D D Kosambi: Selected Works in Mathematics and Statistics by Ram Ramaswamy

Re-posted from: And then...
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After 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 http://tinyurl.com/jgn2djj. 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 Wordsworth,  Bliss 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.

• D D Kosambi: Selected Works in Mathematics and Statistics is published by Springer. ISBN: 978-81-322-3676-4

Sandesh Kadur talk at festival of ideas

PANAJI: With a camera in hand and a mind full of wonder, Sandesh Kadur would often cycle to the outskirts of Bengaluru to shoot images of the wilderness.

Back then, little was he aware that on a given night, the sounds of a Nightjar bird and the sawing call of the leopard would soon lead him on a path dedicated to documenting animals for NatGeo, discovering new species and saving the endangered ones.

An award-winning wildlife photojournalist and documentary filmmaker, Kadur, through the use of still images and videos, is known for advocating the need for conservation and protection of the planet's biodiversity.

Speaking on day one of the 10th D D Kosambi Festival of Ideas on Monday, he shed light on the forested valleys and snow-covered peaks of the Himalayas besides commenting on burning issues of Goa's biodiversity.

"Less than 5% of India's land mass is protected forest area, which is very little. We need to stop with the assault on our green areas and start conserving them," he urged.

His tryst with wildlife has led to the discovery of several new species that are endemic to the mountain regions. "Over 564 species were found until 2014 and they are being discovered on a continuous basis in the Himalayas," he said.

This, in turn, has also led to the shattering of myths about certain animals in India. He explained this through his picture of a tiger scavenging on the carcass of a rhino.

"The image has shattered all romantic stories about a tiger being a gentlemanly creature that feeds on his own kill," he explained.

His expeditions also led him to capture peaks of the Western Ghats in light as well as shadow, a rare sight of purple frog, a foot-flagging frog, purple Nilakuranji flowers that bloom once every 12 years, among others; images of which he showcased to the awe-struck audience in the packed auditorium.

A firm believer of free rivers, Kadur stressed on the need to let water bodies flow sans restriction, "Mountains harness the power of monsoon and create rivers. If we stop that by building dams, it will affect the ecosystem. There are countries removing dams therefore and making rivers free again because they realise that hydropower is not as green".

Sharing his thoughts on the Goa-Karnataka battle over the Mhadei issue, he said, "Rivers initially were protected in the birth places by temples but now they're being affected by too much 'love.' During the riots and bandhs in Bengaluru and Chennai due to Mhadei issue, it was estimated that there were losses of over Rs 25,000 crore per day. If that money had just gone to protect these rivers we wouldn't have to fight over rivers and have a positive impact on the environment".

Elaborating further, he said that building dams do more harm than good, "Respecting rivers and allowing them to flow as they are is very important. Damming them or curtailing them or diverting them can affect everything downstream. Stopping the river from flowing into the ocean gradually leads to a multitude of fish species being destroyed as well."

Kadur also commented on the state's potential for hinterland tourism. "Tourism is a very economic one-way game but that's the shortsighted view. We need to bring about tourism in the most responsible and low-impact manner. If we can bring that about then we can save those places while showcasing them to visitors. We also need education by way of an interpretation centre at the tourist spot so that experts can explain to people the value of the place."

He further pointed out that hinterland tourism should be within a certain limit so as to not cause imbalance in the natural surrounding. "We need to spread out the tourism and have less people in each place instead of too many in one place. Thus keep the density of tourism low and not go beyond the place's carrying capacity."

Source: Times of India

D D Kosambi Festival of Ideas sees diverse line-up

Wildlife photographer Sandesh Kadur

PANAH: The 10th edition of D D Kosambi Festival of Ideas is scheduled to be held from February 13 to 17 at Kala Academy, Panaji.

This year will also have an impressive line-up of stalwarts from various fields who will conduct intellectually stimulating sessions for the Goan audience. Speakers this years are National Geographic explorer and wildlife photographer, Sandesh Kadur who will speak on India's mountains of life on February 13; while professor at Tata institute of fundamental research, Mumbai, Shubha Tole, will speak on 'wiring up the brain' on February 14.

A professor at Newcastle University, UK, Sugata Mitra will speak on the future of learning on February 15. Professor of international mental health and welcome trust principal research fellow in clinical science, UK, Vikram Patel will speak on 'People's health in people's hands: Reimagining health care' on February 16. The concluding session on February 17 will be by founder, BoP HUB, world toilet organization, Jack Sim. He will speak on creating a global movement for sanitation. Live telecast of the lectures will be screened on local channels as well as on the website of directorate of art and culture.

‘Experts over celebs’ at Kosambi festival this year

Panaji: Experts with great oratory skills have been given priority over celebrity status at the 10th edition of DD Kosambi Festival of Ideas, that will be inuagurated on February 13 at 5pm at Kala Academy.

"Over the decade, we have had to attract crowds by inviting glamourous speakers. But this year, we have given importance to good orators over celeb quotient. These speakers will deliver strong content in their talks," said art and culture director Prasad Lolyekar.

The festival will open with Sandesh Kadur's talk on India's mountains of life on February 13. An award-winning wildlife photojournalist and documentary filmmaker, Kadur, through the use of still images and videos, exposes the need for conservation and protection of the planet's biodiversity.

On February 14, Shubha Tole, a neuroscientist whose research involves investigating the development and evolution of the mammalian brain, will speak on 'wiring up the brain'.

Sugata Mitra, known for his 'Hole In The Wall' experiment wherein a computer was embedded in a Delhi slum wall in 1999 for children's use, will speak on the future of learning on February 15.

Co-founder of NGO Sangath, Vikram Patel will speak on 'people's health in people's hands: reimagining health care' on February 16. Patel was listed in TIME Magazine's 100 most influential persons of the year in 2015.

The concluding session on February 17 will be by Jack Sim, who founded the World Toilet Organization in 2001. Sim, widely known as 'Mr Toilet' for breaking the taboo around sanitation, will speak on creating a global movement for sanitation. It is due to Sim's efforts that November 19 has been declared as UN World Toilet Day.

The festival will be inaugurated by IAS officer Daulat Hawaldar.

Source: The Times of India

‘Govt must honour D D Kosambi’: GN Devy

Source: The Times of India

TNN | Updated: Nov 20, 2016, 11.10 AM IST

MARGAO: Stating that Buddhist scholar and Pali language expert D D Kosambi, who had no formal education, was the most original thinker the country had seen in the last 500 years. Literary scholar and cultural activist, G N Devy said the Goa government must consider setting up a centre in his name.

"It was he who introduced B R Amedkar to Buddhism and who introduced Marxism to India. India wouldn't have known about the ancient Pali language, if it wasn't for Kosambi who revived it. He made the entire world his domain for thinking," Devy said, adding that a centre named after him will be a great contribution to his legacy.

Confusing history with myth: Why ICHR should stick to history

Source: Indian Express

Scholars have written copiously on the foolishness of discounting the role that myths play in understanding life and society, and the value of fiction, stories and tales passed on.

Written by Seema Chishti | New Delhi | Updated: August 18, 2016 8:38 pm

In legendary historian DD Kosambi’s excellent work on ancient India titled ‘Myth and Reality’ (1962), he writes about his essays, almost as if for 2016 India; “they are based upon the collation of field-work with literary evidence. Indian critics, whose patriotism outstrips their grasp of reality are sure to express annoyance or derision at the misplaced emphasis..”

Broadly defined as a story of the past, history has come to mean much more. In a society which is so diverse, it has often come to mean very different things to different people. History is a story that needs to be told cautiously sometimes but nevertheless must be told, taught and studied.

The bid of the Indian Council for Historical Research (ICHR) to announce that it is now going down the route of collecting detailed “folklore”, “custom” and “only documenting what is heard”, about the very distant past, appears fraught with monumental issues.

Scholars have written copiously on the foolishness of discounting the role that myths play in understanding life and society, and the value of fiction, stories and tales passed on. To be unmindful of prevalent legends would leave us the poorer in comprehending much harder material truths. But problems begin, when legends, myths and history are all sought to be confused.

The function of recording, teaching or studying History, is surely to learn lessons from the past, to be familiar with compatriots, to learn and unlearn about other lives, or at least that is the purpose we hope history serves for us, when taught in schools and beyond.

Historiography is serious and contested terrain but ground rules about what constitutes evidence and what hearsay suggests that it is very important that the difference be maintained.

There is no harm therefore in knowing about myths and legends, but to be able to tell clearly what a piece of pottery, jewellery, a grave or a monument or cooking utensils tell you about people long gone before us should be a priority in a vast and old civilisation like ours.

History is more important, when governments are involved in writing (and rewriting) textbooks. Textbooks being among the most useful ammunition to control young minds. The1980s phase in our neighbouring state of Pakistan survives uptil today in dangerously altered textbooks, or how history is studied in middle-schools. A recent project by two Pakistani scholars, Qasim Aslam and Ayyaz Ahmed, studies how differently Indian and Pakistani textbooks, learn about exactly the same facts. Not that India has got it all right, but the necessity of feeding myths to Pakistan was such a dominant idea there, that History was firmly pushed out of the frame.

Myths, being privileged over history writing, have been known to serve a useful political purpose. The myth of Aryan supremacy would have been a useful account to spin support for the Nazi view of the world in its time. When the ‘superiority’ of White-skinned plunderers in Africa had to be established, myths and legends, hearsay and anecdotes over years would have been a useful tool to establish why it was the way things should be. Which of us has not heard a story whispered at a monument which says the exact opposite of what we have known to be a recorded fact about the monument/area/people?

If only to avoid history from repeating itself, either as tragedy or a farce, it may be well worth the while of institutions like ICHR, tasked with serious historical research to do exactly that. Myths have a place, but for India to have a functional present and future, they must not be confused with history.

‘Kosambi memory’ today

Source: The Hindu

The Centre for Gandhian and Peace Studies, Manipal University, in association with Centre for Vedic and Linguistic Inquiry will organise a seminar titled ‘Kosambi memory’ here on July 2 in memory of the late D.D. Kosambi, historian, mathematician, numismatist, and statistician.

A press release here on Thursday said that the seminar was being organised on the occasion of Prof. Kosambi’s 50th death anniversary.

The speakers will include K.P. Rao, founder-director, Centre for Vedic and Linguistic Inquiry, Manipal, Surendra Rao, retired professor of History, Mangalore University, and Varadesh Hiregange, Director, Centre for Gandhian and Peace Studies.

The seminar will begin at 10.30 a.m. at LH 1, first floor, Old TAPMI building.

Kosambi was not an ‘official Marxist’, says historian

Kosambi was not an ‘official Marxist’, says historian

Source: The Hindu

K.P. Rao, software expert and Director of Centre for Vedic and Linguistic Inquiry, speaking at a seminar on D.D. Kosambi in Manipal.

B. Surendra Rao, retired Professor of History, Mangalore University, has said that though the late D.D. Kosambi used Marxist notions of history, he was not a reductionist.

He was speaking on ‘D.D. Kosambi’s contribution to history’, a seminar organised by the Centre for Gandhian and Peace Studies, a constituent of Manipal University, and the Centre for Vedic and Linguistic Inquiry, here on Saturday.

According to a press release issued here on Sunday, Prof. Surendra Rao said that Kosambi considered himself a Marxist, but “official Marxists” did not consider him as a Marxist. In this context, the differences between Kosambi and S.A. Dange were worth noting, he said.

A historian was one who looked at the present rooted in the past. Myth was a different order of reality. Socialism would not be redundant so long as there was socio-economic injustice.

In his ‘Exasperating Essays’ and ‘Myth and Reality’, Kosambi was precisely trying to make use of this perspective. Eminent historians such as Romila Thapar and Irfan Habib had profusely acknowledged Kosambi’s contribution to history, Prof. Rao added.

K.P. Rao, software expert and Director of Centre for Vedic and Linguistic Inquiry, said that about five decades ago, Kosambi argued in favour of solar energy against atomic energy even while working with nuclear scientist Homi J. Bhabha.

Recalling his memories and association with both Kosambi and Bhabha, Prof. K.P. Rao said that Kosambi was then itself quite concerned about the “rise in temperature” of the world. It was Kosambi’s hope that sun being the “natural source of energy” was the way forward. On this point, he parted ways with Bhabha in Tata Institute of Fundamental Research, he said. Responding to the view that Kosambi was a Marxist, Prof. K.P. Rao said, “If this is Marxism, then Marxists are welcome.”

Varadesh Hiregange, Director of Gandhian and Peace Studies, who delivered a lecture on Prabhaker Acharya’s essay on Kosambi’s thesis with regard to ‘Urvasi myth of Rigveda’, said Kosambi’s approach to Rigveda was anthropological.

Make hay while the sun shines!

by  KULDEEP KUMAR

Source: The Hindu 13th May 2016

D.D. Kosambi’s essays aptly titled “Adventures into the Unknown” reveal how the scientist pushed for solar power more than half-a-century ago when the world was busy playing with atoms

Believe it or not, India has set an ambitious target of adding 100 gigawatts of solar power by 2022. Before the Paris Climate Summit, it had pledged that by 2032, it would increase its share of non-fossil fuels to 40 per cent of the total power generation capacity. These decisions have come many years after India under the leadership of Prime Minister Manmohan Singh had signed the controversial civil nuclear agreement with the United States with a view to meet its energy requirements. So, clearly, solar energy is the flavour of the season.

This reminds me that there was a time in the 1950s and early 1960s when those who advocated solar energy could be pitted against the scientific and technological establishment of the country and viewed with suspicion. D. D. Kosambi, a polymath genius who made seminal contributions in pure mathematics, quantitative numismatics, Sanskrit studies and the study of ancient Indian history and culture, was one such individual who came in direct conflict with the Department of Atomic Energy because of his strong views against the use of nuclear energy as he favoured solar energy in its place. He also had to cross swords with Homi Jehangir Bhabha, widely recognised as the father of the Indian atomic energy programme.

It was Bhabha who had invited Kosambi in 1945 to join the recently established Tata Institute of Fundamental Research (TIFR) and help set up the School of Mathematics. In the initial years their relations were very cordial (as it is clear from Kosambi’s scribble on the newspaper cartoon that he forwarded to Bhabha) but soon differences cropped up as Kosambi emphasised that a country like India that received sunshine in abundance must place greater reliance on solar energy. That he was a die-hard Marxist, who was very active in the international peace movement, did not help matters.

In the 1950s, the Department of Atomic Energy had started funding TIFR and Kosambi’s continuance there became untenable. Moreover, the fact that he had also emerged as a major historian who had brought about a paradigmatic shift in the study of ancient Indian society also made his fellow scientists view him with suspicion as his non-scientific interests were not considered compatible with his senior position in TIFR.

Recently, Three Essays Collective brought out a collection of Kosambi’s essays titled “Adventures into the Unknown”. Ram Ramaswamy, Professor of Physics at the Jawaharlal Nehru University, has edited this volume that contains hitherto unpublished material. In his preface, Ramaswamy informs that in 1960 Kosambi gave a talk to the Rotary Club of Poona and the text has been published here as “Atomic Energy for India”. In this essay, he underlines the need for research and development in the field of solar energy, a need to which our government seems to have woken up only recently. “Solar energy,” Kosambi says, “is not something that any villager can convert for use with his own unaided efforts, at a negligible personal expenditure, charkha style. It means good science and first-rate technology whose results must be made available to the individual user.” Nuclear disasters like Chernobyl and Fukushima have proved visionaries like Kosambi right.

In 2013, Prof. Meera Kosambi, the sociologist daughter of D. D. Kosambi, edited a book that contained writings of her as well as on her father. Titled “Unsettling the Past”, it was published by Permanent Black. It also contains two other essays of Kosambi on the question of solar energy that were written between 1957 and 1964. In “Sun or Atom?”, Kosambi draws our attention to the fact that scientific and technological research in the developed world is inextricably tied to the military-industrial complex and therefore solar energy was being ignored.

He says, “The research is of no use for war purposes. That is why it attracts some of us, but does not attract those who control the funds.” In another essay “Solar Energy for Underdeveloped Areas”, Kosambi cites another reason why significant technological advances were not being made to solve the problem of storage of solar energy: “The lands where technology is most advanced are just those which have very little sunlight as compared to India and Africa and where conventional forms of energy are highly developed.” However, he was quite confident that ultimately solar energy would become affordable and gave the example of aluminium. “But extracting this metal was a most costly process and aluminium was, a century ago, costlier than gold. Technology has made the metal cheap…”

As India finally turns to solar energy, it is very refreshing to read these essays that were written more than half-a-century ago.

The writer is a senior literary critic

Government revises D D Kosambi Research Fellowship scheme

Source: the Times of India

TNN | Apr 26, 2016, 10.46 AM IST

Panaji: The state government has revised the D D Kosambi Research Fellowship scheme. The objective of the scheme is to encourage Goan scholars to undertake research in the field of Goan history, culture, arts, social studies and related areas. Three fellowships, under the scheme, will be awarded every year by the state - at the junior level, at the senior level and at the post-doctoral level.

"Only topics that are closely connected to Goa will be accepted. However, authentic topics pertaining to Goa may also be considered for the fellowship depending upon the decision taken by the expert committee," the revised scheme document reads.

An individual who has completed post-graduation and is 35 and younger will be eligible to undertake research in the junior category. For the senior category an individual who has completed post-graduation and is above the age of 35 will be eligible. And for eligibility at the post-doctoral level, the individual will have to have completed PhD. There is no age bar for the third category.

"In case of exceptionally talented scholars of proven record with authentic work to their credit, the rules regarding educational qualifications may be relaxed, if recommended by the selection committee. The fellowship shall be awarded to any scholar only once in his lifetime under each category," the scheme states.

Eligible scholars for junior category will be awarded a fellowship up to Rs 10,000 per month for a maximum period of two years, on case-to-case basis. Scholars in the senior and post-doctoral category will be awarded a fellowship of Rs 20,000 per month for a maximum period of two years, again on case-to-case basis.

Every year, the department of art and culture will release an advertisement inviting applications for the "D D Kosambi Research Fellowship" for scholars and a selection committee constituted by the government will select scholars for the fellowship.

The project report in the form of two hard copies and a soft copy will have to be submitted within a period of 30 days after the completion of two years of the fellowship. The project submitted will be exclusively the property of department of art and culture, as per the scheme guidelines.