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century that the Jain texts Ganitasar Samgraha of Mahaviracharya dealt with mathematics independently. For the last fifty years or so, efforts are being made by the Jain scholars to present the mathematical contents of Jains, at various National and International Seminars on the History of Mathematics.
The growth of Jain Mathematics was mainly based upon the geometry of figures and the concept of numbers. Mathematics, particularly Altar geometry, bionomical series, originated in the Vedic rituals and in general social and economic conditions. The Vedic Hindus already gave evidence of their striking interest in large numbers built up on the basis of 10 and its powers. Thus place names have been given up to parardha 102. The Pancavimsa Brahmana uses these numbers in fixing the daksinas of various sacrifices. Yajurveda, 17/2 mentions upto Mahasankha, in which 20 digits are included.
Similarly, the Jains imbibed this interest in large numbers and went upto ten places of decimal and beyond. Their biggest number, called Shirsprahelika, comprises 54 digits followed by 140 zeros. A familiar question, which the Jains used to ask was what is the number of mustard seeds required to fill a hemispherical trough as large as the Jambodvipa with a diameter of 100,000 yojans? Then there are other dvipas and bowels of the oceans, which are to be similarly filled with mustard seeds. The total number of total seeds will still be less than the highest numerable (samkhyeya). This part of Mathematics is known as Upama-simile ganita. Their units are pallayopama, the sagarropama, the avasarpini, and the utsarpani. They are employed in mentioning the longevity of bios in various life forms. Beyond the highest numerable is the group called the innumerable (asamkhyeya) and beyond that the third group the infinite (ananta). This concept of large numbers gave a new dimension to Jain Cosmology and Cosmography.
Jains developed the basic geometry and used it to explain the shape and extent of the universe, its center (ruchak pradesha), heaven, hell, etc. Besides curved directions, Krishna Rajji (Black holes equivalents) etc. are also described using Geometry. Geometry helped in explaining the existence and nature of six dravyas which constitutes LokaUniverse. The interesting part is that the geometrical systems were used not only on the material substances but also on non-material substances. Though soul is a shapeless existence but according to Jain philosophy soul possesses innumerable pradesas. These pradesas expand and contract according to the shape of the body. It is remarkable to note that when the soul finally leaves karma and becomes Siddha, its volume remains two-third only. This change shows that there is something significant in the geometrical structure of the soul. We find in Vedic literature also that there is division in the objects with shape and objects without shape. In Sankhya philosophy 'Purusa' i.e. soul is shapeless and Prakriti is with form. Space is an extension of Prakriti. Hence space has a form. Jains describe certain substances like space, medium of motion, medium of rest, time, soul as non-material in universe, however they are represented by their smallest units' i.e. pradesas. This discussion needs more research work.
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