History of Indian Mathematics
Certain excavations in Harappa and Mohenjodaro suggests of practical Mathematics being used during that time. They used bricks and other weights of various geometrical shapes which demonstrated the fact they had sound knowledge of basic geometry. The inhabitants of Mohenjodaro had developed a special ruler which was more accurate in measuring heights of things. Thus it was very evident that from early times the civilisation that originated in India had a niche for accuracy with regard to measurements. It has also been recorded that the decimal place-value system which is used today had first originated in India and then it passed to Islamic countries and Europe.
It was during the Vedic Period that the concept of large numbers was used in Indian Mathematics. Although it is said that the ancient geometry was described in detail in the Sulbasutras but history has given evidence that the essential concepts of geometry was first found in the Vedic mythological texts like the Shatapatha Brahmana and the Taittiriya Samhita. It has also been found that the study of mathematical astronomy dates back to the third millennium BC and it is obvious that the study of geometry and mathematics existed even during that time to support the study of mathematical astronomy. The earliest Mathematics in India had developed in the Indus Valley Civilisation.
Baudhayana Sulba Sutra, the best-known Sulba Sutra, contains the examples of Pythagorean triples. The Harappans were known for a uniform system of measures and weights.
Source of Indian Mathematics
Indian Mathematics to a large extent is also linked with some of the religious texts. It mainly consisted of Sulbasutras which gave rules to construct altars. Thus it can be said that it contained a lot of geometrical knowledge but this geometrical knowledge was developed not for pure mathematical reasons but the most important reason associated with it was mostly religious. The main Sulbasutras were composed by Baudhayana, Manava, Apastamba and Katyayana.
As the period of Sulbasutras were about to end around the middle of the third century BC, the Brahmi numerals had begun to appear. The Brahmi numerals were in fact the earliest numerals that had developed in the realm of Indian Mathematics. It was the Brahmi numerals which have developed today into the numerals which are generally used by people in their daily lives.
Soon the Vedic Religion with its sacrificial rites began to take a back seat and other religions started taking primacy. One such religion which developed in India during 6th century BC was Jainism.
Influences on Indian Mathematics
It can be said that Vedic religion gave primacy to Mathematics to construct sacrificial altars, Jain Mathematics brought in the concept of infinite. In the later stages the development of Mathematics was driven by the development of astrology. Astrology was of prime importance in the Indian subcontinent because it was with the help of Astrology that the movement of planets and stars could be easily studied. At the same time religion also played an important role in the development of mathematics in the Indian subcontinent because without the knowledge of mathematics it was not possible to develop calendars which would fix dates for the performance of religious ceremonies. In India for many centuries Mathematics was an applied science and mathematicians went on developing mathematical solutions in order to solve practical problems.
Earlier the theories of Mathematics were transmitted orally but with growing complication the oral tradition of Mathematics got replaced with written works and the first written work in Indian Mathematics was done by Aryabhata in 499 BC.
Jain Mathematics was important to the history of Indian Mathematics because it served as a link between Vedic Period and the Classical Period. A significant contribution of Jain Mathematics lay in freeing Indian Mathematics from religious and ritualistic clutches. The main topics with which Jain Mathematics dealt with included the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quadratic equations, and permutations and combinations. It was Jain Mathematics which had classified numbers into three categories namely the enumerable, innumerable and infinite.
Some of the notable works in Mathematics of Jainism were Surya Prajnapti, Vaishali Ganit, the Sthananga Sutr, the Anoyogdwar Sutra and the Satkhandagama. The popular Jain Mathematicians of the age were Bhadrabahu and Umasvati.
The Kerala School of Mathematics finds an important place in the field of Indian Mathematics. Chitrabhanu was a notable mathematician from Kerala in the sixteenth century. It was he who gave integer solutions to twenty-one types of systems of two algebraic equations.
Finally with the beginning of 500 AD the classical era of Indian Mathematics ushered in with the emergence of Aryabhata. His work included a summary of Jain Mathematics and also began the new era of astronomy and mathematics in India. The ideas of astronomy which were discovered by him were in the true sense revolutionary. It was he who had brought in the concepts of eclipses instead of Rahu, the Dhruva Rahu and the Parva Rahu. He had also brought in the concept of trigonometry in order to solve his astronomical problems and also used integers to make his solutions easier.
In the classical period the other Mathematicians who had emerged in the Indian subcontinent were Varahamihira, Brahmagupta, Bhaskara I, Mahavira and Bhaskara II. Indian Mathematics is greatly indebted to Aryabhata for mathematical operations like calculus, differential equations, exponential functions and a lot more. These Mathematicians had given wider dimensions and clearer shape to many branches of Indian Mathematics. Their contribution was unlike Vedic Mathematics because it included contributions in the field of astronomy as well. In fact during that time mathematics was included in the domain of astral science. The main subdivisions of that time were mathematical sciences, horoscope astrology and divination.
Varahamihira on the other hand had made important contributions in the field of trigonometry. It was he who had brought in the concept of sine and cosine. It was during the seventh and eighth centuries that two different fields of mathematics evolved namely arithmetic and algebra. Brahmagupta on the other hand had made major contributions in the field of mathematics by bringing in a number of theorems. He had also worked on a number of equations and integers.
Bhaskra I another notable mathematician of the classical period had expanded the work of Aryabhata. He had given solutions to indeterminate equations, had given a rational explanation of the sine function and had given the formula of calculating the sine of an acute angle without the use of table up to two decimal places.
Some of the other well known Mathematicians of the era were Govindaswami, Mahavira, Sankara, Sridhara, Aryabhata II, Vijayanandi and Bhaskara II and it was believed that with Bhaskara II development in the field of Indian Mathematics had abated.
Hence it can be concluded saying that Indian Mathematics is greatly rich and varied in nature. A lot of countries owe its mathematical traditions to India because only a few countries were developed so greatly in the field of mathematics at such an early age. The entire modern mathematics including the computer language is indebted to ancient Indian Mathematics.