Abstract: Ramanujan was an inventive genius, but did he have a way of thinking which made him an inventive genius? Since paper was expensive, Ramanujan worked on a slate. He recorded his results without recording how he obtained them. Thus, there is a bit of a mystery to how he may have done mathematics. Here we examine how Ramanujan could have obtained a few of his results on continued fractions. We review some of his continued fractions, and get lessons about how we can become more like Ramanujan in our thought process.

About the Speaker: Gaurav Bhatnagar obtained his Ph.D. in Mathematics from The Ohio State University in 1995. After his Ph.D., he spent one year each at Ohio State and the Indian Statistical Institute, Delhi. Subsequently, he joined the educational technology industry, where he has been able to make a significant contribution to the teaching and learning processes of Indian schools. 

He has co-edited (with Sugata Mitra and Shikha Mehta) An Introduction to Multimedia Systems (Academic Press, 2002) and written Get Smart: Maths Concepts (Penguin, 2008), a book on middle school mathematics. His latest book (written with Tejasi Bhatnagar) is: Maths Puzzles for Smart Kids (Hachette, 2023). 

His research interests are in Combinatorics and Special Functions, more specifically, hypergeometric, q-hypergeometric, and elliptic hypergeometric series, their multiple series extensions over root systems, continued fractions, orthogonal polynomials, partitions and elementary number theory. He is also interested in providing a discovery approach to Ramanujan’s identities.