Philosopher Mathematicians of India

Philosopher Mathematicians of India
India is a religious country. In ancient India people used to give much importance to the religion and religious ceremonies. They evaluate the utility of any knowledge by its use in understanding the religion and its philosophy or its utility in performing religious ceremonies. Due to these special circumstances the religious centres and religious texts are very important sources to bring out the development of knowledge in any field. In the old age, the hermitages were the centres of research and higher learning. Learned Philosophers and saints of India at these Centres composed almost all the religious literature. The literature which either used in understanding these Philosophical texts or useful in performing religious ceremonies were also composed there. The Geometrical knowledge used in the preparation of different types of Altars is available in Sulba Sýtra composed prior to the age of Euclid (300 B.C.) and Pythāgoras (540 B.C.). The details are very explicit and clear. The old Jaina and Buddhist texts contain the details of number systems, use of large numbers and other Mathematical information. In the Vedic tradition Upanadas, Brāhmaa, Arayaka and Sa´hitās are good sources of Mathematical knowledge available in the contemporary periods. At present the contribution of āryabhata (499 A.D.), Brahmagupta (628 A.D.), Sridharācārya (799 A.D.), Mahāvîrācārya (850 A.D.), Bhāskarācārya (1150A.D.), Nārāyaa (13th C.A.D. etc.) have come into light by the constant efforts of B.B.Datta, A.N.Singh, K.S.Shukla, G.S.Pande, R.C.Gupta, A.K.Bag, T.A.Sarswati & L.C.Jain but the mathematical material available in Non-Mathematical/ Philosophical texts are still to be explored. Of course  some efforts has been made here & there but a more extensive and systematic effort is still required for the evaluation of the Philosophical texts of Vedic, Jaina and Bauddha Traditions. Here I am giving the list of certain Non-Mathematical Canons which may be evaluated

Vedic Tradition
1. Vedas 2. Baudhāyan Sulba Sýtra 3. āptastambh Sulba Sýtra 4. Vājasneyî Sa´hitā 5. Atreya Brāhmaa B. Jaina Tradition : 6. Pancāstikāya 7. Sýrya Prajñapti & its Commentary 8. Sthānāga Sýtra & its Commentary 9. Bhagavatî Sýtra & its Commentary 10. Anuyogadvāra Sýtra & its Commentary 11. Tiloyapaattî 12. Dhavalā Commentary 13. Jambuddivapaati Sa´gaho 14. Trilokasāra & its Commentary 15. Gomma²asāra & its Commentary 16. Lokavibhāga & its Commentary 17. Samyajñāncandrikā Commentary C. Bauddha Tradition : 18. Abhidharma Ko¹a 19. Dhamma Sangiî 20. Lalita Vistara We want to make it clear that the authors of these texts never intended to develop any mathematical principle or produce any new mathematical thought but they used mathematics as a tool to explain the concerning philosophical thoughts. For e.g. in Jaina canons, mathematics appear in giving geographical and cosmographical details of cosmos and to explain the concepts of Karma theory, while in the Vedic tradition, geometry is found in the preparation of   religious Altars & explaining the other rituals. In Buddhist Canons the large number and the fractions appear in giving the authentic details of their faith. I am listing here the mathematical concepts and rules which are available in the Indian philosophical texts prior to any mathematical text.

Mathematical concepts
I. The concept & use of zero and decimal place value system. II. Binary system. III. Classification of Numbers in        different ways like- A.	Countable (Sa´kyāta), Uncountable (Asa´kyāta), Infinite (Ananta) B.	Even (Yugma) and odd (Oja) IV. Statement of Pythāgoras Theorem. V. Concept and use of combination and permutation. VI. Process of making fundamental operations on fractions. VII. Concept and use of logarithms with base 2, 3, & 4 and antilogarithms VIII. Formula for finding Area,                     Circumference, Volume and surface of several unique Geometrical figures. IX. Use of several types of sequences. X. Concept of continued fraction. XI. Concept and use of set and operations on set. XII. Concept of probability under the name avaktavya. Several other concepts and rules are also available. All these formulae and concepts are first time found in Indian philosophical texts. Therefore the credit for the invention of these concepts/rules may be given to the Indian philosophers. Recently two Ph.D.s have been awarded by two different universities. 1. Dr. Pragati Jain,  ācārya Vîrasen & his Mathematical Contribution C.C.S.              University, Meerut, 2006. 2. Dr. N. Shiv Kumar, ācārya Yatîvâabha & his Mathematical Contribution Mysore University, Mysore, 2008 One Research Project completed by Dr. Anupam Jain in Jain Vishva Bharti- Ladnun-  Mathematical Content of Ardhamāgadhî Prākât Literature”,  2008 One Ph.D. work is going on in D.A. University by Deepak Jadhav on Mensuration in Ancient India (with Special Reference to Nemicandrācārya) We feel that rather than these scattered work, the comprensive study should be made under the title Philosopher Mathematicians of India.