Title: Square roots from ancient times

Abstract: 

Understanding square roots constituted one of the first challenges faced by various early civilizations, after the basic arithmetical operations were reasonably in place. Grappling with the issues involved eventually led to various developments, both in terms of theoretical understanding and applications. This talk will be an exploration of the historical roots in this respect, and their significance in our present day mathematical framework. 

About the Speaker

Prof. Shrikrishna Gopalrao Dani

Early Life and Education

Prof. Shrikrishna G. Dani did a BSc from the Institute of Science and MSc from the University of Mumbai, in 1969, following which he joined the Tata Institute of Fundamental Research (TIFR), Mumbai. After an extended and successful career at TIFR he retired in 2012 as Distinguished Professor. Subsequently he was affiliated with IIT Bombay for five years, and is currently with the UM-DAE Centre for Excellence in Basic Sciences, Mumbai.

He has made extensive research contributions in many areas of mathematics, including Ergodic theory, Dynamics, Number theory, Lie groups, and Measures on groups, published in many leading journals around the world. He has also published articles in history of mathematics from ancient India. He was an invited speaker at the International Congress of Mathematicians at Zurich, 1994. The awards received by him include the Shanti Swarup Bhatnagar Prize, the Srinivasa Ramanujan Medal, and the Mathematical Sciences Prize of TWAS, the Academy of Sciences of the Developing World. He is a Fellow of all the three major academies of science in India. He is currently President of the Indian Society for History of Mathematics, and President of the newly founded Mathematics Teachers’ Association.

Research Contributions

He has been a member of the NBHM since 1996 and was the Chairman of the NBHM. He is also the chairman, Commission for Development and Exchange (CDE) of International Mathematical Union, for the period 2007–2010. He has served as Editor of Proceedings (Math. Sci.) of the Indian Academy of Sciences, Bangalore for many years since 1987.

Major Awards

•  The Shanti Swarup Bhatnagar (SSB) Prize

•  TWAS Prize

Legacy

Prof. Dr. Shrikrishna Gopalrao Dani is a distinguished mathematician whose research has made a notable impact across dynamical systems, number theory, and topology. His seminal contributions focus primarily on ergodic theory and the properties of orbits of Lie group actions on homogeneous spaces. Alongside his collaborators, he has also achieved significant progress on the complex problem of embedding infinitely divisible probability distributions on groups into continuous one-parameter convolution semigroups. Prof. Dani’s prolific academic career began at the Tata Institute of Fundamental Research (TIFR), Mumbai, where he served from 1969 until his retirement as a Distinguished Professor in 2012. He subsequently brought his expertise to IIT Bombay for five years before joining the UM-DAE Centre for Excellence in Basic Sciences, Mumbai, in 2017, where he currently serves as the Chair of the School of Mathematical Sciences. Over the years, he has authored well over 100 research papers in international journals, cementing his legacy as a leading figure in advanced mathematics.

Beyond his core mathematical research, Prof. Dani has dedicated the last two decades to exploring and documenting the history of mathematics in India. His exceptional contributions to science have been recognized with numerous prestigious honors, including the Shanti Swarup Bhatnagar Prize, the TWAS Mathematical Sciences Prize, and the Srinivasa Ramanujan Medal of the Indian National Science Academy. He holds fellowships with TWAS and all three national science academies in India (INSA, IASc, and NASc), and is an Honorary Fellow of TIFR as well as an Honorary Member of the Marathi Vidnyan Parishad. A dedicated leader in the global mathematical community, he served as President of the Indian Society for History of Mathematics (2008–2019) and on the Executive Committee of the International Commission for History of Mathematics (2015–2018). Having served on various international editorial boards—including his tenure as Editor of the Proceedings of the Indian Academy of Sciences (Mathematical Sciences) from 1987 to 2000—he continues his influential academic stewardship as the Editor of Ganita Bharati, the Bulletin of the Indian Society for History of Mathematics, a position he has held since 2010.