Date & Time: February 11, 2013, 16:00-17:00.

Venue: Ramanujan Hall

Title:The Kuttakadhyayah of Brahmagupta: Emergence of Algebra in Ancient India

Speaker:Prof. Amartya Dutta, Indian Statistical Institute, Kolkata

Abstract:Algebraic ideas seem to pervade Indian thought from remote antiquity. Ancient mystics freely used symbols and symbolic language to express psycho- spiritual knowledge. In mathematics, the constructive geometry of the SulbaSutras, the oldest extant mathematics texts, involve algebraic formulae in geometric form. The discoveries of certain algorithms in computational arithmetic are also indicative of a subtle algebraic acumen. The Classical Age in India witnessed the efflorescence of classical algebra. The treatise of Aryabhata (c. 500 CE) already contains several algebra results and techniques. Brahmagupta (628 CE) was perhaps the first to recognise algebra as a distinct and powerful branch of mathematics. His Kuttakadhyayah (chapter on algebra) articulates the foundations of the subject: use of varna for unknowns, the formation and manoeuvring of equations, operations with negative numbers and zero, etc. Further, key ideas of modern abstract algebra and number theory are implicit in [UTF-8?]Brahmagupta’s treatment of the indeterminate equation Dx^2 + 1 = y^ 2 . We shall discuss certain aspects of the evolution of algebra in ancient India up to the time of Brahmagupta, with special emphasis on his Kuttakadhyayah.