2:30 pm,Seminar Hall Ancient Indian Mathematics for modern Mathematicians Satyanad Kichenassamy Université de Reims ChampagneArdenne. 021219 Abstract Part I : Monday, December 2, 2:30 PM Part II: Wednesday, December 4,2:30 PM Title : Ancient Indian Mathematics for modern Mathematicians Part I : Recent progress on the analysis of ancient Indian mathematical texts Part II: The impact and modern relevance of ancient Indian Mathematics Abstract: Ancient Indian Mathematics is relevant to modern mathematics in two ways: as a remote source, but also as inspiration, because it contains concepts and results that are absent from modern mathematics. We show in modern terms to what extent our mathematics are the outgrowth of ancient Indian mathematics, and how they suggest new results and directions. We first consider: (i) Baudh\=ayana's approximate quadrature of the circle (early first millennium B.C.), (ii) Brahmagupta's geometry of the cyclic quadrilateral (seventh century); (iii) Brahmagupta's treatment of algebra and congruences. We have established the following results (in a series of papers from 2006 onwards); (a) in all three cases, the Sanskrit text is an \emph{apodictic discourse} that contains precise definitions and statements, motivation and outlines of derivations, that would have been easy to follow by professional mathematicians of the time; (b) the resulting derivations and results, are mostly new: they are found in no later work up to the present; (c) they were not recovered by modern mathematics, either because the latter lacks concepts that were natural to our authors, or because it is blinkered in ways Indian mathematicians were not. We then show that on selected examples that: (i) Indian science has had significant impact on the Mathematics of other cultures, and was part of the synthesis that is called "modern" Mathematics. (ii) There a continuity between ancient Indian Mathematics and current issues in Mathematics. (iii) Ancient Indian Science suggests improvements of known results, as well as new scientific developments.
