‘The Calculator’s Key’),
written in Samarkand in the fifteenth century. This has been known and studied for over a century.
Besides several editions in Farsi (the work was popular in Iran), and a translation into Russian
by B. A. Rosenfeld in 1956, there is a modern Arabic edition, published in Cairo in 1967, and
again long out of print. I know of no English translation, or even of any plans for one; although
again one can learn something of the work’s unusual features from descriptions in Berggren (and
Youschkevitch).
There is now some serious translation underway; and since the field is very large, it is bound to
be selective. One could single out A. S. Saidan’s version of the (recently discovered) arithmetic of
al-Uql ̄idis ̄i, a fascinating work to which we shall return; and numerous translations into French by
Rashed, notably the works of Shar ̄af al-D ̄in al-T.us ̄ ̄i (1986), and of ibn al-Haytham (a large project,
ongoing). These translators (and others), being active researchers, will necessarily be selecting
those authors of most interest to them, so that the act of editing and translating is often part of the
construction of a personal ‘canon’ of what the translator considers major works. However, in the
impoverished situation already described, any such work is invaluable.
It could be argued that a serious research engagement with Islamic science should include
the acquisition of the ability to read Arabic (which some readers may have anyway). This seems
misconceived, insofar as the works concerned are considered as major historical texts. The time is
past when the student was expected to be able to have the leisure to learn languages as part of a
general liberal education, and while the specialist might need to read Euclid in Greek or thePrincipia
in Latin, no one would expect it of the student on a history course. In any case, as already stated,
modern Arabic editions are not easily available, and the deciphering of the difficult manuscripts
which are still our primary sources (Fig. 1) is an advanced research skill comparable to reading
Sumerian. If the major works of Islamic mathematicians deserve study on an equal footing with the
classics of other times, then they should be equally accessible. Those who research the Greek classics
are in a fortunate position, in that critical editions and translations have been made available by
scholars who (a century ago) considered it an essential part of their work. A commitment to fair
treatment for the Islamic classics is now driving a similar effort as far as they are concerned. In
a spirit of optimism, one could hope for a significant part of this vast literature, together with a
variety of analytical histories, to be readable by students in 20 years time. (And perhaps a start
should be made with al-K ̄ash ̄i, see item 4.)
A good recent bibliography of sources and articles (which omits Russian works, but is other-
wise comprehensive) is by Richard Hogendijk at http://www.math.uu.nl/people/hogend/Islamath.html.