Remembering D D Kosambi: In conversation with Prof. Ramakrishna Ramaswamy

Visiting Professor, Department of Chemistry, IIT-Delhi
Author of D.D. Kosambi: Selected Works in Mathematics and Statistics

More about him at

In the Homi Jehangir Bhabha (HJB) vs D D Kosambi (DDK) tussle, a supremely talented, definitively democratic and readily disagreeable personality was terminally
sidelined, and our elitist nuclear ambition caused a solar eclipse
that has cost us dear. Do you agree?

At the time when DDK and HJB were disagreeing about energy sources
(around 1958-1960), harvesting solar energy was not simple. Silicon
technology was many years into the future. All known routes involved
rare elements like Ruthenium. As an idea, solar was great, but it was
not practical. What we see today is that DDK's instinct was right, but
it was much more important for HJB to set up the Department of Atomic
Energy, etc. DDK's disagreeableness was only part of the story.

How did the idea of presenting and elucidating DDK's mathematical
treasure trove to people at large germinate in your mind? Did
mathematics lead you to DDK or was it the other way round? 

As I mentioned in the book, the original push came from Prof. Romila
Thapar who only knew of DDK's contributions to History. I had heard of
him first as a student in IIT Kanpur around 1973, and at TIFR where I
spent a few years, mainly in the context of mathematics. One thing led
to another, and I decided to at least collect his maths and look at
how he moved from one area to the other.

Twenty four papers each with a commentary and key technical review
extracts - the structure is God sent for someone who wishes to put
Kosambi in perspective in optimal time. 

The total number of maths papers of DDK is about 70 (give or take). I
also realized that most people would not be interested in all the
maths papers, just the ones that had a historical or mathematical
significance. Once I decided that, the choices were mainly clear. The
first paper. The Bourbaki paper. The paper that started the
numismatics. The Kosambi distance. The paper with Cartan. The
orthogonal decomposition. The Riemann paper, etc.

I must inevitably turn to DDK's controversial approach to the
Riemann hypothesis. Notwithstanding the embarrassment rooted in what
most term as a monumental blunder, I learn that he had made it amply
clear that his work based on Tauberian theorems was only a conditional
proof ("if the primes in suitably defined covering intervals behave
like an unbiased random sample, then the Riemann hypothesis follows")

"Amply" is overstating the case. No self-respecting mathematician
would have published these papers. If you discover that if A is true,
then B would be true, but you cannot prove A is true, then you really
are left nowhere. It would have been more mature to say something like
"Ah, I have discovered that B would follow if the following statement
A is true, but I have no way of proving A, unfortunately ..." If you
read my essay "A Scholar in his time" you will see that a posthumous
review of this work says that effectively Kosambi replaced the Riemann
Hypothesis by an even more involved hypothesis that the reviewer
proposed to call the Kosambi Hypothesis. DDK himself (in his essay
Adventure into the Unknown) tries to make it out that he was "a
maverick who could not fit into the scheme of things" but the argument
does not fly.

Continuing the same thread, while Kosambi’s 'Agricultural sciences'
prank does seem bizarre, could it be that his detractors pounced on
the opportunity to defame DDK, also burying the prospective worth of
his paper, and the possibilities inherent in it.

I don't call it a prank. No serious mathematician does that,
especially not one who has position at TIFR.

I would also love to know your thoughts on his practice-driven work
– for instance the Proper Orthogonal Decomposition analysis and the
study of seasonal death rates that advocated proactive anti-typhoid
work to avert an epidemic. I am sure he would have done something
about  the corona scare as well, had he been in our midst.

I'm sure that he would be out there collecting data, and the fact that
Pune is a major centre would probably enthuse him no end! He was an
intensely practical man, but his interests were many and time was at a
premium. So he flitted into many areas and did not complete his work
or follow it up in many cases.   It is clear, for instance, that he
constructed the Kosmagraph at St Xavier College, but nobody else has
written about it so we have no other validation. Both his books have
been lost, one of them in 1946 and one in 1966. No copies were kept?
Why? All this makes for a very confusing image of a very intelligent
person who could not keep a sustained interest in most things.

How would you summarize DDK's work concerning "Law of large
numbers"? I am keen to know about your thoughts given the applications
of this intuitive law in AI.

The LLN paper is an expository paper in Mathematics Student in which
he basically explains this law (as a way of understanding it himself,
no doubt). There is little that is original in the paper, except
perhaps the presentation.

I believe you have consulted C D Deshmukh’s book for biographical
information (indeed a delightfully detached account of Kosambi’s life
and work) Hope the translation has done justice to the original.

I don't read Marathi, so I wouldn't know how the translation works! I
got a fair amount of information from Meera Kosambi also.