12 papers on mathematical genius published in Special issue of Society’s journal

The Royal Society has just brought out a Special Issue of the Philosophical Transactions of the Royal Society - A, this being the refereed proceedings of a conference held at The Royal Society, London, in October 2018, in celebration of the centenary of Srinivasa Ramanujan’s election as Fellow of the Royal Society (FRS). The online issue was published on Dec 9, 2019, with the print issue to follow later in the month. The Special Issue is edited by Professor Ken Ono, now at the University of Virginia.

Each year, about 50 Fellows and 10 Foreign Members are elected to the Royal Society.

This number was smaller in the past. In any case, each year is the centenary of some group of eminent academicians elected as Fellows a century earlier. But the Royal Society does not hold conferences for the centenary of the election of such Fellows. That the Royal Society held a conference in London last year for the centenary of Ramanujan’s election as FRS indicates the high esteem in which he is held by the Society, and how unique he is among the scientific luminaries.

The organisers of the October 2018 conference were Ken Ono (then at Emory University), Manjul Bhargava (Princeton University), George Andrews (The Pennsylvania State University), and Robert Vaughan, FRS (The Pennsylvania State University). There were 14 invited speakers at the conference and their talks covered a broad arena of current research where Ramanujan’s brilliant ideas have had influence. Besides the well known fundamental fields of mathematics such as number theory, modular forms and automorphic forms, the conference covered areas like signal processing and black holes!

The Philosophical Transactions of The Royal Society has an illustrious history. It was established in 1665 as the very first journal devoted to science. It is therefore the world’s longest running scientific journal. The word philosophical refers to natural philosophy, nowadays called science. The Philosophical Transactions was the journal that introduced the peer review process. Isaac Newton’s first paper on “A new theory about Light and Colours” appeared in this journal in 1672. It is to be appreciated that the refereed conference proceedings appeared in this journal which has such a hallowed tradition.

Twelve of the invited speakers have published in this Special Issue. George Andrews’ paper discusses how Ramanujan may have discovered the mock theta functions. It is nearly impossible to understand how the mind of Ramanujan worked, but Andrews probably can make the best guess of this. Bruce Berndt (University of Illinois), who spent most of his life analysing Ramanujan’s Notebooks, has contributed an article to this issue entitled “Living with Ramanujan for forty years”. Jeff Harvey of the University of Chicago discusses Ramanujan’s influence on string theory, black holes, and a mathematical topic of great importance called moonshine. The topic of the paper by Alex Lubotzky and O. Parzanchevski of the Hebrew University is on Ramanujan graphs and Ramanujan complexes. And then there is a paper on Ramanujan sums and signal processing by P. P. Vaidhyanathan (Caltech) and S. Tenneti.

The celebrated Ramanujan Conjectures on bounds for the coefficients of certain types of automorphic forms, are at the very heart of mathematics. Professors Peter Sarnak (Princeton University), and Winnie-Li (Penn State University), spoke about this at the conference in two separate lectures; Prof. Li has contributed to the special issue on this topic. While what I have mentioned here does not cover all the papers in the Special Issue, it gives a good idea of the range of Ramanujan’s influence in today’s research.

My contribution to the special issue is based on the talk I gave at the conference on “Ramanujan’s Legacy: the work of the SASTRA Prize Winners”. In my paper, I describe the work of the seventeen SASTRA Ramanujan Prize Winners as of 2018 and the impact this has had on the development of mainstream mathematics.

The Philosophical Transactions publication based on the 2018 Royal Society conference, is yet another recognition of Ramanujan’s stature in the mathematical firmament.

(Professor Krishnaswami Alladi is with the Department of Mathematics, University of Florida, Gainesville, Florida, U.S.)