**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?]Brahmaguptaâ€™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.