Bibliography of Mathematics in Medieval Islamic Civilization

Version 13 January 1999.

This bibliography is a revised, enlarged and updated version of the bibliography on Islamic mathematics by Richard Lorch on pp. 65-86 of Joseph W. Dauben's The History of Mathematics from Antiquity to the Present: A Selective Bibliography, New York and London: Garland, 1985.

This bibliography of Islamic mathematics will appear as a chapter in the updated (1999?) version of Dauben's book which will be made available as a CD-Rom. Reactions and suggestions are very welcome, and can be sent to J.P.Hogendijk_at_uu.nl In this preliminary form, no attention has been paid to diacritical marks in Arabic names. The items in the bibliography have been numbered *1, *2, ... *122, *122a, *122b, *123 etc. and many cross-references have been provided.

General Introduction
Introductory Works
Bibliographies and Handbooks
Illustrated Works
Texts and Commentaries (Specific Authors in Chronological Order)
Studies on Specific Subjects
Transmission of Mathematics
Mathematics in Specific Areas in the Islamic World
Arithmetic
Irrational Magnitudes
Algebra
Number Theory, Indeterminate Equations and Magic Squares
Geometry
Trigonometry
Timekeeping
Interpolation, Tables, Analysis of Tables
Cultural Context: Islamic Aspects
Mathematical Astronomy and Astrology
Instruments
Mathematics, Art and Architecture
Optics
Geography
Reprinted Works and Collections of Articles

General Introduction

Islamic mathematics and Arabic mathematics are modern historical terms for the mathematical sciences in Islamic civilization from the beginning of Islam (A.D. 622) until the 17th century. Although most of the mathematicians in this period of Islamic civilization were Muslims, some prominent mathematicians had other religious backgrounds (Christian, Jewish, Zoroastrian). Arabic was the main scientific language but not necessarily the native language of a mathematician, who might have been Persian, Turkish, etc.

The Islamic mathematical tradition was a continuation of the traditions of ancient Greece, India and pre-Islamic Iran. Some texts from the medieval Islamic period are lost in Arabic but available in medieval Latin or Hebrew translations. Thus material relevant to Islamic mathematics can also be found in the sections on Greek (available through the internet), Indian, Hebrew and Latin mathematics in Dauben's (updated) bibliography.

Although the field of Islamic mathematics is still under-researched, the literature is already so extensive that only a small part can be listed in a bibliography of this size. The present selection focuses on recent literature on Islamic mathematics in Western languages. More literature in Western languages can easily be found in the bibliographical works *8 and *9. References to the literature on Islamic mathematics in other languages can be found in *9 for publications in Russian, Arabic, Turkish and Uzbek, *8 for publications in Arabic and Turkish and *13 for publications in Persian. Unfortunately, it is not easy to trace all publications in Eastern languages on a given subject.

This bibliography includes references to non-trivial applications of mathematics to other sciences in Islamic civilization. Examples are publications on the mathematical construction of the astrolabe, technical mathematical explanations of planetary models, optical problems leading to complicated geometrical problems, and so on. However, I have not included publications on topics which are only indirectly related to mathematics, such as the theory of vision, star names, descriptions of the use of the astrolabe, and natural philosophy. I would like to warn the reader that this is not a bibliography on Islamic astronomy, or on optics, or on instruments.

Once a reference to an article or book has been found, it is often a major problem to find the article or book in question. A special section at the end of this bibliography lists collections of articles and reprinted works, containing articles on Islamic mathematics which are often difficult or impossible to find otherwise.

The following journals specialize in Islamic science:

Articles on Islamic mathematics also appear in journals on the general history of mathematics or science, on Oriental studies, etc. The best sources of information on current research are the sections 01A30 of the Mathematical Reviews (free author-lookup available through the internet) and the Zentralblatt der Mathematik the Abstracts section in Historia Mathematica, and the Isis Cumulative Bibliography.

Introductory Works

Good introductions to the history of Islamic mathematics are found in:

Bibliographies and Handbooks

The two most important works are:

Illustrated Works

Texts and Commentaries (Specific Authors)

What follows is a listing of the major edited texts currently available in good translations in Western languages, together with some introductory historical studies which focus on a single author. Because an alphabetic listing of Arabic names is somewhat problematic, the authors will be listed in chronological order. The major Greek authors whose works were translated into Arabic have been included in the list. The reader should be aware that many texts have been published in Arabic editions (without translation in a Western language) or in facsimile, and that some important texts are available (only) in Russian translations. References to these publications can be found in the bibliographies *8 and *9.

Euclid

See also *52a, *99, *133a, *201 vols. 14-20.

Archimedes

Apollonios

Diocles

Diophantos

Menelaos of Alexandria

Pappos

Al-Khwarizmi (Irak-Iran, ca. 830)

See also *201 vols. 1-6.

Ibn Turk (Turkey? Irak? ca. 830?)

Al-Kindi (Irak, ca. 800-870)

Banu Musa (Syria-Irak, ca. 830)

See also *53.

Thabit ibn Qurra (Syria-Irak, 835-901)

See also *152, *201 vol. 21,22.

Al-Hashimi, `Ali ibn Sulayman (Irak? ca. 850-900)

Al-Battani (Syria, ca. 900)

Abu Kamil (Egypt? ca. 900)

See also *201 vol. 23.

Ibrahim ibn Sinan (Irak, 909-946)

See also *53.

Al-Khazin, Abu Ja`far (Irak-Iran, ca. 920-980)

See also *53.

Al-Karabisi (Irak? 10th century?)

Ikhwan al-Safa' (Irak, first half of 10th century)

The Ikhwan al-Safa' ("brethren of purity") were a (mystical?) group in the city of Basra in Irak. The group authored a series of more than 50 letters on science, philosophy and theology. The first letter is on arithmetic and number theory, the second letter on geometry.

Al-Uqlidisi (Irak-Iran, 10th century)

Al- Saghani, Abu Hamid (Irak-Iran, ca. 940-1000)

Al-Kuhi, Abu Sahl Wayjan ibn Rustam (Irak-Iran, ca. 940-1000)

See also *49, *53.

Abu al-Wafa' (Irak-Iran, ca. 940-998)

Abu Sa`d al-`Ala' ibn Sahl (Irak-Iran, ca. 940-1000)

Al-Sijzi, Ahmad ibn Muhammad (Iran, ca. 940-1000)

Ibn Yunus (Egypt, ca. 950-1010)

See also *201 vols. 24,25.

Abu Nasr ibn `Iraq (Irak-Iran, ca. 950-1030)

See also *38.

Kushyar ibn Labban (Iran, ca. 960-1010)

Al-Karaji (Iran, ca. 970-1030)

Ibn al-Haytham (Irak-Egypt, ca. 965-1040)

See also *34.

Al-Biruni (Iran-Afghanistan, 973-1048)

See also *7, *201 vols. 32-36.

Ibn Mu`adh al-Jayyani (Spain, ca. 1030-1090)

Ibn al-Zarqalluh (Azarquiel, al-Zarqali) (Spain, ca. 1030-1090)

Items *182 and *194 contain various other papers on Ibn al-Zarqalluh.

Al-Mu'taman ibn Hud (Spain, ca. 1080)

See also *53.

al-Khayyam, `Umar (Iran, ca. 1050-1130)

al-Tusi, Sharaf al-Din (Iran, ca. 1150-1215)

See also *142.

Ibn Mun`im (Maghreb, ca. 1210)

al-Marrakushi (Morocco, 13th century)

al-Tusi, Nasir al-Din (Iran, 1201-1274)

Ibn Baso, Abu `Ali al-Husayn (Spain, ca. 1250-1320)

Ibn al-Banna' (Maghreb, ca. 1300)

Al-Farisi, Kamal al-Din (Iran, ca. 1300)

Al-Khalili, Shams al-Din (Syria, ca. 1350-1400)

Ibn al-Shatir (1306-1375)

Al-Kashi, Ghiyath al-Din Jamshid ibn Mas`ud (Iran, Uzbekistan, ca. 1420)

Ulugh Beg (Iran, Uzbekistan, 1394-1449)

Al-Qalasadi (Maghreb, 15th century)

Studies on specific topics

Transmission of Mathematics

See also *17, *29 - *39, *69, *147, *149, *150. *184, *185.

Mathematics in Specific Areas of the Islamic World

For mathematics in Islamic Spain see also *4, *15, *182, *194, for the Maghreb see also *20, *108, *135.

Arithmetic

See also *41, *66, *79, *85, *113, *118, *123.

Irrational magnitudes

See also *39, *99, *136, and see the section on Algebra.

Algebra

See also *40, *45, *52, *56, *57, *81, *104, *105, *106, *107, *107a.

Number theory, Indeterminate Equations, Magic Squares

See also *36, *37, *59, *60, *62, *63, *65a, *65b, *73b, *80, *84a, *113a.

Geometry

See also *30a, *34, *35, *38, *47, *49, *52a, *53, *58, *61, *64, *65, *67, *68, *69, *71 - *76, *82 - *84, *88, *89, *103, *119, *133a, *189, and the section on Trigonometry.

Trigonometry

See also *38, *78, *79a, *91 - *95, *98, *110, *118a, *120, *180, *189, and see the sections on Timekeeping, Instruments, Mathematical Astronomy and Astrology.

Timekeeping

See also *43, *50, *51, *77, *93, *180, *182, *187, *189.

Interpolation, tables, analysis of tables

See also *19, *42, *44, *55, *77, *79b, *180, *181, *186, and the section on Astronomy.

Cultural context; Islamic Aspects

Most items in this bibliography on Islamic mathematics involve the cultural or Islamic context to a greater or lesser extent. See especially *7, *24, *24a, *70, *86, *97, *114, *122, *122a, *122b, *125, *126, *133a, *137, *172, *188, *193, and see the section on Mathematics, Art and Architecture.

Mathematical astronomy and astrology

See also *7, *8 vols. 6, 7, *43, *48, *54, *73a, *77a, *90, *96, *100, *101a, *102, *111, *117, *161, *172, *174, *176, *177, *180 - *183, *186 - *189, *194, *196, *201, and see the section on Instruments.

Instruments

See also *67, *101, *109, *112, and the sections on Timekeeping and astronomy. For a brief elementary explanation of the astrolabe in English, see North, J. D. The Astrolabe, Scientific American 230 (i) (January 1974), pp. 96-106.

Mathematics, art and architecture

See also *28, *73, *121, *122.

Optics

See *35, *74, *75, *87, *114, *115, *116, *183, *192, *193.

Geography

See *19, *92, *92a, *95.

Reprinted works and collections of articles

Since 1985 the Institute of the History of Arabic-Islamic Sciences in Frankfurt (Germany) has reprinted almost all of the literature on Islamic mathematics published before ca. 1960. These publications are enormously useful for finding obscure articles and books in the field. A list of the most important reprints on Islamic mathematics in Western languages follows. In addition, the Institute is also putting out reprints of Arabic editions and facsimiles of Arabic manuscripts of mathematical and astronomical texts. These will not be mentioned below.

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Jan Hogendijk <J.P.Hogendijk_at_uu.nl>
1 dec. 2000 *79b, *73b, *101a, *149 (rev.)