If modern mathematics could be, and fairly appropriately too, compared to a mighty river, its origins, like that of any river, would consist of trickles and rivulets, said Dr. Ramaiyengar Sridharan, the Adjunct Professor and INSA Senior Scientist at Chennai Mathematical Institute, Chennai. He was delivering the frontier series lecture on ‘Mathematics of two cultures: ancient Indian and Greek.’
Mathematical awakening at the dawn of human civilization does indeed belong to the category of “undefinable” - the “Anfang” in Hegel’s language - the beginnings with a primacy”. The fulfilment of its inherent potency had to wait for the growth of human civilization. This fulfilment in mathematics came substantially from two different cultures - the ancient Indian and the Greek.
Mathematics owes its form and content to the happy confluence of the “complementary” contributions of these two cultures. This complementarity arises mainly from the differing attitudes to life and reality of the peoples of the civilizations.
The roots of the ancient Indian mathematics, like most of the intellectual heritage of the country, go vastly to the Vedic tradition and, to a large extent, remain deferential to the Vedic thoughts. It dealt with arithmetic, arithmetic geometry and algorithms. The Greeks, however, dissatisfied with the “irrationality” of the actual reality, aspired and dreamt for an ideal world - a “rational” world.
A strong conviction in rationality brought, as a consequence, the deductive method exemplified by Euclid’s geometry. By a true miracle, there was a confluence of these two differing approaches that led eventually to the emergence of modern Mathematics, as it is understood today.