Pathfinders

by Jim Al-Khalili

  Ibn Jubayr Ibn Jubayr (1145–1217); Arab geographer, traveller and poet from Andalusia; born in Valencia, descendant of a tribe of Andalusian (Visigoth) origins; studied at Granada. He travelled widely around the Muslim world and wrote extensively about the people and customs in his Rihlat Ibn Jubayr (Ibn Jubayr’s Journey).

  Abū Kāmil Abū Kāmil Shujā al-Hāsib al-Masri (‘the Egyptian Calculator’); Egyptian mathematician who flourished in the late ninth and early tenth century. He developed al-Khwārizmi’s work on algebra and studied geometric shapes algebraically. His work in turn influenced al-Karkhi and Leonardo of Pisa (Fibonacci).

  al-Karkhi Abū Bakr Muhammad ibn Hassan al-Hāsib (‘the Calculator’) al-Karkhi (from the Baghdad suburb of Karkh); also known as al-Karaji (since his family originated from the Persian city of Karaj); flourished in Baghdad during first decades of the eleventh century; died c. 1029; Muslim mathematician who made important advances in arithmetic and algebra. Little is known about his life, as his original Arabic manuscripts are lost. His most significant contribution is his table of binomial coefficients (the numbers that multiply powers of x in polynomial expansions). He also advanced algebra beyond the work of al-Khwārizmi by distancing it further from the shackles of Greek geometric solutions.

  al-Kāshi Ghiyāth al-Dīn Jamshīd ibn Mas’ūd al-Kāshi, born in Kāshān, central Iran, c. 1380; died in Samarkand in 1429; Persian astronomer and mathematician and one of the last of the great scholars of Arabic science. He worked at Ulugh Beg’s scientific institute in Samarkand, produced a zīj entitled the Khaqani Zīj and wrote on the determination of distances and sizes of heavenly bodies. He wrote a treatise on astronomical observational instruments and invented several new devices himself to solve a range of planetary problems. He is best known for providing the first explicit statement of the cosine rule (still known in French as the théorème d’al-Kashi).

  Ibn Khaldūn Abū Zayd ’Abd al-Rahmān ibn Muhammad ibn Khaldūn al-Hathrami (1332–1406); Arab polymath: economist, historian, jurist, theologian, mathematician, astronomer, philosopher, social scientist and statesman; born in Tunis into an upper-class Andalusian family, the Banū Khaldūn, which had emigrated to Tunisia after the fall of Seville to the Christians. He was the founder of several social scientific disciplines: demography, cultural history, historiography and sociology, and is widely regarded as the father of economics. Best known for his Muqaddima (The Prolegomenon).

  Ibn al-Khatīb Lisan al-Dīn ibn al-Khatīb, born 1313 near Granada; died 1374; Andalusian poet, writer, historian, philosopher, physician and politician. He spent most of his life as vizier to Muhammad V, the Nasrid sultan of Granada, but was exiled to Morocco.

  Omar Khayyām Abū al-Fatah Umar ibn Ibrahīm al-Khayyāmi, born and died in Nishapūr (1048–1131); his laqab, al-Khayyāmi, means ‘tentmaker’; Persian mathematician, astronomer and poet; one of the greatest mathematicians of the medieval world. He made contributions to the geometric solution of cubic equations and played a major role in devising the Persian Jalali calendar, based on his highly accurate measurement of the length of the year.

  al-Khwārizmi Abū Abdullah Muhammad ibn Mūsa al-Khwārizmi, Latin, Algorithmus; Muslim mathematician, astronomer and geographer and one of the greatest scientists of the medieval world; born c. 780 in Khwārizm, south of the Aral Sea, and flourished in Baghdad under al-Ma’mūn; died c. 850. He brought together Greek geometry and Hindu arithmetic and wrote most famously the first book on algebra, Kitab al-Jebr. He was influential in promoting the Hindu decimal system, to both the Islamic world and Europe; he produced a famous star chart and associated trigonometric tables as well as a geographical text that improved on the work of Ptolemy.

  al-Kindi Abū Yūsuf Ya’qūb ibn Ishāq ibn al-Sabbāh al-Kindi, Latin, Alkindus; born in Basra at the beginning of the ninth century, flourished in Baghdad under al-Ma’mūn and al-Mu’tasim (813–42); died c. 873; known as ‘the Philosopher of the Arabs’. His numerous works covered mathematics, physics, astronomy, music, medicine, pharmacy and geography. He wrote several books on Hindu numerals (introducing them to the Muslim world, along with al-Khwārizmi). Many translations from Greek to Arabic were made by him or under his direction.

  Kūshyār ibn Labbān Abū al-Hassan Kūshyār ibn Labbān ibn Bāshahri al-Jīli (from Jīlān, south of the Caspian Sea); flourished c. 971–1029. A Persian mathematician and astronomer who made contributions in trigonometry and compiled astronomical tables, al-Zīj al-Jāmi’ wal-Bāligh (The Comprehensive and Mature Tables).

  Maimonides (Mūsa ibn Maymūn) Arabic: Abū ’Imrān Mūsa ibn Maymūn ibn Abdallah al-Qurtubi al-Isra’īli; Hebrew: Moses ben Maimon; Hispano-Jewish philosopher, theologian, astronomer; born in Córdoba 1135; died in Cairo 1204. A contemporary of Ibn Rushd and just as great a scholar, though he worked independently; almost all his works were in Arabic, but were promptly translated into Hebrew, in which form they were far more influential. His most famous text was his Dalālat al-Hā’irūn (The Guide for the Perplexed). He was influenced by Ibn Sīna and his Aristotelianism and attempted to reconcile it with Jewish theology, just as others had done for Islamic theology (combining faith with reason).

  al-Marwarrūdhi Khālid ibn abd al-Malik al-Marwarrūdhi; Muslim astronomer who flourished under al-Ma’mūn. He took part in the solar observations in Damascus in 832–3.

  Mashā’allah The name means (in Arabic) ‘What God has willed’, but his real name was probably Manasseh; an Egyptian Jew who flourished in Baghdad under al-Mansūr in the second half of the eighth century. He was one of the earliest astronomers/astrologers in Islam and took part in the preliminary surveys of the site of the foundation of Baghdad. Only one of his writings is extant in Arabic, though many translations in Hebrew and Latin survive. His most popular work in the Middle Ages was the De scientia motus orbis, translated by Gerard of Cremona.

  Ibn al-Nadīm Abū al-Faraj Muhammad ibn Ishāq ibn abī Ya’qūb al-Nadīm al-Warrāq al-Baghdādi (‘the Stationer of Baghdad’); died 995; historian and biographer, who wrote the famous Fihrist al-Ulūm (Index of the Sciences) or, simply, al-Fihrist. This invaluable reference book (completed in 988 in Constantinople) was, in al-Nadīm’s own words, ‘an index of all the books of all peoples of the Arabs and non-Arabs whereof somewhat exists in the language and script of the Arabs on all branches of knowledge’. It also included useful biographies of all the authors. Only a tiny fraction of the books mentioned in the Fihrist survived the sacking of Baghdad in 1258.

  Ibn al-Nafīs Ala’ al-Dīn Abū al-Hassan Ali ibn Abi al-Hazm al-Nafīs al-Qurāshi al-Dimashqi; born Damascus 1213, died Cairo 1288; Arab Muslim polymath: physician, anatomist, physiologist, surgeon, ophthalmologist, lawyer, Sunni theologian, philosopher, logician and astronomer. His most famous work, Sharh Tashrīh al-Qānūn (Commentary on Anatomy in Ibn Sīna’s Canon), contained many new anatomical discoveries, most importantly his discovery of pulmonary and coronary circulations. His huge Comprehensive Book on Medicine remains one of the largest medical encyclopedias of all time. He was a proponent of post-mortem autopsies and human dissection.

  Nawbakht Persian astronomer/astrologer and engineer; flourished in Baghdad under al-Mansūr; died c. 777. Together with Mashā’allah, he made preliminary surveys of the site for the construction of the Round City of Baghdad.

  al-Qalasādi Abū al-Hassan ibn ’Ali al-Qalasādi; born Baza, Spain, 1412, flourished in Granada, died in Tunisia 1486; Arab Muslim mathematician who wrote numerous books on arithmetic and algebra, including al-Tafsīr fi ’Ilm al-Hisāb (Clarification of the Science of Arithmetic). He developed symbolic algebra beyond the early notations of Diophantus and Brahmagupta by using, for the first time, symbols for mathematical operations as well as numbers.

  Qusta ibn Luqqa Qusta ibn Luqqa al-Ba’labakki (that is, from Baalbek, or Heliopolis); died c. 912; Christian of Greek origin who flourished in Baghdad as a physician, philosopher, mathematician and astronomer. He translated a number of Greek texts into Arabic and wrote many origin
al works on medicine and geometry, including a treatise on the astrolabe.

  Fakhr al-Dīn al-Rāzi Abū Abdallah Muhammad ibn Umar Fakhr al-Dīn al-Rāzi (1149–1210), often called Imām al-Rāzi; born in Rayy; Persian philosopher, historian, mathematician, astronomer, physician, theologian. He wrote prodigiously in both Arabic and Persian. He dealt with the physical sciences and cosmology from an Islamic perspective and, like his predecessor al-Ghazāli, was critical of Ibn Sīna and Aristotle.

  Ibn Zakariyya al-Rāzi Abū Bakr Muhammad ibn Zakariyya al-Rāzi, Latin, Rhazes (c. 854–c. 925); born in Rayy; physician, philosopher, chemist, and the greatest clinician of Islam and the Middle Ages. He flourished in Rayy and Baghdad, where he oversaw the running of several hospitals. In medicine, he combined Galenic theory with Hippocratic wisdom. His Kitab al-Hāwi (Liber continens) and his monograph on smallpox and measles, Kitab al-Judari wal-Hasba, were two of the most important medical books in Europe for many centuries. He made one of the earliest serious attempts to classify the chemical elements, was an early proponent of the scientific method and even carried out one of the first clinical trials.

  Robert of Chester English mathematician, astronomer, alchemist and translator from Arabic into Latin; flourished in Spain in the first half of the twelfth century before returning to London. He completed the first Latin translation of the Qur’an in 1143 as well as the first Latin translation of al-Khwārizmi’s Kitab al-Jebr. He is therefore regarded as the first person to introduce algebra into Europe.

  Ibn Rushd Abū al-Walīd Muhammad ibn Ahmed ibn Muhammad ibn Rushd, Latin, Averroës (1126–98); one of the greatest and certainly best-known philosophers of medieval times. He was responsible more than any other for introducing Aristotelian philosophy to Europe. Born in Córdoba, he studied law and medicine and even worked as the Almohad caliph’s personal physician in Marrakesh. He was the last of the great Muslim philosophers, and deeply influenced both Christian and Jewish thought.

  Ibn Sahl Abu Sa’ad al-’Alā’ ibn Sahl (c. 940–1000); Muslim mathematician and physicist, who flourished in Baghdad. His treatise On the Burning Instruments set out his understanding of the refraction of light that was to influence Ibn al-Haytham shortly after. Famous for his discovery of the law of refraction, today known as Snell’s law, over six centuries before Snell himself.

  Sahl al-Tabari Jewish astronomer and physician (c. 786–845), also known as Rabbān al-Tabari (‘The Rabbi of Tarabistan’). He flourished in Baghdad and is said to have made one of the first translations into Arabic of Ptolemy’s Almagest.

  al-Samaw’al Al-Samaw’al Ibn Yahyā al-Maghribī; born in Baghdad c. 1130, died in Marāgha c. 1180; Arab mathematician and astronomer; Muslim convert and son of a Jewish rabbi from Morocco. He wrote the treatise al-Bahir fi al-Jebr (The Brilliant in Algebra) at the age of 19; later he developed the concept of proof by mathematical induction, which he used to extend the work of al-Karkhi on the binomial theorem.

  Sanad ibn Ali Abū al-Tayyib Sanad ibn Ali al-Yahūdi; Muslim astronomer, the son of a Jewish astrologer; flourished under al-Ma’mūn; died after 864. He constructed the Shammāsiyya observatory in Baghdad to carry out al-Ma’mūn’s mission of checking and improving many of the astronomical observations of the Greeks.

  Ibn al-Shātir Ala’ al-Dīn Abu’l-Hassan Ali ibn Ibrahīm ibn al-Shātir (1304–75); one of the greatest Arab astronomers; worked as a muwaqqit (timekeeper) at the Umayyad mosque in Damascus. He reformed and improved the Ptolemaic system by eliminating the cumbersome eccentrics and equants in the lunar and planetary models. His mathematical models were in better agreement with observations than Ptolemy’s and were used by Copernicus a hundred and fifty years later. He constructed a magnificent sundial for one of the minarets of the Umayyad mosque, the fragments of which are in a Damascus museum, making it the oldest polar-axis sundial still in existence.

  al-Shirāzi Qutb al-Dīn Shirāzi (1236–1311); Persian Muslim polymath who made contributions in astronomy, mathematics, medicine, physics, music theory and philosophy. Born in Shiraz in 1236, he studied medicine under his father and uncle, both physicians, and astronomy under al-Tūsi at Marāgha; then spent time in Khurasan, Qazwīn, Isfahan and Baghdad. He wrote important treatises on astronomy and optics and began the work that would lead to his student al-Fārisi’s explanation of the rainbow.

  al-Sijzi Abū Sa’īd Ahmed ibn Muhammad al-Sijzi (al-Sijistāni) (c. 950–c. 1020); astronomer and mathematician who developed geometrical solutions of algebraic equations. He was a contemporary of al-Bīrūni; little is known about him but he is said (by al-Bīrūni) to have built a heliocentric astrolabe.

  Ibn Sīna Abū Ali al-Hussein ibn Abdullah ibn Sīna, Latin, Avicenna; born 980 at Afshāna near Bukhara, died in Hamadan 1037; by far the most famous and influential scholar in Islam and one of the most important thinkers in history. He is best known as a philosopher and a physician and was hugely influential in Europe in both disciplines for many centuries. His two greatest works were his Qānūn fi al-Tibb (Canon of Medicine), a codification of all medical knowledge, and the philosophical encyclopedia Kitab al-Shifā’ (Book of Healing). He is regarded as almost as influential on Western philosophy as Aristotle. His ideas in mathematics and physics were more philosophical than technical (as distinct from his two contemporaries al-Bīrūni and Ibn al-Haytham). Nevertheless, he made a profound study of such concepts as light, heat, force, motion, vacuum and infinity, and was strongly influenced by the work of Aristotle. In a sense, his contribution to science was so complete that it discouraged further original investigations and sterilized intellectual life in the Muslim world.

  Sinān ibn Thābit Abū Sa’īd Sinān ibn Thābit ibn Qurra; Muslim physician, mathematician and astronomer; flourished in Baghdad; died 943; son of the more famous Thābit ibn Qurra. A brilliant administrator of a number of Baghdad hospitals, he worked tirelessly to raise the scientific standards of the medical profession.

  al-Tabari Abū Ja’far Muhammad ibn Jarīr al-Tabari; born in Tabaristan c. 839; flourished in Baghdad where he died 923; Persian historian and theologian and one of the most important historians in Islam. His most famous work is a history of the world, written in Arabic, from creation to the year 915, his Akhbār al-Rusūl wal-Mulūk (Annals of the Prophets and Kings).

  Ibn Tāhir al-Baghdādi Abū Mansūr ’Abd al-Qāhir ibn Tāhir ibn Muhammad al-Baghdādi; historian, philosopher, theologian and mathematician; born and grew up in Baghdad but flourished at Nishapūr (d. 1037). He wrote on philosophy and theology, but his most famous work was on algebra, called Kitab al-Takmīl (The Completion).

  Thābit ibn Qurra Abū al-Hassan Thābit ibn Qurra ibn Marwān al-Harrāni (c. 836–901); pagan Arab from Harrān in north-west Mesopotamia who flourished in Baghdad; mathematician, astronomer, physician and one of the greatest translators from Greek and Syriac into Arabic. He made a number of impressive advances in number theory.

  Ibn Tufayl Abū Bakr Muhammad ibn abd al-Malik ibn Muhammad ibn Muhammad ibn Tufayl, Latin, Abubacer; Andalusian Muslim philosopher and physician; born in the first decade of the twelfth century near Granada; died 1185. He wrote one of the most original and best-known books of the Middle Ages, Asrār al-Hikma al-Ishrāqiyya (Secrets of Illuminative Philosophy), which was a theological romance, often described as a metaphysical Robinson Crusoe.

  Nasr al-Dīn al-Tūsi Muhammad ibn Muhammad ibn Hasan al-Tūsi, better known as Nasr al-Dīn al-Tūsi; born 1201 in Tūs, Khurasan, died Baghdad 1274; Persian polymath and one of the great scholars of medieval times. He was an astronomer, biologist, chemist, mathematician, philosopher, physician, physicist and theologian. He fled the Mongols to join the Hashashīn, an offshoot of the Isma’īlis, in their fort at Alamūt, where he made his most important contributions in science, but later joined Hūlāgū Khān’s ranks and persuaded the Mongol leader to build him a new observatory in Marāgha, which became the most important centre for astronomy in the world for several centuries. He invented a geometrical technique called a Tūsi-couple,
which improved on Ptolemy’s problematic equant. He was the first to present observational evidence of the earth’s rotation. He also wrote extensively on biology and was the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy.

  al-Uqlīdisi Abū al-Hassan Ahmad ibn Ibrahīm al-Uqlīdisi; Arab mathematician who flourished in Damascus and Baghdad; his name derives from Uqlīdis (Arabic for ‘Euclid’), suggesting his main occupation was as a translator or copier of Euclid’s texts. He is famous for writing the earliest known text on decimal fractions around the mid-tenth century, five hundred years before the work of al-Kāshi in Samarkand, who was commonly believed to have been the first to use decimal fractions.

  al-’Urdi Mu’ayyad al-Dīn al-’Urdi (died 1266); Arab astronomer, mathematician, architect and engineer; born in Aleppo and flourished at the Marāgha observatory under the guidance of al-Tūsi. He was the first of the Marāgha School to develop a non-Ptolemaic model of planetary motion. The methods he developed were later used by Ibn al-Shātir in the fourteenth century and in the heliocentric model of Copernicus in the sixteenth.

  Abū al-Wafā’ Abū al-Wafā’ Muhammad ibn Muhammad al-Būzjāni (940–98); astronomer and mathematician; born Būzjān, Qūhistān. One of the last Arabic translators and commentators on Greek works, he wrote an astronomical text (probably based on the Almagest) called al-Kitab al-Kāmil (The Complete Book); he contributed to trigonometry and was probably the first to show how the sine rule generalizes to spherical angles.

  Ibn Wahshiyya Abū Bakr Ahmed ibn Ali ibn Wahshiyya al-Kaldāni; born Iraq of Chaldaean/Nabataean (descendants of the Babylonians) family; alchemist who flourished at end of the ninth and beginning of the tenth century. He partially deciphered Egyptian hieroglyphics and Babylonian cuneiform texts.