Abul Wefa

Persian mathematician and astronomer

• Born: June 10, 0940
• Birthplace: Buzjan, Khorāsān (now in Iran)
• Died: July 15, 0998
• Place of death: Baghdad (now in Iraq)

Abul Wefa played a major role in mathematics by developing sines and cosines as they apply to the field of trigonometry and used them to correct astronomical calculations carried forward from classical into Islamic times.

Early Life

Born in 940, during the reign of the ՙAbbāsid caliph al-Mutaqqī, Abul Wefa (ah-BEWL weh-FAH) lived during a period of extraordinary cultural and intellectual productivity. His own fields of accomplishment, mathematics and astronomy , were already widely recognized as essential elements of high Islamic civilization. Very little seems to be known about Abul Wefa's early life. Apparently, his early education in mathematics occurred under the tutelage of two uncles, one of whom (Abū ՙAmr al-Mughazili) had received formal training from the famous geometrician Abū Yahya al-Marwazī.

Whatever the possible source of patronage for the young man's further education may have been, his decision to move to Baghdad at the age of nineteen (in 959) greatly benefited the ՙAbbāsid court. Baghdad at this time was troubled politically, following the seizure of de facto control by a military clique headed by the Persian Buyid emirs; thereafter, the Buyids dominated the house of the caliphs until their fall from power in 1055. The Buyids were inclined to favor talented Persians who were drawn toward scholarly circles in the center of the empire. It is reported, for example, that it was Abul Wefa, himself then forty years of age and well established (c. 980), who introduced the Persian scholar and philosopher Abū Ḥayyān al-Tawḥīdī into the Baghdad entourage of the vizier Ibn Saՙdān. Abū Ḥayyān soon became famous under the vizier's patronage, composing a major work, Al-Imta՚ wa՚l mu՚anasa (a collection of notes drawn from philosophical and literary salon meetings), under a dedication to Ibn Saՙdān.

Patronage for Abul Wefa's work in courtly circles, however, must have come from a different milieu, that of the so-called Baghdad School. This scientific assembly flourished in the ՙAbbāsid capital in the last century before its conquest by the Seljuk Turks in 1055. According to some historians, patronage for the natural sciences in particular came precisely during the period in which Abul Wefa passed into the main stages of his scholarly career. The Buyid emir ՙAdūd al-Dawlah (r. 978-983) had nurtured an interest in astronomy through his own studies. He passed this interest on to his son, Saraf al-Dawlah, who built an observatory next to his palace and called scholars from all regions of the empire to glorify the reputation of his reign by carrying out scientific experiments. Abul Wefa was among this group.

Life's Work

The environment for learning in the Baghdad School, with its circle of eminent Islamic scientists, may explain how the young Persian scholar mastered so many technical fields in such a limited period of time. Beyond mere speculation regarding Abul Wefa's early personal contacts, however, one must consider the importance of translation work in the Baghdad School. Abul Wefa himself translated the work of the Greek algebraist Diophantus (fl. c. 250), who had explored the field of indeterminate algebraic equations. Abul Wefa was also known for his studies of, and commentaries on, Euclid. There are, however, no surviving texts to indicate what use he made of the work of these two forerunners from the classical pre-Islamic period.

By contrast, Abul Wefa's attention to the work of the second century Greek astronomer Ptolemy not only contributed to the preservation and transmission to the medieval West of the classical knowledge contained in Ptolemy's MathĪmatikĪ suntaxis (c. 150; Almagest, 1952) but also earned for him an original and lasting reputation as an Islamic mathematician. The Almagest examined the field of trigonometry, which proposed mathematical relationships in terms of the angles and sides of right triangles. This called for the development of sines, or systematic relationships defined in a right triangle working from one of the acute angles, symbolically represented as A. Modern trigonometry expresses this relationship as sin A = a/c, or sin A is equal to the ratio of the length of the side opposite that angle (a) to the length of the hypotenuse (c).

Ptolemy, in pioneering the field of spherical trigonometry, had laid down an approximate method for calculating sines (which he described as chords). Abul Wefa, however, drew on his studies of Indian precedents in the field of trigonometry that were unknown to Ptolemy, as well as models provided by Abul Wefa's predecessor al-Battānī (858-929), to perfect Ptolemy's chords. This was done by applying algebraic, instead of geometric, methods of systematizing the sines. In particular, Abul Wefa's development of the half-chord made it possible to achieve much more precise measurements that would eventually be used in surveying and navigation. The most immediate application of his tables of sines, however, was in the field of astronomy.

One of Abul Wefa's contributions that left a legacy that lasted for many centuries involved the study of evection, or irregularity, in the longitude of the Moon. Later European commentators, including Louis Pierre E. A. Sédillot in the nineteenth century, looked at the Islamic astronomer's work and concluded that he, not Tycho Brahe (1546-1601), had been the first scientist to posit the theory of the “third inequality of the moon.” Although this theory was later proved to be erroneous, the debate at least drew attention to the importance of Abul Wefa's originality in the field.

Abul Wefa himself compiled, in addition to his well-known tables of sines, a book of astronomical tables entitled Zij al-wadih (that which is clear). Like his earlier work on sines, this text is not extant in the original. Scholars tend to agree, however, that certain anonymous manuscripts preserved in European libraries, such as the Zij al-shamil, are taken from Abul Wefa's work.

Works that have survived and that have been at least partially translated include a book of arithmetic entitled Kitāb fi ma yahtaj ilayh al-kuttab wa l-՚ummal min ՙilm al-hisab (961-976; book on what is necessary from the science of arithmetic for scribes and businessmen), the Kitāb fi ma yahtaj ilayh al-sani ՙmin al-a՚mal al-handasiyha (after 990; book on what is necessary from geometric construction for the artisan), and a book entitled Kitāb al-kamil (translated by Carra de Vaux in the Journal Asiatique of 1892). It is thought that Abul Wefa may have still been in Baghdad at the time of his death in 998.

Significance

Study of the Islamic cultural milieu in which Abul Wefa lived suggests a high level of syncretic interaction between ethnic subjects of the Baghdad caliphate Arab, Persian, Greek, and other minorities. Abul Wefa's own career seems also to provide an example of a syncretic social hierarchy. Scientists and intellectual figures, it seems, had no reason to doubt that their accomplishments would be appreciated and supported by a ruling military elite whose social status was obviously determined by very different criteria. In this rather cosmopolitan period in Islamic history, there was room not only for scholars of diverse national origins at the caliph's court but also for representatives of different disciplines, secular and religious, to live side by side in a community that was truly representative of a world civilization. One can only understand the flourishing in Islam of such different disciplines (and the pure sciences in particular), however, if attention is given to the multiplicity of pre-Islamic sources that contributed both to the Baghdad caliphate itself and to the highly developed cultural institutions that it supported.

Bibliography

Bell, Eric T. The Development of Mathematics. New York: McGraw-Hill, 1945. Begins with a historical review of the field of mathematics from the first-known texts through successive stages of discoveries, ending at midpoint in the twentieth century. The chapter of most interest to students of Islamic science is entitled “Detour Through India, Arabia, and Spain, 400-1300.” This title underscores the importance of the medieval period of Oriental history for the conservation of classical Western sources that only returned to Europe via the Islamic core zone, from eastern Iran to Spain.

Cajori, Florian. A History of Mathematics. 1931. 5th ed. Providence, R.I.: AMS Chelsea, 2000. This classic work has several important characteristics that still merit mention. It covers not only standard non-Western mathematical traditions (Hindu and Islamic) but also traditions from little-studied areas such as Mayan Central America and Japan. Includes detailed information on individual mathematicians’ original findings.

Hogendijk, Jan P., and Abdelhamid I. Sabra, eds. The Enterprise of Science in Islam: New Perspectives. Cambridge, Mass.: MIT Press, 2003. A collection of essays surveying the history of Islamic science, including mathematics and astronomy. Illustrations, bibliography, index.

Huff, Toby E. The Rise of Early Modern Science: Islam, China, and the West. 2d ed. New York: Cambridge University Press, 2003. Provides a strong cross-cultural background for the rise of science in the Muslim world. Illustrations, bibliography, index.

Kennedy, Edward S. Astronomy and Astrology in the Medieval Islamic World. Brookfield, Vt.: Ashgate, 1998. Discusses astronomy, astronomers, math, and mathematicians, including Abul Wefa’s calculation of the distance between Baghdad and Mecca. Index.

Kennedy, Edward S, ed. Studies in the Islamic Exact Sciences. Beirut: American University of Beirut Press, 1983. Provides a rather technical treatment of several scientific disciplines that flourished in early Islamic times, including the development, through trigonometry, of accurate astronomical calculations. A specific elaboration of Abul Wefa’s work is included.

Nasr, Seyyed Hossein. Islamic Science: An Illustrated Survey. London: World of Islam Festival, 1976. A carefully researched photographic record of the tools of Islamic science. Textual treatment of historical figures such as Abul Wefa is more limited than in Nasr’s text below. The choice of illustrations, however, particularly from Islamic astronomy, is so rich that the field itself becomes a much more coherent entity.

Nasr, Seyyed Hossein. Science and Civilization in Islam. Cambridge, Mass.: Harvard University Press, 1968. Because this work deals with the subject of science in Islamic civilization only, it can take time to explore individual contributions at some length.