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Abu Ar-Rayhan Muhammad Ibn Ahmad al-Biruni  

/ ahl-BYEROO-nee/

973–c. 1052
Persian Mathematician, Geographer, Historian, Astronomer, Ethnographist and Anthropologist
Mathematics Ranking 41st of 46
Al-Biruni - BOOK - 1973 USSR - Portrait.

Issued on the 1,000th anniversary of

  Al-Biruni’s birth (1973) by the USSR.

Al-Biruni gave the best medieval account of the Hindu numerals.(1) He contributed theorems to geometry that thereafter bore his name.(2) Al-Biruni also composed an encyclopedia of astronomy, a treatise on geography and most significantly, a History of India (Tarikh al-Hind).(3) He was the most original polymath the Islamic world had ever known.(4) He wrote 146 titles in all, almost half were on astronomical and mathematical subjects. Unfortunately, only 22 titles survived, and only about half of that has been published.

Al-Birnui lived during a period of unusual political turmoil in the eastern Islamic world. He served more than six different princes, all of whom were known for their warlike activities and a good number had violent deaths. Little is known of his early life. He was educated by a Khwarezm-Shah prince, Abu Nasr Mansur Ibn Iraq, a member of the dynasty that ruled the area. Some of the mathematical works of this prince were written especially for al-Biruni and are at times easily confused with al-Biruni's own works.

After a period in which al-Birnui undertook extensive travels--or rather escapes from wars, and a constant search for patrons--the entire domain of the Samanids fell under the brutal reign of Mahmud, son of Sebuktigin. Mahmud took Ghazna as his capital in 998 and demanded that both al-Biruni and Avicenna join his court. Avicenna managed to escape, but al-Biruni did not, and he worked in Ghazna until the end of his life when he was not accompanying Mahmud on his campaigns into northern India. 


Al-Biruni’s arrival in India in 1018 with the invading army of Mahmud was an important landmark in the scientific contact between Islam and India. During his enforced stay in India, which he profitably occupied by learning the language and culture of the country, al-Biruni translated from Arabic into Sanskrit Euclid’s Elements, Ptolemy’s Almagest, and his own work on the construction of the astrolabe. Unfortunately, none of these Sanskrit translations are extant today.

He also penned the acute observations about India that would earn him fame as an ethnographer, anthropologist, and eloquent historian of Indian science.

Discussion of al-Biruni's Works

Related to his work on India is al-Biruni's The Chronology of Ancient Nations, which is a universal anthropological account of various cultures and the lore of long-dead cultures or of other cultures that were about to disappear. With the History of India, these two works preserve the best premodern description of the cultures al-Biruni came to know. In the Chronology, for example, is the most elaborate treatment of the Jewish calendar -- more extensive than any surviving medieval Hebrew source and much more scientifically reasoned than any other treatment that this calendar had received up to that time.(5)

An equally encyclopedic scientific work is the inimitable Al-Qanun al-Mas'udi (The Mas'udic Canon), dedicated to Mas'ud, the son of Mahmud of Ghazna, in which al-Biruni gathered together all the astronomical knowledge from such sources as Ptolemy's Almagest and "Handy Tables" after having these two particular works updated. Nevertheless, al-Biruni's original input is clearly noticeable in almost every chapter. For example, al-Biruni developed new algebraic techniques for the solution of third-degree equations, drew a subtle distinction between the motion of the solar apogee and the motion of precession, and explored many other applied mathematical techniques to achieve much higher precision and ease of use of tabulated astronomical results.

His Al-Tafhim li-awa'il sina'at al-tanjim (Elements of Astrology) is still the most comprehensive treatment of the topic as it was then known. Despite the fact that most people believed that astrology was "the fruit of the mathematical sciences," as al-Biruni called it, his personal opinion of the discipline was "as weak as that of its least adherents." However, he was fully aware of the importance of astrology as a tool for teaching mathematical and astronomical disciplines. Under the pretext of teaching astrology, he devoted almost two-thirds of this voluminous work to teaching his patron, Rayhanah, for whom the book was written, elementary mathematics, astronomy, geography, chronology, and the making of the astrolabe as an observational instrument. After all those disciplines were clearly laid out in a question-and-answer format, al-Biruni then allowed his patron to venture into astrology proper--but not before warning him that he himself thought little of the subject.

The Tahdid nihayat al-amakin li-tashih masafat al-masakin (Determination of the Coordinates of Places for the Correction of Distances Between Cities) is al-Biruni's masterpiece in mathematical geography. In it he not only defended the role of the mathematical sciences against the attacks of religious scholars who could not understand the utility of the mathematical sciences but also detailed all that one needed to know about determining longitudes and latitudes on land. He capped that particular discussion with a solution to the complex spherical trigonometric problem of determining the direction of Mecca along the local horizon at Ghazna. Besides being a challenging mathematical problem, determining the direction of Mecca is a religious requirement for the completion of the ordained five daily prayers in Islam. Thus, not only did al-Biruni not miss a chance to demonstrate the very useful role of mathematics in religion, but he also used the occasion (as he had done in his treatise on astrology) to include other scientific matters. For example, he raised questions about the formation of mountains and explained the existence there of fossils by positing that Earth was once underwater. (He also raised these questions in his book on India). In both cases he treated these matters with a scientific objectivity that matches the modern explanation.

His relatively minor works are only minor in size, for they are at least as sophisticated as his major works. Al-Biruni's Maqalid 'ilm al-hay'ah (Keys to Astronomy), Al-jamahir fi ma 'rifat al-jawahir (Gems), Kitab al-saydanah (Pharmacology), and Ifrad al-maqal fi amor al-zilal (The Exhaustive Treatise on Shadows), to name only a few, dealt with specific subjects, but in each case the subject was given comprehensive treatment. Furthermore, in a perfect al-Biruni manner, each work contains extremely original comments on seemingly unrelated subjects. For example, in the introduction to his book on gems, al-Birnui gave an elaborate description of man's place in nature and society and the social need for economic systems. In that context he wrote of precious metals and gems, which were considered foundational for any economic system and he wrote of diamonds and their particular social importance.



(1) Will Durant, The Age of Faith -- The Story of Civilization: Volume 4 (New York, 1950), p. 244.

(2) Ibid., p. 244.

(3) Ibid., p. 243-244.

(4) George Saliba, Al-Biruni, accessed 4/30/2019, 

(5) Saliba, p. 3.


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