India – World Guru of Mathematics (Part – 6)

Posted on August 28, 2011

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ALGEBRA (BIJAGANITAM)

“As for as other countries are concerned we find that in the golden time of Greece Mathematics there was no sign of Algebra with respect to modern concept of Algebra. In classical period Greece people had ability to solve tough questions of Beez Ganit (Later the name Algebra became more popular) but there all solutions were based on Geometrical Mathematics. For the first time in Greece world, the concept of Beez Ganit (Later the name Algebra became more popular) is described in a books of Diofantus (275 AD). By that time Indians were far ahead. This is worth noting that the shape and form of current Beez Ganit (Later the name Algebra became more popular) is originally Indian.”

In ancient India conventional mathematics termed Ganitam was known before the development of algebra. This is borne out by the name – Bijaganitam, which was given to the algebraic form of computation. Bijaganitam means ‘the other mathematics’ (Bija means ‘another’ or ‘second’ and Ganitam means mathematics). The fact that this name was chosen for this system of computation implies that it was recognised as a parallel system of computation, different from the conventional one which was used since the past and was till then the only one. Some have interpreted the term Bija to mean seed, symbolizing origin or beginning. And the inference that Bijaganitam was the original form of computation is derived. Credence is lent to this view by the existence of mathematics in the Vedic literature which was also shorthand method of computation.

But whatever the origin of algebra, it is certain that this technique of computation Originated in India and was current around 1500 years back. Aryabhatta an Indian mathematican who lived in the 5th century A.D. has referred to Bijaganitam in his treatise on Mathematics, Aryabhattiya. An Indian mathematician – astronomer, Bhaskaracharya has also authored a treatise on this subject. The treatise which is dated around the 12th century A.D. is entitled ‘Siddhanta-Shiromani’ of which one section is entitled Bijaganitam.

Thus the technique of algebraic computation was known and was developed in India in earlier times. From the 13th century onwards, India was subject to invasions from the Arabs and other Islamised communities like the Turks and Afghans. Along with the invaders: came chroniclers and critics like Al-beruni who studied Indian society and polity.

The Indian system of mathematics could not have escaped from their attention. It was also the age of the Islamic Renaissance and the Arabs generally improved upon the arts and sciences that they imbibed from the land they overran during their great Jehad. The system of mathematics they observed in India was adapted by them and given the name ‘Al-Jabr’ meaning ‘the reunion of broken parts’. ‘Al’ means ‘The’ & ‘Jabr’ mean ‘reunion’. This name given by the Arabs indicates that they took it from an external source and amalgamated it with their concepts about mathematics.

Between the 10th to 13th centuries, the Christian kingdoms of Europe made numerous attempts to reconquer the birthplace of Jesus Christ from its Mohammedan-Arab rulers. These attempts called the Crusades failed in their military objective, but the contacts they created between oriental and occidental nations resulted in a massive exchange of ideas. The technique of algebra could have passed on to the west at this time.

During the Renaissance in Europe, followed by the industrial revolution, the knowledge received from the east was further developed. Algebra as we know it today has lost any characteristics that betray its eastern origin save the fact that the term ‘algebra’ is a corruption of the term ‘Al jabr’ which the Arabs gave to Bijaganitam Incidentally the term Bijaganit is still use in India to refer to this subject.

In the year 1816, an Englishman by the name James Taylor translated Bhaskara’s Leelavati into English. A second English translation appeared in the following year (1817) by the English astronomer Henry Thomas Colebruke. Thus the works of this Indian mathematician astronomer were made known to the western world nearly 700 years after he had penned them, although his ideas had already reached the west through the Arabs many centuries earlier.

In the words of the Australian Indologist in his work, The Wonder That was India says

Arthur Llewellyn Basham

 “… the world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.”

Thus Indians could take their mathematical concepts to an abstract plane and with the aid of a simple numerical notation devise a rudimentary algebra as against the Greeks or the ancient Egyptians who due to their concern with the immediate measurement of physical objects remained confined to Mensuration and Geometry.

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…. Continues (Ancient Trignometry, Geometry, Algorithm)

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Posted in: Mathematics