History of Hindu Mathematics: A Source Book v1.c7.s16: 16. Hindu Numerals in Europe
History of Hindu Mathematics: A Source Book v1.c7.s16
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16. Hindu Numerals in Europe
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**Boethius Question.** It cannot be definitely said when and how the Hindu numerals reached Europe. Their earliest occurrence is found in a manuscript of the Geometry of Boethius (*c.* 500), said to belong to the tenth century. There are several other manuscripts of this work and they all contain the numerals. Some of these contain the zero whilst the others do not. If these manuscripts (or the portions of them that contain the numerals) be regarded as genuine, it will have to be acknowledged that the Hindu numerals had reached Southern Europe about the close of the fifth century. There are some who consider the passages dealing with the Hindu numerals in the Geometry of Boethius to be spurious. Their arguments can be summarised as below :
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(1) The passages in question have no connection with the main theme of the work, which is geometry. The Hindu numerals have not been mentioned in the Arithmetic of Boethius. They have not been used by him anywhere else. Neither Boethius' contemporary Capella (*c.* 475), nor any of the numerous mediaeval writers who knew the works of Boethius makes any reference to the numerals.
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(2) The Hindu numeral notation was perfected in India much later than the fifth century, so that the numerals, even if they had been taken to Europe along the trade routes, had no claim to any superiority over the numerals of the west, and so could not have attracted the attention of Boethius.
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Of the above arguments, the second is against facts, for it is now established that the Hindu numeral notation with zero was perfected and was in use in India during the earliest centuries of the Christian era. The numerals could have, therefore, easily reached Europe along the trade routes in the fifth century or even earlier. The first argument is purely speculative and throws doubt on the authenticity of the occurrence of the numerals in Boethius' Geometry. It does not prove anything. It seems to us unfair to question the genuineness of the occurrence of the numerals, when they are found in all manuscripts of the work that are in existence now. Their occurrence in the Geometry can be easily explained on the ground that Boethius' knowledge of those numerals was very meagre. He had obtained the forms from some source—from the Neo-Pythagoreans or direct from some merchant or wandering scholar—but did not know their use. He might have known their use in writing big numbers by the help of the principle of place-value and zero, but he certainly did not know how the elementary operations of arithmetic were to be performed with those numerals. Hence he could make no use of them in his arithmetic or any other work. The writings of Sebokht (*c.* 650) show that the fame of the numerals had reached the west long before they were definitely introduced there. The question of the introduction of the Hindu numerals through the agency of Boethius may, therefore, be regarded as an open one, until further investigations decide it one way or the other.
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**Definite Evidence.** The first writer to describe the *ghobâr* numerals in any scientific way in Christian Europe was Gerbert, a French monk. He was a distinguished scholar, held high ecclesiastical positions in Italy, and was elected to the Papal chair (999). He had also been to Spain for three years. It is not definitely known where he found these numerals. Some say that he obtained them from the Moors in Spain, while others assert that he got them from some other source, probably through the merchants. We find that Gerbert did not appreciate these numerals (and rightly, for there was neither zero nor the place-value), and that in his works, known as the *Regula de abaco computi* and the *Libellus*, he has used the Roman forms. We thus see that upto the time of Gerbert (died 1003) the principle of place-value was not known in Europe.
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As early as 711 A.D., the power of the Goths was shattered at the battle of Jarez de le Frontera, and immediately afterwards the Moors became masters of Spain, and remained so for five hundred years. The knowledge of the modern system of notation which was definitely introduced at Baghdad about the middle of the eighth century must have travelled to Spain and from there made its way into Europe. The schools established by the Moors at Cordova, Granada, and Toledo were famous seats of learning throughout the middle ages, and attracted students from all parts of Europe. Thus although Europe may not be directly indebted to the Moors for its numerical symbols, it certainly is for that important principle which made the ordinary *ghobâr* forms superior to the Roman numerals.
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Several instances of the modern system of notation are to be found in Europe in the twelfth century, but no definite attempt seems to have been made for popularizing it before the thirteenth century. Perhaps the most influential in spreading these numerals in Europe was Leonardo Fibonacci of Pisa. Leonardo's father was a commercial agent at Bugia, the modern Bougie, on the coast of Barbary. It had one of the best harbours, and at the close of the twelfth century was the centre of African commerce. Here Leonardo went to school to a Moorish master. On attaining manhood he started on a tour of the Mediterranean and visited Egypt, Syria, Greece, Italy and Provence, meeting with scholars and merchants and imbibing a knowledge of the various systems of numbers in use in the centres of trade. All these systems, he however says, he counted as errors compared with that of the Hindus.¹ Returning to Pisa he wrote his *Liber Abaci* in 1202, rewriting it in 1228.² In this the Hindu numerals are explained and used in the usual computations of business. At first Leonardo's book met with a cold reception from the public, because it was too advanced for the merchants and too novel for the universities. However, as time went on people began to realise its importance, and then we find it occupying the highest place among the mathematical classics of the period.
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¹ "Sed hoc totum et algorismum atque arcus pictagore quasi errorem computavi respectu modi indorum."
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² Smith and Karpinski, *l. c.*, p. 131.
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Among other writers whose treatises have helped the spread of the numerals may be mentioned Alexander de Villa Die (*c.* 1240) and John of Halifax (*c.* 1250).
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A most determined fight against the spread of these numerals was put up by the abacists who did not use zero but employed an abacus and the apices. But the writings of men like Leonardo succeeded in silencing them, although it took two or three centuries to do so. By the middle of the fifteenth century we find that these numerals were generally adopted by all the nations of western Europe, but they came into common use only in the seventeenth century.