Pramāṇa · Search · About · API

Hindu Achievements in Exact Science: A Study in the History of Scientific Development c7: I. Arithmetic

Hindu Achievements in Exact Science: A Study in the History of Scientific Development c7

Language
English

I. Arithmetic

c7.2

A GENERAL idea of the achievements of the Hindu brain may be had from the following remarks of Cajori:

c7.3

"It is remarkable to what extent Indian mathematics enter into the science of our time. Both the form and the spirit of the arithmetic and algebra of modern times are essentially Indian and not Grecian. Think of that most perfect of mathematical symbolisms, the Hindu notation, think of the Indian arithmetical operations nearly as perfect as our own, think of their algebraic methods, and then judge whether the Brahmins on the banks of the Ganges are not entitled to some credit. Unfortunately some of the most brilliant of the Hindu discoveries in indeterminate analysis reached Europe too late to exert influence they would have exerted, had they come two or three centuries earlier."

c7.4

As De Morgan admits, "Hindu arithmetic is greatly superior to any which the Greeks had. Indian arithmetic is that which we now use."³³

c7.5

The Hindus were the greatest calculators of antiquity. They could raise the numbers to various powers. The extraction of square or cube root was a child's play to them.

c7.6

The two foundations of arithmetic were discovered by the Hindus:

c7.7

(1) The symbols of numbers, or numerals as they are called, and

c7.8

(2) The decimal system of notation.

c7.9

Numerals have been in use in India since at least the third century B.C. They were employed in the Minor Rock Edicts of Asoka the Great (256 B.C.). In modern times the numerals are wrongly known as "Arabic" because the European nations got them from their Saracen (Arab) teachers.⁶¹

c7.10

The decimal system was known to Aryabhata (A.D. 476) and Brahmagupta (A.D. 598–660), and fully described by Bhaskaracharya (1114). In Subandhu's "Vasavadatta," a Sanskrit prose romance (A.D. 550–606?) the stars are described as zero. In "Vyasa-bhasya," also, the system is referred to. The transformation of substance in chemical fusion through the "unequal distribution of forces" is there illustrated by a mathematical analogy: "Even as the same figure '1' stands for a hundred in the place of hundred, for ten in the place of ten, and for a unit in the place of a unit." The "Vyasa-bhasya" cannot have been composed later than the sixth century A.D. The decimal system was therefore known to the Hindus long before its appearance in the writings of the Arabs or Græco-Syrians.⁵⁹

c7.11

The Saracens learnt from the Hindus both the system of numeration and the method of computation. Even in the time of Caliph Walid (705–15) the Saracens had to depend on alphabetical symbols. They had no figures for numbers yet. A Hindu scientific mission reached Mansur’s court from Sindh in 773. This introduced the Moslems to Hindu astronomical tables. The Saracen astronomical work thus compiled was abridged by Musa, the Librarian of Caliph Mamun (813–33). “And he studied and communicated to his countrymen the Indian compendious method of computation, i.e., their arithmetic, and their analytic calculus.”⁷

c7.12

This was the first introduction of the decimal system among the Saracens (830). They have ever since acknowledged their debt to the Hindus. Alberuni (1033) wrote: “The numeral signs which we use are derived from the finest forms of the Hindu signs.”

c7.13

It was probably in the twelfth century that the Europeans learnt this Hindu science from their Saracen masters. Leonardo of Pisa,⁶¹ an Italian merchant, was educated in Barbary, and thus became acquainted with the so-called Arabic numerals and Musa’s work on Algebra based on the Sanskrit. In 1202 was published his “Liber Abbaci.” This was the beginning of modern arithmetic in Europe. The pioneering work may have been done by Gerbert, a Frenchman, who learnt the Hindu system from the Mohammedan teachers at Cordova in Spain (*c* 970–80).⁶⁹ Musa, the distinguished Moslem mathematician, was thus the connecting link between the algebra and arithmetic of the Hindus and the mediæval European mathematics.

c7.14

At the commencement of the Christian era, the Chinese “adopted the decimal system of notation introduced by the Buddhists, and changed their ancient custom of writing figures from top to bottom for the Indian custom of from left to right.” ⁷⁵

Linked texts (2)