A History of Mathematics From Mesopotamia to Modernity

Islam,Neglect andDiscovery 103

what is once again a dauntingly long historical period. It should be easy for the student to approach

Islamic mathematics, like Greek, without prejudice and make a fair evaluation. Assuming this

possible, one could, if only to fix ideas, pose some questions:

1. Can one give a unified description of ‘Islamic mathematics’, given the length of time and space
   and the variety of fields covered —indeed, should we even try to do so?


2. How would we evaluate the ‘Islamic contribution’ to the development of mathemat-
   ical thought?

2. On access to the literature

One would naturally like to recommend, as a follow-up to the general agreement on the import-

ance of Islamic mathematics, that the student could consult texts and histories and examine—

for example—the questions raised above. Unfortunately, this is not yet the case; and here an accus-

ation of ‘neglect’ can still be made, in that access to the relevant materials remains extremely

difficult. If we start with secondary texts, that of Berggren (1986) is full, readable, and well-

informed. It is, in our current situation, where any reader should start. Rashed’s work (1994) is

more specialist, aimed at the exposition of particular points in arithmetic and algebra; it is also

expensive and less often stocked by libraries. And while Youschkevitch’s rather older text (1976) is

fuller than either of these and contains much which they exclude, it is (a) in French and (b) long

out of print. The situation for the student entering the field could be worse, but it is not very good.

With regard to primary sources, what is available reflects a long and patchy history of transla-

tion by individual enthusiasts. The relevant section in Fauvel and Gray, though it contains some

essential texts, is relatively brief; and while the works of Euclid, Archimedes, and other major Greek

mathematicians can often be found in libraries and are reprinted, this is far from being true of

the classics of the Islamic world. One initial problem is that there is no longer a canon of a few

great writers, rather a large collection of texts whose differing contributions are still in process

of assessment.^4 More translation is now in progress, but there are major gaps. To take just a

few examples:

1. The earliest, founding book on algebra which underlies all subsequent work is (Muh.ammad
   ibn M ̄usa) al-Khw ̄arizm ̄i’s H.isab al-jabr wa al-muq ̄abala(‘Algebra’, lit. ‘calculating by restoring
   and comparing’, date about 825). This exists in a translation by F. Rosen, dated 1831 (The
   Algebra of Muhammed ben Musa, London, Oriental Translations Fund). It has been reprinted
   by Olms (1986), and is therefore in a better situation than most (useful extracts are in Fauvel
   and Gray).


2. Much later, but equally important, is the algebra of Omar Khayyam (‘Umar al-Khayy ̄ ̄ am ̄i),
   dating from about 1070. This has been known about for a long time; while it was first translated
   in the nineteenth century by Woepcke (into French), there is a more ‘modern’ English translation


3. By an irony in the history of research schools, a large number of very interesting texts were translated into Russian by
   Youschkevitch and his group in the 1950s and 1960s. Even for the readers, whoever they may be, for whom Russian is an easier
   option than Arabic, they are not accessible in most libraries.