Ibn Khaldun’s (1332 - 1395) Indian Numerals in the Islamic World

[KALKI]

It was the Indians who invented zero and the place-value system, as well as the very foundations of written calculation as we know it today. These highly significant inventions date back at least as far as the fifth century CE.

The Arabs encountered them at the beginning of the 8th century CE, when Hajj sent out an army under Muhammad Ben al-Qasim to conquer the Indus Valley and the Punjab. But it is far more likely that the army had nothing to do with it, and that it was necessary to wait for a delegation of scholars before Indian science was transmitted to the Islamic world. This is, indeed, Ibn Khaldun’s (1332 - 1395) explanation, who says in his Prolegomena that the Arabs received science from the Indians, as well as their numerals and calculation methods, when a group of erudite Indian scholars came to the court of the caliph al-Mansur in year 156 of the Hegira (= 776 CE) Muqaddimah, translated by M. De Slane, II, p. 300).

Ibn Khaldun’s version corresponds closely with earlier texts, especially with a tale told by the astronomer Ibn al-Adami in about 900, which is referred to by the court patron Hasan al-Qifti (1172-1288) in his Chronology of the Scholars.

“Al-Husayn Ben Muhammad Ben Hamid, known as Ibn al-Adami, tells in his Great Table, entitled Necklace of Pearls, that a person from India presented himself before the Caliph al-Mansur in the year 156 (of the Hegira = 776 CE) who was well versed in the sindhind method of calculation related to the movement of heavenly bodies, and having ways of calculating equations based on kardaja calculated in half-degrees, and what is more various techniques to determine solar and lunar eclipses, co-ascendants of ecliptic signs and other similar things. This task was given to Muhammad Ben Ibrahim al-Fazarri who thus conceived a work known by astronomers as the Great Sindhind. In the Indian language sindhind means “eternal duration”.

Much can be learned from this. The repetition of the word sindhind is significant; it is the Arabic translation of the Sanskrit “ siddhanta, the general term for Indian astronomic treatises, which contained a complete set of instructions for calculating, for example, lunar or solar eclipses, including the trigonometric formulae for true longitude. The “sindhind” method thus stands for the set of elements contained in such treatises. As for the word kardaja, which is also frequently used, it means “sine” and derives from an Arabic deformation of the Sanskrit ardhajya (literally “semi-chord”) which Indian astronomers used, from the time of Aryabhatta, for this trigonometric function which is the basis of all calculations in the Indian siddhanta system.





All Indian astronomers noted their numbers by using Sanskrit numerical symbols: this notation gave them a solid base for noting numeric data and was based on a decimal place-value system using zero.

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This method is presented in the mathematician and astronomer Brahmagupta’s (628) Brahmasphutasiddanta and the astrologer Varahamihira’s (575) Panchasiddhanta. But is was explained long before these treatises in the astronomer Aryabhata’s Aryabhatiya (510). All Indian astronomers noted their numbers by using Sanskrit numerical symbols: this notation gave them a solid base for noting numeric data and was based on a decimal place-value system using zero. In other words, when the Arabs learnt Indian astronomy, they inevitably came up against Indian numerals and calculation methods. So that the arrival of the two branches of knowledge precisely coincided. This is confirmed by Al-Biruni’s Kitab fi tahqiq I ma li’l hind (c. 1030), which tells of his 36 years stay in India.

Long before the Arabic conquest, the Persian king Khosroes Anushirwan (531- 579) sent a cultural mission to India and brought back many Indian scientists to Jundishapur. It was at Edese, Nisibe, Keneshre and Jundishapur…..that the first works in Sanskrit were discovered. During the assimilation of Indian science, the Arabs were helped by many Hindu Brahmins, who were often received at the court of Baghdad by enlightened Caliphs. They were assisted by Persians and Christians from Syria and Mesopotamia, who, being fervent admirers of Indian cultures, had gone so far as to learn Sanskrit. The Buddhists also greatly contributed, especially those converted to Islam, such as Barmak who was sent to India to study astrology, medicine and pharmacy and who, on his return to Muslim territory, translated many Sanskrit texts into Arabic.

Abu’l Hasan al-Qifti ( ? ) Arab scholar and author of Chronology of the Scholars, speaks of Arab admiration for Indian place-value system and methods of calculation.

“Among those parts of their sciences which came to us, the numerical calculation….it is the swiftest and most complete method of calculation, the easiest to understand and the simplest to learn; it bears witness to the Indians’ piercing intellect, fine creativity and their superior understanding and inventive genius.”

(source: The Universal History of Numbers - By Georges Ifrah p. 511 - 589). For more refer to chapter on Hindu Culture1 and Quotes321_340). For more refer to chapter on Greater India: Suvarnabhumi and Sacred Angkor