Mathematics

While Dr. Ramanujam is a researcher in logic and automata theory, he also has been active in adult education and school science and mathematics education over the last three decades in India, mostly with the poorest sections of society. This work has also led him  to participate in committees at the national and state level. These two views of education, from high above in the committees, and from the ground in villages and urban slums, are in sharp contrast, and he will talk about his learning from this.

In this lecture, Dr. Vijay Bhatkar shares his mystical romance with Mathematics in his long career. After recalling the amazing contributions of Pingala, Aryabhatta, Madhava, Ramanujan, and the contemporary scientists, from the mathematical viewpoint, he jumps to his own unbelievable philosophical entry in Mathematics, where as an engineer, he was called upon to develop   India’s electronic industry, that introduced him to computers and information technology.

The most common notion of symmetry in mathematics and its applications is associated with groups, for instance the rotations, reflections, and translations of the euclidean plane.    In recent years, a more general structure known as a groupoid has been found to provide a broader notion of symmetry.

I will explain what a groupoid is, will give some basic examples, and will tell about some subjects to which they have been applied, including dance patterns, the "15 Puzzle", networks of coupled systems, and patterns like the tiles on a floor.

We start by explaining the nature of theory-building. Roughly, a "theory" is an organization of our thoughts on accumulated data on some domain of (human) experience. We shall apply this consideration to the atomic theory in chemistry which arose as an explanation of the philosophical notion of "matter". We shall then explain the role that Mathematics has played in this theory-building. In turn, this raises the question about the nature of Mathematics. In the process, we attempt to offer a definition of Mathematics.

We shall first briefly discuss the Indian Knowledge System and its parts such as Vedas, Philosophy, Puranas and Epics,  Linguistics, Mathematics, Astronomy, Engineering and Technology,  Health and Psychology, Governance and Public Administration. We shall then concentrate on Development of Mathematics in India in Arithmetic, Algebra, Geometry and Calculus  from the times of Bodhayana (800 BC) to Madhavacharya (14th Century AD).