Prof Bruce C Berndt shared a history of Ramanujan’s lost notebook and described some of its contents.
On fifth of November, the institute hosted a public lecture on Srinivasa Ramanujan, the great Indian mathematician. Prof Bruce C Berndt, a former senior faculty at the University of Illinois at Urbana-Champaign, USA, and one of the world’s foremost authorities on the work of Ramanujan, delivered the lecture Living with Ramanujan for 40+years. The lecture was focused on the life of Ramanujan as well as Professor Berndt’s association with Ramanujan and his mathematics.

Professor Berndt began his lecture with a short summary of Ramanujan’s life through four of his photographs taken in England. He also shared his photographic memory of visiting Ramanujan’s village home, meeting his family members and holding Ramanujan’s slate as a schoolboy. He described the latter as a thrilling experience of his life.

He went ahead to share a description and history of Ramanujan’s (earlier) three notebooks. He shared that his interest in Ramanujan’s notebooks begun in 1974. He spoke about the significant events in his quest to find proof for Ramanujan’s claims in his notebooks. He also touched upon Ramanujan’s serious illness and related correspondences between Ramanujan, G H Hardy and other contemporaries. He described some of Ramanujan’s work in the notebooks spanning several areas of mathematics viz. Theta functions, elliptic functions, Hypergeometric series, q-series and Number theory, among others.

He also provided a history of Ramanujan’s Lost Notebook, and then described some of its contents, especially, Mock Theta Functions. Lastly, he discussed the final result from the notebook that has now been proved – the second double Bessel series identity that is connected with the divisor problem. At the conclusion, he put forth some probing questions about the possible loss of some of Ramanujan’s work, including
● What happened to the “trunk full of papers” that Ramanujan brought back to India?
● Some of Ramanujan’s discoveries in England are not in his papers, notebooks, or other manuscripts; some are in Ramanujan’s letters to Hardy from the nursing home.
● One page of Ramanujan’s first letter to Hardy was lost.
● A portion of Ramanujan’s last letter to Hardy was lost.

“My life with Ramanujan will continue”, Professor Berndt concluded.

About the Speaker
Prof Bruce C Berndt joined the faculty of the University of Illinois in Urbana-Champaign in 1967. After 52 years of teaching and research at the University of Illinois, he retired in May, 2019. During this time, he supervised the doctoral dissertations of 37 students. He is a former Guggenheim Fellow and received the Steele Prize for Mathematical Exposition from the American Mathematical Society in 1996. He has published five volumes on Ramanujan’s notebooks with Springer in 1985-1998, and he and George Andrews have published five volumes on Ramanujan’s lost notebook with Springer in 2005-2018.

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