Doctors and Scientists People Science, Medicine and Technology

Muslim Contributions to Mathematics and Astronomy: Al Khwarizmi


By Zakaria Virk BA LLB, Canada

Mathematics was introduced into Muslim culture through the Holy Qur’an where complex rules of inheritance are outlined[i]. Learning is greatly emphasised in the Holy Qur’an, the first word of the revelation being a command to ‘read!’ The sayings of the Prophet of Islam (sa) also emphasise learning to a great extent, with the Prophet (sa) stating that, ‘The acquisition of knowledge is an obligation on every Muslim (whether man or woman)’[ii]. It is also recorded that Prophet Muhammad (sa) would free prisoners of war on condition that they teach ten Muslim children how to read and write[iii].

Next to medicine, Islamic civilisation has produced the most conspicuous creative work in mathematics and astronomy.

The cultural awakening in the Islamic world took place during the second half of the eighth century (750), which undoubtedly saved the ancient sciences being lost forever. By 766 we learn that an astronomy book, Surya Sidhanta (Sindhind), was brought to Baghdad from India. In 775 this book was translated into Arabic and not long afterward Claudius Ptolemy’s Tetrabiblos was translated from Greek. Baghdad, being the seat of a world power as well as the centre of industry and commerce, became also an academy of learning[iv]. Scholars belonging to all faiths were called from Syria, India, and Iran to take part in this intellectual storm.

Translation work

It was under three caliphs, al-Mansur (754-775), al-Haroon (786-802), and al-Mamoon (813-833), that translation work received royal patronage. However, it was during the caliphate of Abdullah al-Mam’un that Muslim scholars fully indulged their passion for translation. The Caliph is said to have had a dream in which Aristotle appeared to him. Consequently, he decided to have Arabic translations made of all Greek books including Ptolemy’s Almagest and Euclid’s Elements. From the Byzantine empire the Caliph acquired Greek scientific and philosophical manuscripts through political treaties. It is related that one of the terms of peace which he forced on all whom he fought and conquered was unconditional surrender of all literary and scientific books.[v] He went to considerable trouble to obtain Greek manuscripts and obtained many holographs by paying a hefty price. He even sent a diplomatic mission to the Byzantine emperor Leon the Armenian (812-820) in this connection. It is said that a collection of rare books came from Cyprus also.

Al-Mam’un (786-833) established at Baghdad in 830 CE an academy of science, Baitul Hikmat, at a cost of 200,000 dinars. It consisted of a vast library with a regular staff, residence for students, a translation bureau, an observatory, and a core team of translators and copyists. In this observatory, scholars verified the length of the solar year, the precession of the equinoxes, the obliquity of the ecliptic and studied sunspots.

Al-Mamun built another observatory on the mount overlooking Damascus and thirty others followed soon after. The astronomers of Baghdad performed one of the most delicate geodisc operations here when they measured the length of a terrestrial degree. The study yielded 56.666 miles as the length of a degree of a meridian, only half a mile more than our current calculation.  Needless to say, Muslim astronomers have left on the skies traces of their legacy in the names of stars such as Acrab (scorpion), algedi (kid), Altair (flyper) and Deneb (tail). Besides these there are technical terms such as azimuth, nadir and zenith which are Arabic in origin.

During Caliph al-Mamun’s reign translation work became a government-sponsored activity. Translators worked in groups, each supervised by an expert and assisted by a copyist. The earliest translations into Arabic were the works of Euclid, Ptolemy’s Almagest, and the physics of Aristotle. The first translations were not made from original Greek but from Syriac and Persian versions. In the case of many difficult passages in the original, the translation was done word for word, and when no Arabic equivalent was available the Greek term was simply transliterated with some adoption[vi]. Works translated from Syriac were checked against the Greek originals when possible. And Arabic translations were revised by competent scholars in the light of newly acquired manuscripts.                 

Some of the prominent translators of this period were Ummayad prince Khalid bin Yazeed (704), Ibn Masawaih (857), al-Kindi (873), Hunain ibn Ishaq, Isa b. Ali (925), Hubaish abul Hassan (912), Isa ibn Yahya (987), Abu Yakub Ishaq (910) and Kosta ibn Luka (864-923). There was one Persian by the name of Ibn Nawbakht, who made translations for Caliph Haroon from Pahlvi into Arabic. Al-Fazari was an Arab whom Caliph Mansur ordered to work with an Indian from Sindh on the translation of Sindhind from Sanskrit. There is a general consensus that some of the Arabic translations of the ancient Greek texts were more correctly transmitted than those which had been done by Latin translators. For instance, Galen’s Anatomy was far more accurately described in Arabic than any previous translation.

The age of translation lasted for about a century (till 850 CE) and thereafter original scientific works in Arabic began to appear. This made Baghdad an unparalleled scientific capital of the world. The independent work done by Muslim scholars and scientists in medicine, mathematics, astronomy and geography was far more conspicuous than in philosophy. Prof Neuberger states that ‘these Arabic translations are even today of great value, partly for exegetical reasons, partly because they fill many of the gaps in the ancient literature.’[vii]


“That fondness for science…that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala, confining it to what is easiest and most useful in arithmetic” – Al Khwarizmi.[viii]

Islamic mathematics can be divided into four parts:

  1. Arithmetic, derived from India and based on the principle of position
  2. Algebra, which though coming from Greek, Hindu and Babylonian sources, assumed a new and systematic form
  3. Trigonometry, to which Muslims applied the Hindu form and added new functions and formulas
  4. Geometry, which came from Greece but to which Muslims contributed generalizations.

The Muslim mathematicians were, however, more attracted to algebra and trigonometry than to geometry, but one aspect of geometry held a special fascination for them, namely the proof of Euclid’s fifth postulate.

Abu Jaffar Muhammad ibn Musa Al-Khwarzimi (790-850) was born in Khowrzam (now Khiva in Uzbekistan). His most important work was Kitab al-Mukhtasar fee Hisab Al Jabar wal Muqabala (Compendius Book on Calculation by Completion & Balancing) written in 830 CE, which gave us the word ‘algebra’. The word ‘Jabr’ means ‘to restore’ and the word ‘Muqabala’ means ‘to compare’, referring to the processes of algebra.

This treatise classifies the solutions of quadratic equations and gives geometric methods for completing the square. No symbols were used, and everything was expressed in words, without negative or zero coefficients. This book was translated by Gerard of Cremona who described it as ‘the cornerstone of the mathematical edifice built by the Arabs.’ Algebraic calculus, Arabic numerals (0-9, which originated in India), and decimal arithmetic were introduced into Europe through this book.
Fig. 1: Soviet stamp dedicated to Al-Khwarizmi (790-850 C.E)

The book remained a principal textbook in several European universities up to the eighteenth century.  A manuscript can be seen at the Bodleian Library in Oxford.
Fig. 2: Al-Khwarizmi’s book on Mathematics, Al-Jabr

His work on arithmetic Kitab Aljama Watafriq bil Hisab al Hindi was also translated into Latin by Italian scholar Gerard of Cremona in the 12th century.  In Latin this book is called Algorithmic de Numero Indorum and is preserved in the university library of Cambridge, UK, and an English version with Arabic text titled Algebra of Muhammad ben Musa was produced by Frederic Rosen in 1831.

Fig. 3: Al-Khwarizmi statue in his place of birth, Khiva, Uzbekistan

When Al-Khwarzimi arrived in Baghdad, he wanted to become a member of its Institute of Science and he thus wrote a dissertation on mathematics and sent it to the academy. After some questioning by its members and approval, he was made a member and subsequently became its director. Incidentally, this method of selection is still employed in universities for post-graduate students[ix]. On Caliph al-Ma’mun’s urging, he wrote another book, Ilm ul-Hisab, which has been rendered into many European languages.

He introduced Hindu-Arabic numerals probably after his travels in India. The Arabic text is lost but Latin translations of his book, Liber Algorismi, gave rise to the word algorithm, a corruption of his last name.

The first use of zero as a place-holder in positional base notation was due to him. He developed the calculus of two errors, which led him to the concept of differentiation. He also refined the geometric representation of conic sections. During his tenure as director of the Baghdad academy of science he, as part of the Baitul Hikmat, participated in a study that was intended to determine the size and circumference of the earth. In his book of geography Kitab Suratul Ardh (Form of the Earth) composed in 817, he corrected Ptolemy’s views and presented his own planetary model. A text of this book was published from Leipzig in 1926. In 830 CE, seventy geographers worked tirelessly under his able leadership to produce the first map of the then-known world for Caliph al-Ma’mun.

His work in astronomy was Zij al-sindhind, which is the first astronomical work to survive in its entirety.  He prepared astronomical tables (zij) the first of its kind in the world. The zij was translated into Latin (1126) by English scientist Adelard of Bath, serving as a basis for all future planetary tables in Europe.  He prepared for al-Ma’mun an atlas of the maps of heaven, which is preserved along with the text. Another work that has survived is Istikhraj Tarikh al-Yahud (Extraction of the Jewish era). It is accurate and well informed. He wrote two books on the astrolabe, Kitab amal al-Astrulab (On the Construction of the Astrolabe), and Kitab al-amal bil–Asturlab (On the Operation of the Astrolabe), manuscripts of which are in the Berlin library. Kitab al-Tarikh (The Chronicle) written in 826, did not survive.    

[i] Holy Qur’an 4:12-13

[ii] Sunan Ibn Mājah 224

[iii] Rahiq al-Makhtoom (The Sealed Nectar); Safi al-Rahman Mubarakpuri 

[iv] History of Medicine by Prof. Neuberger, page 349, 1910

[v] Ibn Khaldoon, Muqaddama, p. 526 

[vi] Abdus Salam by Dr. A. Ghani, page 105, , 1982, Karachi

[vii] M. Neuberger; History of Medicine; p.350

[viii] Victor J. Katz [2009]; A History of Mathematics: An Introduction, p.271

[ix] Musalaman Sciencedan (Urdu) by I.A. Nadvi, page 37. 1993, New Dehli

About the author:

Zakaria Virk is the author/translator of twenty one books in both English and Urdu, four of which are on the life of Dr. Abdus Salam. As a historian of science, his particular interest has been Muslim contributions to sciences. His insightful articles have been published in leading magazines of India, Pakistan, US and Canada for over twenty years. He has been in the editorial board for several magazines and also received prizes in essay-writing competitions.