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HISTORICAL NOTE: THE JAINA SCHOOL OF INDIAN MATHEMATICS
class, the mathematicians contained in it are very important with regard to ancient and medieval Indian mathematics. The reason behind to be the small list is that the Jaina school of Indian mathematics has generally been under the domination of its canonical class. The authors of the exclusive class pay obeisance to those of the canonical class and state that they have gleaned material from the treatises of the canonical class (Padmavathamma 2000, vv. 1.17-1.19, p. 6; v. 1.70, p. 20; v. 7.49, p. 453). This is why the status of the canonical class can be said to be upper than that of the exclusive class in the Jaina school of Indian mathematics.
This claim and others, including the one regarding laukika ganita and alaukika ganita, of the present author get support from the following facts revealed and views expressed by Catherine Morice-Singh.
"During the one hundred and odd years since 1912, much has been written on the Ganitasarasangraha's mathematical contents, but no attempt has been undertaken to re-examine the text established by <M.> Rangacharya<, its first editor,> nor to trace the Jaina philosophical and cosmological elements in it, in spite of the fact that Jaina Studies has developed rapidly during the 20th century. The importance given to mathematics (ganita) by the Jaina thinkers who wanted to quantify in full details the entities existing in the universe is now well known, and the technical and specialized Jaina vocabulary attached to it is also better understood (Morice-Singh 2016, p. 41)."
Here it may be noted that Mathématiques et cosmologie jaina Nombres et algorithmes dans le Ganitasarasangraha et la Tiloyapanṇatti is her doctoral thesis. "In the Ganitasarasangraha," further writes she, "the exceptionally developed and well-written introductory chapter supplies a great amount of details about the organization of mathematical topics and many explicit references to the Jaina context. The Ganitasarasangraha's
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first two chapters are then both fundamental, and in my thesis I have proposed a deep study of them along with a French translation. In order to reexamine Rangacharya's text and to identify his editorial choices, I examined some manuscripts available at the Government Oriental Manuscripts Library (Madras) hoping to find traces of his work and, in order to get a wider view on the elements of mathematics linked to the Jaina universe, I explored excerpts of different original texts (Dhavala, Trilokasāra, etc.) but mainly of the Tiloyapanṇalli, a Prakrit text (-6th to 9th century) belonging to the same Digambara tradition <to which the Ganitasarasangraha belonged›. The study of the impressive mathematical content of these texts has led me to propose answers to the two questions about the Ganitasarasangraha's structure... To express numbers, Mahāvīrācārya makes an intensive use of the word-numeral (bhūta-samkhyā) system, choosing often words belonging to the Jaina terminology, as for example lesya, associated to number 6. Here, Rangacharya, probably not knowing the meaning of lesya, deliberately corrected it into lekhya (v. 2.34)», which is incorrect... Mahāvīrācārya has, in every aspect of his work, managed to retain the essential and to separate "alaukikaganita" from "laukikaganita" without departing from the teachings of his tradition. For instance, the units of length in the Ganitasarasangraha (<v.> 1.25) start with the atom (anu) which is made of an ananta quantity of ultimate particles (paramānu), and an asamkhya number of samaya is required to constitute the first unit of time, the avali (<v.> 1.32): The distinction between ananta and
asamkhyāta is kept here, even if its utility doesn't appear in a mathematical text (Morice-Singh 2016, pp. 41-43)."
5.3. As far as their chronological order is concerned, the exclusive class must have appeared later than the canonical class. We do not know who all were the mathematicians of the exclusive class prior to Śrīdhara. However, it is certain that this class was in existence long before him.
