Shameless Self-Promotion

DDKCover.pngAfter what seems an agonizingly long time since the first ideas of the book took root, I got the following letter from my publishers (how sweet that sounds!) last week,

“We are very pleased to inform you that your book has been published and it is available on Customers can order it […] etc.”

D D Kosambi: Selected Works in Mathematics and Statistics is finally done, and is now available in both e and paper formats. The cover on the right shows DDK at three stages of his life, at Harvard, in Aligarh, and finally, in his TIFR years.

To quote from the blurb: This book fills an important gap in studies on D. D. Kosambi. For the first time, the mathematical work of Kosambi is described, collected and presented in a manner that is accessible to non-mathematicians as well. A number of his papers that are difficult to obtain in these areas are made available here. In addition, there are essays by Kosambi that have not been published earlier as well as some of his lesser known works. Each of the twenty four papers is prefaced by a commentary on the significance of the work, and where possible, extracts from technical reviews by other mathematicians.

My personal contribution to the book, other than to edit is, is fairly minimal. Apart from a preface, I have basically tried to describe the academic milieu in which Kosambi found himself at different points in his life, and have also tried to infer what others thought of him in another prefatory essay, “A Scholar in His Time”.

Kosambi gave his academic manifesto in the essay, “Adventure into the Unknown” which also is one of the places where he wrote that Science is the cognition of necessity. (It is quite another matter that the phrase is not one that can be understood in a straightforward manner. Anyhow, as a quote its famous enough.) Reprinting that essay in its entirety seemed appropriate, as also another note “On Statistics” that gives a flavour of DDK’s interdisciplinarity, mixing statistics, erudition, Marxism, etc. The last of the non-mathematical writings is a project completion report submitted by DDK to the Tata Trust in 1945 and it permits, among other things, an inner view of a vastly gifted and somewhat frugal scholar who, in parallel, and for Rs 1800, carried out  6 research projects on issues as diverse as writing a mathematical monograph on Path Spaces, editing a concordance of Bratrihari’s epigrams, and constructing an electromechanical computational device (the Kosmagraph),  among others.

The remainder of the book is a set of reprints. Of his 67 or so papers in mathematics and statistics, about a third are presented, starting with some of his first papers, Precessions of an Elliptical Orbit and  On a Generalization of the Second Theorem of Bourbaki, and ending with one of the papers he wrote under the peculiar alias of S. Ducray,  Probability and Prime Numbers.

An attempt was made to include all the important papers, in particular the ones that made his reputation such as Parallelism and Path-Spaces that along with two other notes by Cartan and Chern are the basic of the Kosambi-Cartan-Chern theory,  the various papers that laid the foundations of scientific numismatics, as well as the papers that he should have followed up but didn’t, such as Statistics in Function Space that foreshadowed the K-L decomposition. The Kosambi distance in genetics was elaborated in  The Estimation of Map Distances from Recombination Values, and this is also reprinted.

Kosambi’s obsession with a statistical approach to the proof of the Riemann hypothesis resulted in several papers of which An Application of Stochastic Convergence, Statistical Methods in Number Theory, and The Sampling Distribution of Primes are reprinted here.  These, as is well-known, effectively ruined his reputation as a serious mathematician.

Chinese. Japanese. French. German. English. DDK published papers in all these languages, sometimes exclusively, and twice the same article in translation. Also reprinted in this volume are three of the foreign language papers, the ones in German, French, and Chinese. The last is of particular interest since it was written during an exchange visit to China in the late 1950’s and only later published in English.

A number of people have helped me along the way and it is my pleasure to thank them all here. For the initial suggestion that the book be done, and for sustained and general encouragement, I am very grateful to Romila Thapar. I’ve written about this before.  Meera Kosambi was keen to see her father’s mathematical legacy appreciated and was very enthusiastic about bringing out this collection and helped greatly in more ways than I can describe. She passed away in January 2015, when she knew the project was afoot, but not in any way certain as to how it would all come out. Michael Berry, S. G. Dani, and Andrew Odlyzko discussed and advised on various  points of the mathematics.  Indira Chowdhury and  Oindrila Raychaudhuri helped vis-à-vis archival matters.  Rajaram Nityananda had had many of DDK’s papers digitized, a great boon, and one that made the reproduction of some material much easier! Kapilanjan Krishan,  Rahim Rajan, and Mudit Trivedi  helped me locate some of the more obscure of DDK’s papers. K. Srinivas retyped almost all the papers, and Cicilia Edwin painstakingly proofread most of them.  Toshio Yamazaki and Divyabhanusinh Chavda  told me of their interactions with DDK, helping to flesh out the personality. Finally, Aban Mukherji was gracious with permissions, as were all the journal editors who kindly permitted the several articles to be reprinted.

DDK maintained a charmingly frank notebook diary during his Harvard years. On the 19th of January 1927 he notes: A most restless day. I have forgotten to mention Monday the 17th and an important conference with Birkhoff thereon […] Problems: Fermat’s Last Theorem, the Four color map, the functional equation […] Today was unusually restless with a great deal of time spent, possibly wasted in the Widener. Looked up old issues of Outing, Shakespear’s Hindi Readers, most of Burton’s works [of him more later], Roosevelt on African and Brazilian ‘sporting’ – worthless – Stefansson’s excellent and much remembered Friendly Arctic

All this variety in a single day! To recall WordsworthBliss indeed it was in that dawn to be alive! Kosambi, just out of his teens, was just bursting with energy, both intellectual and physical (for which one must read the diaries in some detail). The earnestness that only comes at that age shines through on the pages quite unselfconsciously:


Exuberance indeed, but also some simplicity: Deep interest, well sustained, is essential in the acquisition of knowledge upon any subject. And the third realization of the day: Life is good.  Yes indeed, to be young was very heaven.


Carrying on

ccxCommenting on my last post, an old classmate wrote to say “Ram, we are both at an age where we mark the passage of time by composing eulogies for our friends and loved ones. One day someone else will do the same for us….”

True enough. I found that in the past year or so, I’ve done this four times, and each time has been painful in its own way… The passage of the years does indeed makes these occasions more frequent, but every passing is none the easier for that. And every cliché in the book has some ring of truth to it, each day has its own new regrets.

I have been overwhelmed by the several letters that friends from all over the world have written in the past few weeks. And touched by the genuine expressions of grief, by the concern and the affection. I am beginning to respond to these, but each response goes with its own memories, so this note is both to acknowledge how heartwarming it has been to read each message and to say  I will write back, but maybe slowly.  We will meet, and when we do we will speak of other things, without forgetting this connection.

A Physicist and a Gentleman

Dr Deepak Kumar (1988)My friend and colleague, Deepak Kumar, passed away all of a sudden late Monday (25th January) night. I had seen him that day, sharing a cup of tea with another member of the faculty in the afternoon sun on the lawns of the School of Physical Sciences at JNU. The spot where he sat was directly visible from my office window- Deepak often sat there and had his lunch. I hadn’t spoken to him that particular day, but that was not unusual – there were many days like that. But it was not just another day, not like any other.

Deepak was one of the first to join the School as Professor when it was formed, and he brought a decade or more of experience at the University of Roorkee. As it happened that greatly helped the School in its early, formative years, and set the mark for how it developed subsequently, defined what it’s core values were, and the sense of purpose and commitment that it has had since.

Colleague for almost 30 years, Deepak has been a friend for a little over that, and if I were to have to characterize him, the title of this post says it as well as anything. Deepak was a scholar in the true sense of the word, and one for whom the world of physics was all absorbing. Although his professional interests were in condensed matter physics, he was both knowledgeable about, and was interested in a huge range of topics. One could go to him for just about any doubt, count on him to give the right bit of advice, and if the matter happened to be something that he knew well, his intellectual generosity was limitless.

This is not exaggeration. Not for nothing was Deepak the most collaborative colleague that we have at the SPS:  of the 20 or so faculty that we have in physics, Deepak has actually written papers with no less than seven of us. And with something like twice that many students, either as their formal or informal supervisor, as a mentor in the best tradition.  Indeed, he mentored the first Ph. D. that was awarded from the SPS, and both directly and indirectly showed many of us the way in which one could bring out the very best in our students.

There is so much to say about Deepak- his academic contributions in condensed matter and statistical physics, the several awards, the recognition. But this above all: This was too soon and too sudden. There were many many good years of physics one could have had from him, and many years of physics that he would have enjoyed.  Even the last day, on Monday, he gave a lecture, there was another scheduled this week. And last semester he taught a course for the MSc Physics seniors. He was working to the end, and he went with his academic boots on…

I know his ethos will continue to guide us, and I can only hope that we will not forget his calming spirit that often brought hot tempers down, his somewhat other-worldly smile, and his gentle sense of humour that helped us all see that there were many ways of reaching conclusions. We all will miss him deeply, the community that he helped build at JNU, and the larger community of physicists in the country that knew and admired him.

The Mother of All Chemistry Departments

snake1972 was a very good year to join the IIT Kanpur Chemistry Department as an MSc student. Some 15 of us, bright eyed and bushy-tailed for the most part, did. There was an incredible air of modernity about the place, from the architecture, to the teachers, their teaching, the labs, the hostels, the facilities. The passing years have coloured the memories and blurred some of the edges, but nevertheless, I can still remember the freshness of the campus and the feeling that we had arrived somewhere special.

Most of us- barring the Delhi University sophisticates- were from colleges in somewhat provincial universities. And in those days, universities in Madras, Kolkata, Pune and Bombay all were to varying degrees provincial, and we had classmates from Madurai, Kolhapur and Burdwan as well… All plagued by poor and outdated syllabi, bad teaching, the works. Many of us were also scholarship holders of the National Science Talent Scheme, that great initiative of the NCERT, and we had been exposed to some of the more modern ideas, so we knew the good places to go to. And without doubt, IIT-K was the place to go to if you wanted to do chemistry, with the added attraction that if one did reasonably well, it was a direct line thereafter to the US aka “Fatherland”.

The Chemistry Department, to put it mildly, was rocking! Our teachers were (and many still are) legendary. Almost from day one, the classes were in a completely different category from what we had been used to- no notes for one thing, surprise quizzes, open book examinations… It was not unusual to get homework from the latest issue of JACS, the Journal of the American Chemical Society- giving us the feeling that this was what an international education was all about. And it was.

Arguably, the Chemistry Department at IITK in those years was competitive with the best in the US. The faculty line-up was exceptional and the publication standards were better than most. All the big names were there- and let me not name them, the faculty at that time was the who’s who of Indian chemistry. But more than being famous, they were really inspirational. I can still recall- almost verbatim- a course in Group Theory that we all took in the second or third semester (another innovation in 1972!). And the course in Synthetic Organic Chem. or that in Phys. Chem… The geeks amongst us (mostly all) had it good.

It was a time, the first that I remember, when I was immersed in a group that, by and large, loved a subject. We talked chemistry, did homework together, did projects (some crazier than others). My undergraduate years had been spent largely in goofing off- most of those who came to the BSc course were there to pick up a degree and move on to the rest of their life- IAS, MBA, whatever- and the few who were interested in the life academic were oddities.

173_001Peer group pressure (and there was plenty of it!)  and teachers apart, there was a steadily growing set of seniors that were setting standards. The ones who had gotten into Harvard, or Chicago, or wherever. The ones who had written research papers as MSc students (and in Nature, no less). The ones who were clearly going to be the next big things… This made us, for the most part, academically very ambitious. In the days before rankings had reduced everything to labels like top ten and so on, there was mostly reputation to go by, and when we applied, the bar was always set high. A few in our class decided not to go on with a Ph D in chemistry- IIM Ahmedabad and BARC were the alternate choices, but for the rest, the next step was to Harvard, Princeton, Berkeley, Chicago, Indiana, SUNY, and so on. But in 1973 the level of competition that one sees today was just not there; all it took to make an application was a respectable GRE score and an aerogramme…

FB_IMG_1425833106934 copy
Prodipto Banerjea (note the deadpan expression) and I in a friend’s hostel room in Hall V, IITK. Early 1973, given our attire and the cut-outs on the wall.

This post actually started out as a long answer to a short question by one of my students as to what “were your thoughts then?  On aspects of academic/extra-academic life… I mean, how did you see the world that time?”. Truth be told, the thoughts were all in the short term. Very short term (as the pictures on the hostel room wall might suggest). Competition was strong, so one wanted to be at a local maximum at the very least, but one could also see what the milieu was throwing up. The B. Tech. batches were very gifted and this was before the coaching classes had dulled the sheen of the JEE rankings. The talents were visible and aplenty, with enough 10. someones, as well as the clearly very cool set.  The faculty was very liberal- in some ways more than what we see now: I recall, as an MSc Chemistry student, taking MSc and Ph D courses in the Physics Department, for credit. Not too many questions asked, and it figures on my transcript. (At the two Universities where I have taught recently, I can say with certainty that if this happened at all, it happened with much sturm und drang.)

And our teachers experimented with pedagogy. With a lot of thought, as even a casual look at the course curriculum would tell- it is, even now, a surprisingly modern curriculum. And with an ability to change. Willingly, as some teachers introduced Bio into Chem (it was not that common then) and unwillingly, as when some of us trashed the attendance requirement and told the instructor we would only do tutorials and the final exam, not go to his classes.

There was a downside, of course. We did not share a certain kind of easy friendship that a less competitive atmosphere might have engendered. Of my 14 classmates, I have not met 4 in the last 40 years, and only 4 of them more than once or twice in all that time. Five of our class chose careers outside science, four were in industry, one went to a national laboratory. Academics eventually attracted only five of us, two in India and three in the US, making the connections more and more tenuous with the passage of time. And now most of us are reaching retirement, so in retrospect, and there is only retrospect now, this was a major shortcoming. A sense of community certainly helps beyond the science, and grass being greener apart, I think that other groups of the same times have bonded better. Maybe it was that we were only together for two years- not a long time, admittedly- but still.

17235.iconBut there was more, much more to IIT K than just the classes, and enough attention to these aspects had been given when the institute was set up. Extracurricular activities apart, there was an airstrip, and a TV station as well- that actually broadcast programs on campus, including the 1973 England vs. India test match that was played in Kanpur, Gavaskar and Bedi being the stars then. And as for the airstrip, I’ve forgotten the chap’s name, but his nickname was Pilot because he knew flying, and I- in retrospect foolhardily- went up with him in a glider. Given the level of safety that we all subscribed to, its a miracle that there were no major accidents! (I would do it again gladly, of course.)

But to get back to the title of this post, the IIT-K Chemistry department was, in many ways, the progenitor of many others that were set up in the 70’s both in style and in content. Many of those who taught us were to leave shortly thereafter to take up positions in Hyderabad, Kolkata, Bangalore and elsewhere. In a sense, the research and teaching culture spread, and flourished.

There is a very real Masonry of IIT-K Chem alums: strong ties bind us to where it all began. For all of us- teachers and students alike- this was a great initial condition to have.