The Improbable Road to Riemann

Fuji-san on the approach to Narita airport; Debraj Ray (2017) On June 25, 2021, the Sreenidhi Institute of Science and Technology , located in Hyderabad, released the Report of an "Expert Committee," entitled " Open Reviews of the Proof of the Riemann Hypothesis ." The “proof" referred to an unpublished paper by Professor Kumar Eswaran, which claimed to have settled one of the most distinguished open questions in Mathematics, a conjecture stated by Bernhard Riemann in a classic paper written in 1859. As the Preface to the Report states, Eswaran’s contribution “was lying extant on the Internet for nearly four years and had received thousands of reads and downloads but had not received the assent of a mathematical journal to subject it to a detailed peer review." The Committee sought an open review of Eswaran’s paper from 1,200 “eminent mathematicians and scientists." Based on the reports received by the Committee, and its own deliberations, the Commit

The Drèze DUET: Towards employment as a universal right

Published in Ideas for India , September 11, 2020. Jean Drèze has recently proposed a "Decentralised Urban Employment and Training" Scheme, or DUET for short. In his words, "DUET could act as a step towards urban employment guarantee." The essential idea is for state governments to issue job stamps to “approved public institutions”, who would use these to pay wages to suitably registered workers. Workers would present job stamps and a work certificate (from the institution) for reimbursement directly into a bank account. I refer you to   Jean's proposal   for more detail. I personally believe that we should push forward with the agenda of employment as a universal right, one that transcends rural versus urban. DUET would move that needle. With the rising tendency to displace labour – a trend that will only be heightened by the pandemic – such a right provides protection, at least to some minimal degree. So I support this proposal. That said, there are many issue

Dipak Banerjee

These are transcribed notes for a short talk on Dipak Banerjee. Dipak babu has had a fundamental impact on my life, not just on my professional career, but also on the way I think. Dipak Banerjee, Mihir Rakshit and Nabendu Sen --- three great professors at Presidency College --- all did research to varying degrees, but first and foremost they were deeply devoted to teaching. In early 1974, I was 16 years old, and had just been granted admission to study at IIT. I was moving close to making a final decision on the IIT campus when I came across Paul Samuelson's book, Economics. It jolted something in me (of course, it must have been present before but perhaps I was not fully aware of it), and it soon became obvious that I was not cut out for an Engineering degree. It would have to be either pure mathematics or a subject with a strong social component. So I decided to take the entrance exam to study Economics at Presidency College, and I also took the ISI entrance exam. At that time,

The Micro and the Macro of Covid-19

Or, The Case of the Invisible Denominator I've been chatting with Jay Bhattacharya , Professor at the Stanford School of Medicine, and co-author of a very thought-provoking piece on mortality rates under covid-19 . Briefly, these authors study incidence rates in three cases where either a full census of tests was conducted, as in the Italian town of  Vò in Padua, or where a random sample was drawn, as in Iceland. Using incidence rates for covid from these cases, they suggest that the fatality rate for covid is far lower than we think, or fear.   Going beyond these cases, the problem, of course, is a missing denominator: just how many are infected? Assuming we accurately know the deaths from covid-19 --- possibly not , but setting that aside --- the unknown denominator of actual cases moves us along an "isoquant" of fatality rates and contagion rates, which multiply out to the known deaths. The higher the contagion, the lower must be the fatality rate, for some given

India's Lockdown

Migrants at Bandra Railway Station, Bombay, March 2020. Press Trust of India, On the 24th of March, the Government of India ordered a nationwide lockdown for 21 days as a preventive measure against the coronavirus. The lockdown restricts 1.3 billion people from leaving their home. Transport services are suspended. So are services, factories and educational institutions. The lockdown has generally met with approval from international institutions such as the WHO, and is in line with what is deemed appropriate in economically advanced countries. For instance, Francis Collins, Director of the US National Institutes of Health, writes : “ [W]hat we need most right now to slow the stealthy spread of this new coronavirus is a full implementation of social distancing.”  The framing in these countries is “lives versus economics,” and by and large it is the right one.  As Paul Krugman puts it   ( New York Times April 2), “ most job losses are inevitable, indeed necessary … we’re going into

The Trumpet

I recently had occasion to revisit Edgar Allan Poe's masterpiece, "The Raven." If you have not read The Raven, you must. Maybe it's meant to be a forlorn lament for Poe's Lost Lenore, but I found it incredibly funny. Here is the first of several verses ( to read the rest, click here ): Once upon a midnight dreary, while I pondered, weak and weary, Over many a quaint and curious volume of forgotten lore—      While I nodded, nearly napping, suddenly there came a tapping,      As of some one gently rapping, rapping at my chamber door. “’Tis some visitor,” I muttered, “tapping at my chamber door—      Only this and nothing more.” The Raven is written --- wait for it--- in trochaic octameter , with a difficult yet utterly enchanting lilt. David Pearce and I like limericks (and so does Dipankar Dasgupta, in Bengali no less!) but this was something else. Irresistible. So I offer you my attempt at (approximate) trochaic octameter, inspired by the great Poe. Fee