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HISTORICAL NOTE: THE JAINA SCHOOL OF INDIAN MATHEMATICS
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types of infinities are mentioned in canonical texts (Gupta 1993, p. 24)".
These achievements are, according to R C Gupta, from ancient lokottara ganita of the school (Gupta 1993, p. 24). The present author too would like to point out that these achievements belonged to only the canonical class of the school. The exclusive class, which separated from the canonical class to provide mathematics education to common people, never referred to these achievements, perhaps for the reason that it could not find the areas of their application in the contemporary civil life. 5.6. We have noticed, although in brief, above that the Jaina school of Indian mathematics lasted for more than two thousand years. It not only prolonged but also it was varied in terms of using the languages, although Prakrit along with its different forms was the most used one among them, and having different purposes including the demonstration of canonical thoughts using mathematics and providing mathematics education to the civil society. The division, whatever it may be, of the school of this sort cannot be an ideal one. This is illustrated from the following examples.
Madhavacandra Traividya was an immediate disciple of Nemicandra as he himself claims to be so (Mukhtara and Patni 1975, v. 1, p. 768). He wrote a very useful commentary on the Trilokasāra of Nemicandra (981 CE). The most interesting, especially for the historians of mathematics feature about his commentary is that it contains rationales to mathematical rules given in the Trilokasāra. He is said to have authored the Sattrimsikä (“The textbook of thirty six logistics and determinations>'). It is the refined-essence (sodhya-sāra) of the <Ganita»-sära-sangraha of «Mahā Vīrācārya (Jain, Anupam 1988, pp. 65- 72). Since his commentary contains mathematics along with canonical discussion while the
Şattrimsikā is exclusively on mathematics, he must belong to both of our theorized classes. It is hereby decided that a particular mathematician can be placed in both of the classes if his one treatise belongs to the canonical class and the other belongs to the exclusive class but one particular treatise of any mathematician should not be placed in both of them.
The Ganitasāra was composed, in eighty eight Hindi verses, by Hemarāja (c. 1673) exclusively on the twenty one-fold number system. It seems to have been aimed at imparting education of that system to common Jaina Srāvakas (devout listeners) of his time (Jain, Anupam 1988b, 56). This is why the present author suggests placing it in the exclusive class although it contains lokottara ganita.
There are also many such treatises that contain mathematical thoughts not along with canonical discussion nor are written exclusively on mathematics. Example of this sort is the Chando 'nuśäsana of Hemacandra (1088-1172 CE). He was a scholar of Jaina faith. The treatise is on Prakrit prosody. It contains mathematical thoughts pertaining to combinatorics (Alsdorf 1991, pp. 20-31). Since it is independent from the canonical discussion, we suggest placing it in the exclusive class. If not, for it, possibly a miscellaneous class has to be devised. 5.7. The way in which mathematics dealt and developed by the Jainas was much mo tradition. It was a school, which we have noticed from the beginning of this paper. It was not closely related to the mainstream "classical Sanskrit mathematical writings”, as far as language and mathematics are concerned, as most of its treatises were composed in Prakrit and most of the mathematics dealt and developed in the canonical class is entirely different. At the same time, it seems to be closely related to the mainstream
"Earlier to this paper Madhavacandra Traividya was placed in the exclusive class alone by the present author. See Jadhav 2013,
pp. 46 and 48. This paper onwards, he changes his view in this regard.
