Jaina School Of Indian Mathematics

Author(s): Dipak Jadhav
Publisher: Indian Journal of History of Science

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HISTORICAL NOTE: THE JAINA SCHOOL OF INDIAN MATHEMATICS
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included into exclusive class rather than as members of the mainstream classical Sanskrit mathematical tradition, who simply happen to be Jainas.
The present paper is mainly aimed at justifying and discussing the division of the Jaina school of Indian mathematics into the canonical class and the exclusive class. This will be done by means of theorization. In this regard, a set of factual ideas will be developed about the school in order to find some basis. By studying the way in which its treatises contain mathematics along with canonical discussion or exclusively and its mathematicians treat, we will explain how it fits into the above classes. In order to avoid any misunderstanding regarding the exclusive class against laukika ganita (worldly mathematics) and the canonical class against lokottara ganita (postworldly mathematics) an appropriate discussion containing a comparative analysis of these two different divisions has been accommodated.
the essence of mathematics') of Mahāvīra (c. 850) published in 1912, opines that:
"The answer to the questions as to the relation between the schools of India cannot yet be easily given. At first it would seem a simple matter to compare the treatises of the three or four great algebraists and to note the similarities and differences. When this is done, however, the result seems to be that the works of Brahmagupta, Mahāvīrācārya and Bhāskara may be described as similar in spirit but entirely different in detail. For example, all of these writers treat of the areas of polygons, but Mahāvīrācārya is the only one to make any point of those that are re-entrant. All of them touch upon the area of a segment of a circle, but all give different rules. The so called janya operation is akin to work found in Brahmagupta and yet none of the problems is the same. The shadow problems, primitive case of trigonometry and gnomonics, suggest a similarity among these three great writers and yet those of Mahāvīrācārya are much distinct than the one to be found in either Brahmagupta or Bhāskara and no questions are duplicated (Padmavathamma, 2000, p. 762)."
Smith accepts as early as in 1912 in more or less clear terms that there were the schools of mathematics in ancient and medieval India.
In ancient India, mathematics was not separated from astronomy. In fact, the former was developed for the service of the latter. It is now recognized that there was Brāmapaksa in Indian classical mathematical astronomy or Bramagupta school of Indian astronomy after the name of Indian mathematician and astronomer Brahmagupta (628 CE) (Plofker, 2014).
As far as the Jaina school of Indian mathematics is concerned, we shall see that it sustained for more than two thousand years adopting, developing, following and practicing certain kinds of mathematical thoughts in ancient and medieval India.
2. APPROVAL OF THE JAINA SCHOOL
OF INDIAN MATHEMATICS
Every academic discipline, from old theology to modern science and technology, has competing theories and perspectives with which it grows. Mathematics has been no exception. For example, John Napier (1550-1617 CE) and Jobst Bürgi (1552-1632 CE) discovered logarithms, but through an entirely different line of approach. The former's approach was geometric while the latter's was algebraic. Long before them the Jaina school of Indian mathematics approached logarithms on the basis of the number of possible divisions of a quantity by two (Jadhav 2002a; Jadhav 2003; Jadhav 2014).
The studies made on mathematical thoughts developed in ancient and medieval India and about their followers make us to appreciate that the schools of some sort did exist. David Eugene Smith, in the introduction written by him to the Ganita-sāra-sangraha ('Compendium of