Mathematics in the Islamic World and Its Involvement in Geometric Ornament

May 2022 by David Wade

In recent times, there has been a welcome degree of recognition of the enormous contribution made by early Islamic scientists and mathematicians to world knowledge; this is long overdue. In particular, the role of Islamic learning in the recovery and development of Classical texts, and the subsequent transmission of this huge body of scholarship to Medieval Europe, is now widely acknowledged. It is no longer believed that there was an unbroken chain of learning in Europe from the Classical period to the early-Modern – and it is now properly seen that the great rekindling of interest in all the sciences that occurred during the Renaissance was largely fueled by Islamic erudition (Montgomery Watt, 1972; Saliba, 2011).

We have already referred to the “Golden Age” of Islamic science that flourished in the early Abbasid period (in Baghdad between the eighth and tenth centuries CE), which produced such outstanding scholars as al-Khwarizmi, al-Kindi, and Omar Khayyam. But Islamic science, building on the foundations of Classical, Parthian, and Indian knowledge, was to continue making important advances in various centers around the vast Islamic dominions for some centuries to come. Wherever the social, intellectual, and economic conditions were conducive, advances were made – particularly in such fields as mathematics, astronomy, optics, and medicine. Nevertheless, Science, whose pagan philosophical associations were never entirely forgotten, continued to be regarded with some suspicion by the orthodox. Scientifically minded thinkers under royal patronage were usually afforded a measure of protection from the more zealous religious critics – who were in any case less concerned with such abstract fields of study as mathematics. It can be said then that, at least in higher intellectual levels, the study of mathematics (particularly of geometry) was well established and widely taught, throughout the medieval Islamic world and that the Alexandrian Platonists, Euclid and Ptolemy, retained their positions as the revered progenitors of geometry and astronomy, respectively.

However, as indicated earlier, there is little evidence of interaction between “theoretical” mathematicians and artisan geometricists in this Islamic society – although there are a small number of surviving texts indicating that this did occasionally occur. The authors Gülru Necipoglu (1995) and Alpay Özdural (2000) single out a couple of examples – one originating in the tenth century involving the mathematician and astrologer Abu al-Wafa al-Buzjani, and a later, anonymous Persian text from the fourteenth century CE on “Interlocking Figures.”

Al-Wafa al-Buzjani (940–998 CE) was the author of a manual of practical geometry On the Geometric Constructions Necessary for the Artisan (Risâla fimâ yahtâju al-sâni’u min a’mâl al-handasa), of which four known hand-written versions survive – one in Arabic and three in Persian. The original work was written in Baghdad, in Arabic, but no longer exists, and each of the later copies has some missing information and chapters. The surviving Arabic version (which is kept in the Library of Aya Sofya, Istanbul), although not original, is more complete than the others. The best known of the three Persian manuscripts is kept in the National Library in Paris, France. Although clearly directed at artist/craftsmen, the general tone of this work is of a somewhat petulant criticism of their reluctance to adopt “proper” (i.e., Euclidean) methods of geometrical construction.

The On interlocking similar or congruent figures (Fî tadâkhul al-ashkâl al-mutashâbiha aw al-mutawâfiqa) is a geometric manual by an unknown author, probably originating in Tabriz during the Ilkhanid period. There seems to be as much interest here in the “puzzle” aspect of the figures involved as in their use in decorative ornament, indicating that it may not have been directed exclusively at artist/craftsmen.

There are a few other, even less specific, allusions to the involvement of mathematicians with decorative ornamental schemes. The polymath/inventor Al-Jazari drew and described an elaborate plan for a door in his book on Ingenious Mechanical Devices (although the author George Saliba has pointed out that the translation on which this is based may be faulty). And there is a tantalizing reference by Omar Khayyam (no less!) to Meetings of Artisans and Geometers – but this allusion too is vague and open to misinterpretation. In summary, it is difficult on the basis of this and other available evidence to make any substantial claims whatsoever for the notion of sustained academic involvement in the genre of Islamic geometric ornamentation in any period.