History of Hindu Mathematics: A Source Book v1.c7.s15: 15. Hindu Numerals in Arabia

History of Hindu Mathematics: A Source Book v1.c7.s15

Language: English

15. Hindu Numerals in Arabia

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¹ For details consult Cajori's *History of Mathematics*, and Smith and Karpinski's *Hindu Arabic Numerals*.

The regular history of the Arabs begins after the flight of Mohammad from Mecca to Medina in A.D. 622. The spread of Islam succeeded in bringing together the scattered tribes of the Arabian Peninsula and creating a powerful nation. The united Arabs, within a short space of time, conquered the whole of Northern Africa and the Spanish Peninsula, and extended their dominions in the east upto the western border of India. They easily put aside their former nomadic life, and adopted a higher civilisation.

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The foundations of Arabic literature and science were laid between 750-850 A.D. This was done chiefly with the aid of foreigners and with foreign material. The bulk of their narrative literature came to the Arabs in translation from Persian. Books on the science of war, the knowledge of weapons, the veterinary art, falconry, and the various methods of divination, and some books on medicine were translated from Sanskrit and Persian. They got the exact sciences from Greece and India.

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Before the time of Mohammad the Arabs did not possess a satisfactory numeral notation. The numerous computations connected with the financial administration of the conquered lands, however, made the use of a developed numeral notation indispensable. In some localities the numerals of the more civilised conquered nations were used for a time. Thus in Syria, the Greek notation was retained, and in Egypt the Coptic. To this early period belongs the Edict of Khalif Walid (699) which forbade the use of the Greek language in public accounts, but made a special reservation in favour of Greek letters as numerical signs, on the ground that the Arabic language possessed no numerals of its own.¹ The Arabic letters gradually replaced the Greek ones in the alphabetic notation and the *abjad* notation came to be used. It is probable that the Arabs had come to know of the Hindu numerals from the writings of scholars like Sebokht, and aslo of their old *ghobâr* forms from other sources. But as their informants could not supply all the necessary information (*e.g.*, the methods of performing the ordinary operations of arithmetic) these numerals had to wait for another century before they were adopted in some of their mathematical works.

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¹ Theophanes (758-818 A.D.), "Chronographia;" *Scriptores Historiae Byzantinae*, Vol. XXXIX, Bonnane, 1839, p. 575; quoted by Smith and Karpinski, *l.c.*, p. 64, note.

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During the reign of the Khalif Al-Mansûr (753–774 A.D.) there came embassies from Sindh to Baghdad, and among them were scholars, who brought along with them several works on mathematics including the *Brâhma-sphuṭa-siddhânta* and the *Khaṇḍa-khâdyaka* of Brahmagupta. With the help of those scholars, Al-fazârî, perhaps also Yâkub ibn Târik, translated them into Arabic. Both works were largely used and exercised great influence on Arab mathematics. It was on that occasion that the Arabs first became acquainted with a scientific system of astronomy. It is believed by all writers on the subject that it was at that time that the Hindu numerals were first definitely introduced amongst the Arabs. It also seems that the Arabs at first adopted the *ghobâr* forms of the numerals, which they had already obtained (but without zero) from the Alexandrians, or from the Syrians who were employed as translators by the Khalifs at Baghdad. Al-Khowârîzmî (825), one of the earliest writers on arithmetic among the Arabs, has used the *ghobâr* forms.¹ But not long afterwards, the Arabs realised that the *ghobâr* forms were not suited to their right-to-left script. Then there appears to have been made an attempt to use more convenient forms. But as people had got accustomed to the *ghobâr* forms, they did not like to give them up, and so we find a struggle² between the two forms, which continued for about two centuries (10th and 11th) until at last the more convenient ones came into general use. The west Arabs on the other hand did not adopt the modified forms of the east Arabs, but continued to use the *ghobâr* forms, and were thus able to transmit them to awakening Europe. This, perhaps, explains in a better way the divergence in the forms of modern Arabic and modern European numerals, than any theory yet propounded.

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¹ Smith and Karpinski, *l.c.*, p. 98.

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² One document cited by Woepcke is of special interest since it shows the use of the ordinary Arabic forms alongside the *ghobâr* at an early date (970 A.D.). The title of the work is “Interesting and Beautiful Problems on Numbers” copied by Ahmed ibn Mohammed ibn Abdaljalîl Abû Sa'id, al-Sijzî, (951-1024) from a work by a priest and physician, Nazîf ibn Yumn, al-Qass (died 990). Sprenger also calls attention to this fact (in *Zeit. d deutschen-morgenländischen Gesselschaft*, XLV, p. 367). Ali ibn Ahmed Al-Nasâvî (*c.* 1025) tells us that the symbolism of numbers was unsettled in his day (Smith and Karpinski, *l.c.*, p. 98).

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In a theory that was advanced by Woepcke, this divergence is explained by assuming that (1) about the second century after Christ, before zero had been invented, the Hindu numerals were brought to Alexandria, whence they spread to Rome and also to west Africa; (2) that in the eighth century, after the notation in India had been already much modified and perfected by the invention of zero, the Arabs at Baghdad got it from the Hindus; (3) that the Arabs of the west borrowed the Columbus-egg, the zero, from those in the east but retained the old forms of the nine numerals, if for no other reason, simply to be contrary to their political enemies of the east; (4) that the old forms were remembered by the west Arabs to be of Hindu origin, and were hence called *ghobâr* numerals; (5) that, since the eighth century, the numerals in India underwent further changes and assumed the greatly modified forms of modern Devanâgarî numerals.

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Now, as to the fact that these figures might have been known in Alexandria in the second century A.D., there is not much doubt. But the question naturally arises: Why should the Alexandrians use and retain a knowledge of these numerals? As far as we know, they did possess numeral notations of their own; why should they give preference to a foreign notation? These questions cannot be satisfactorily answered unless we assume that along with the nine symbols the principle of place-value and probably also the zero was communicated to them. But as they were unprepared for the reception of this abstract conception, they adopted the nine numerals only and used them on the apices. These numerals were then transmitted by them to Rome and to west Africa.

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The second assumption that the Hindu numeral figures of the eighth century were adopted by the Arabs is not supported by fact. The figures that are found in the old Arabic manuscripts resemble either the *ghobâr* numerals or the modern Arabic more than the Hindu numerals of the eighth century. In fact, we have every reason to believe that the Arabs knew these *ghobâr* forms, perhaps without the principle of place-value and zero, long before they had direct contact with India, and that they adopted zero only about 750 A.D.

Linked texts (2)

Brāhmasphuṭasiddhānta — Brahmagupta, Sanskrit
Khaṇḍakhādyaka — Brahmagupta, Sanskrit