 Damodar Dharmananda Kosambi

D. D. Kosambi Born July 31, 1907
Kosben, GoaDied June 29, 1966
Pune, MaharashtraOccupation Mathematician and Marxist historian Damodar Dharmananda Kosambi (July 31, 1907 – June 29, 1966) was an Indian mathematician, statistician, Marxist historian, and polymath who contributed to genetics by introducing Kosambi's map function. He is wellknown for his work in numismatics and for compiling critical editions of ancient Sanskrit texts. His father, Dharmananda Damodar Kosambi, had studied ancient Indian texts with a particular emphasis on Buddhism and its literature in the Pali language. Damodar Kosambi emulated him by developing a keen interest in his country's ancient history. Kosambi was also a Marxist^{[1]} historian specializing in ancient India who employed the historical materialist approach in his work. He is described as "the patriarch of the Marxist school of Indian historiography".^{[1]} Kosambi was critical of the policies of then Prime Minister Jawaharlal Nehru, which, according to him, promoted capitalism in the guise of democratic socialism. He was an enthusiast of the Chinese revolution and its ideals, and, in addition, a leading activist in the World Peace Movement. In the opinion of the historian Irfan Habib, "D. D. Kosambi and R.S. Sharma, together with Daniel Thorner, brought peasants into the study of Indian history for the first time."^{[2]}
Contents
Early life
After a few years of schooling in India, in 1918 D.D. Kosambi and his elder sister, Manik Kosambi, traveled to Cambridge, Massachusetts with his father; the latter was tasked by Professor Charles Rockwell Lanman of Harvard University to complete compiling a critical edition of Visuddhimagga, a book on Buddhist philosophy, which was originally started by Henry Clarke Warren. There he spent a year in the Grammar school and then was admitted to the Cambridge High and Latin School in 1920. He became a member of the Cambridge branch of American Boy Scouts.
It was here in Cambridge that he befriended another prodigy of the time, Norbert Wiener, whose father Leo Wiener was the elder Kosambi's colleague at Harvard University.
Kosambi excelled in his final school examination and was one of the few candidates who was exempt on the basis of merit from necessarily passing an entrance examination essential at the time to gain admission to Harvard University. He enrolled in Harvard in 1924, but eventually postponed his studies, and returned to India. He stayed with his father who was now working in the Gujarat University, and was in the close circles of Mahatma Gandhi.
In January 1926, Kosambi returned to the US with his father, who once again studied at Harvard University for a year and half. Kosambi studied mathematics under George David Birkhoff, who wanted him to concentrate on mathematics, but the ambitious Kosambi instead took many diverse courses excelling in each of them. In 1929, Harvard awarded him the Bachelor of Arts degree with a summa cum laude. He was also granted membership to the esteemed Phi Beta Kappa Society, the oldest undergraduate honours organization in the United States. He returned to India soon after. He was technical consultant to the Chinese government.
Banaras and Aligarh
He obtained the post of professor at the Banaras Hindu University (BHU), teaching German alongside mathematics. He struggled to pursue his research on his own, and published his first research paper, "Precessions of an Elliptic Orbit" in the Indian Journal of Physics in 1930.
In 1931, Kosambi married Nalini, daughter of a very wealthy and distinguished member of the Madgaonkar family. It was in this year that he was hired by mathematician André Weil, then Professor of Mathematics at Aligarh Muslim University, to the post of lecturership in mathematics at Aligarh.^{[3]} His other colleagues at Aligarh included Vijayraghavan. During his two years stay in Aligarh, he produced eight research papers in the general area of Differential Geometry and Path Spaces. His fluency in several European languages allowed him to publish some of his early papers in French, Italian and German journals in their respective languages.
Fergusson College, Pune
In 1933, he joined the Deccan Education Society’s Fergusson College in Pune, where he taught mathematics for the next 12 years. In 1935, his eldest daughter, Maya was born, while in 1939, the youngest, Meera, a wellknown sociologist and feminist was born.
In Pune, while teaching mathematics and conducting research in the field, he started his interdisciplinary pursuit. In 1944 he published a small article of 4 pages titled ‘The Estimation of Map Distance from Recombination Values’ in Annals of Eugenics, in which he introduced what later came to be known as Kosambi's map function.
One of the most important contributions of Kosambi to statistics is the widely known technique called proper orthogonal decomposition (POD). Although it was originally developed by Kosambi in 1943, it is now referred to as the Karhunen–Loève expansion. In the 1943 paper entitled 'Statistics in Function Space' presented in the Journal of the Indian Mathematical Society, Kosambi presented the Proper Orthogonal Decomposition some years before Karhunen (1945) and Loeve (1948). This tool has found application to such diverse fields as image processing, signal processing, data compression, oceanography, chemical engineering and fluid mechanics. Unfortunately this most important contribution of his is barely acknowledged in most papers that utilize the POD method. In recent years though, it is heartening to note that some authors have indeed referred to it as the KosambiKarhunenLoeve decomposition.^{[4]}
It was his studies in numismatics that initiated him into the field of historical research. He made a thorough study of Sanskrit and ancient literature, and he started his classic work on the ancient poet Bhartṛhari. He published his critical editions of Bhartrihari's Shatakatrayee and Subhashitas during 19451948.
It was during this period that he started his political activism, coming close to the radical streams in the ongoing Independence movement, especially the Communist Party of India. He became an outspoken Marxist and wrote some political articles.
Tata Institute of Fundamental Research
In 1945, Homi J. Bhabha invited Kosambi to join the Tata Institute of Fundamental Research (TIFR) as Professor of Mathematics, which he accepted. After independence, in 194849 he was sent to England and the US as a UNESCO Fellow to study the theoretical and technical aspects of the computer. During this time, he was a visiting professor of geometry at the University of Chicago. He spent some time at the Institute for Advanced Study in Princeton, New Jersey. In London, he started his longlasting friendship with indologist and historian A.L. Basham.
After his return to India, in the Cold War circumstances, he was increasingly drawn into the World Peace Movement and served as a Member of the World Peace Council. He became a tireless crusader for peace, campaigning against the nuclearisation of the world. Kosambi's solution to India's energy needs was in sharp conflict with the ambitions of the Indian ruling class. He proposed alternative energy sources, like solar power. His activism in the peace movement took him to Beijing, Helsinki and Moscow. However, during this period he relentlessly pursued his diverse research interests, too. Most importantly, he worked on his Marxist rewriting of ancient Indian history, which culminated in his book, An Introduction to the Study of Indian History (1956).
He visited China many times during 195262 and was able to watch the Chinese revolution very closely, making him critical of the way modernisation and development were envisaged and pursued by the Indian ruling classes. All these contributed to straining his relationship with the Indian government and Bhabha, eventually leading to Kosambi's exit from the Tata Institute of Fundamental Research in 1962.
PostTIFR days
His exit from the TIFR gave Kosambi the opportunity to concentrate on his research in ancient Indian history culminating into his book, The Culture and Civilisation of Ancient India, which was published in 1965 by Routledge, Kegan & Paul. The book was translated into German, French and Japanese and was widely acclaimed. He also utilised his time in archaeological studies, and contributed in the field of statistics and number theory. His article on numismatics was published in February 1965 in Scientific American.
Due to the efforts of his friends and colleagues, in June 1964, Kosambi was appointed as a Scientist Emeritus of the Council of Scientific and Industrial Research (CSIR) affiliated with the Maharashtra Vidnyanvardhini in Pune. He pursued many historical, scientific and archaeological projects (even writing stories for children). But most works he produced in this period could not be published during his lifetime. On June 29, 1966, he died in Pune. He was posthumously decorated with the Hari Om Ashram Award by the government of India's University Grant Commission in 1980.
His friend A.L. Basham, a wellknown indologist, wrote in his obituary:
 At first it seemed that he had only three interests, which filled his life to the exclusion of all others — ancient India, in all its aspects, mathematics and the preservation of peace. For the last, as well as for his two intellectual interests, he worked hard and with devotion, according to his deep convictions. Yet as one grew to know him better one realized that the range of his heart and mind was very wide...In the later years of his life, when his attention turned increasingly to anthropology as a means of reconstructing the past, it became more than ever clear that he had a very deep feeling for the lives of the simple people of Maharashtra.^{[5]}
Kosambi's historiography
As an historian, Kosambi revolutionised Indian historiography with his Marxist approach, crucially diverting from the mainstream nationalist and imperialist schools. He understood history in terms of the dynamics of socioeconomic formations rather than just a chronological narration of "episodes" or the feats of a few great men  kings, warriors or saints. In the very first paragraph of his classic work, An Introduction to the Study of Indian History, he gives an insight into his methodology as a prelude to his life work on ancient Indian history:
 "THE lighthearted sneer “India has had some episodes, but no history“ is used to justify lack of study, grasp, intelligence on the part of foreign writers about India’s past. The considerations that follow will prove that it is precisely the episodes — lists of dynasties and kings, tales of war and battle spiced with anecdote, which fill school texts — that are missing from Indian records. Here, for the first time, we have to reconstruct a history without episodes, which means that it cannot be the same type of history as in the European tradition."^{[6]}
According to A. L. Basham, "An Introduction to the Study of Indian History is in many respects an epoch making work, containing brilliantly original ideas on almost every page; if it contains errors and misrepresentations, if now and then its author attempts to force his data into a rather doctrinaire pattern, this does not appreciably lessen the significance of this very exciting book, which has stimulated the thought of thousands of students throughout the world."^{[7]}
Professor Sumit Sarkar says: "Indian Historiography, starting with D.D. Kosambi in the 1950s, is acknowledged the world over — wherever South Asian history is taught or studied  as quite on a par with or even superior to all that is produced abroad. And that is why Irfan Habib or Romila Thapar or R.S. Sharma are figures respected even in the most diehard antiCommunist American universities. They cannot be ignored if you are studying South Asian history."^{[8]}
In his obituary to Kosambi published in the Nature, J. D. Bernal had summed up Kosambi's talent as follows: "Kosambi introduced a new method into historical scholarship, essentially by application of modern mathematics. By statistical study of the weights of the coins, Kosambi was able to establish the amount of time that had elapsed while they were in circulation and so set them in order to give some idea of their respective ages."
Books by D.D. Kosambi
Works on history and society
 1956 An Introduction to the Study of Indian History (Popular Book Depot, Bombay)
 1957 Exasperating Essays: Exercise in the Dialectical Method (People's Book House, Poona)
 1962 Myth and Reality: Studies in the Formation of Indian Culture (Popular Prakashail, Bombay)
 1965 The Culture and Civilisation of Ancient India in Historical Outline (Routledge & Kegan Paul, London)
 2002 D.D. Kosambi: Combined Methods in Indology and Other Writings  Compiled, edited and introduced by Brajadulal Chattopadhyaya (Oxford University Press, New Delhi)
 2009 The Oxford India Kosambi  Compiled, edited and introduced by Brajadulal Chattopadhyaya (Oxford University Press, New Delhi)
Edited works
 1945 The Satakatrayam of Bhartrhari with the Comm. of Ramarsi, edited in collaboration with Pt. K. V. Krishnamoorthi Sharma (Anandasrama Sanskrit Series, No.127, Poona)
 1946 The Southern Archetype of Epigrams Ascribed to Bhartrhari (Bharatiya Vidya Series 9, Bombay) (First critical edition of a Bhartrhari recension.)
 1948 The Epigrams Attributed to Bhartrhari (Singhi Jain Series 23, Bombay) (Comprehensive edition of the poet's work remarkable for rigorous standards of text criticism.)
 1952 The Cintamanisaranika of Dasabala; Supplement to Journal of Oriental Research, xix, pt, II (Madras) (A Sanskrit astronomical work which shows that King Bhoja of Dhara died in 105556.)
 1957 The Subhasitaratnakosa of Vidyakara, edited in collaboration with V.V. Gokhale (Harvard Oriental Series 42)
Mathematical publications by D. D. Kosambi
 1930 Precessions of an elliptical orbit, Indian J. Phys., 5(3), 359364.
 1931 On a generalization of the second theorem of Bourbaki, Proc. Acad. Sciences UP, 1
 1932 Modern differential geometries, Indian J. Phys., 7(2), 159164.
 1932 On the existence of a metric and the inverse variational problem, Proc. Acad. Sciences UP, 2, 1728.
 1932 Geometric differentiale et calcul des variations, Rendiconti della Reale Accademia Nazionale dei Linceit, 16(6), 410415.
 1932 On differential equations with the group property, J. Indian Math. Soc., 19(1), 215219.
 1932 Affingeometrische grundlagen der einheitlichen feldtheorie, Sitzungsberichten der Preuss B. Akademic der Wissenschaften, Physikalischmathematische klasse, 28, 342345.
 1933 The classification of integers, J. Univ. Bombay, 2(2), 1820.
 1933 The problem of differential invariants, J. Indian Math. Soc., 20, 185188.
 1933 Parallelism and pathspaces, Mathematische Zeitschrift, 37, 608622.
 1934 Collineations in pathspace, J. Indian Math. Soc., 1(2), 6872.
 1934 Continuous groups and two theorems of Euler, Math. Student, 2(3), 94100.
 1934 The maximum modulus theorem, J. Univ. Bombay, 3(2), 1112.
 1935 Systems of differential equations of the second order, Quarterly J. Math. (Oxford Series), 6(21), 112.
 1935 Homogeneous metrics, Proc. Indian Acad. Sciences, 1(A:12), 952954.
 1935 An affine calculus of variations, Proc. Indian Acad. Sciences, 2, 333335.
 1936 Differential geometry of the Laplace equation, J. Indian Math. Soc., 2, 141143.
 1936 Pathspaces of higher order, Quarterly J. Math. (Oxford Series), 7(26), 97104.
 1936 Pathgeometry and cosmogony, Quarterly J. Math. (Oxford Series), 7(28), 290293.
 1938 Les metriques homogenes dans les espaces cosmogoniques, Comptes rendus, 206, 10861088.
 1938 Les espaces des paths generalises qu'on peut associer avec un espace de Finsler, Comptes rendus, 206, 15381541.
 1939 The tensor analysis of partial differential equations, J. Indian Math. Soc., 3, 249253.
 1940 Pathequations admitting the Lorenz group, J. London Math. Soc., 15(2:58), 8691.
 1940 The concept of isotropy in generalized pathspaces, J. Indian Math. Soc., 4, 8088.
 1940 A note on frequency distribution in series, Math. Student, 8, 151155.
 1941 A bivariate extension of Fisher's Z test, Current Science, 10, 191192.
 1941 Correlation and time series,Current Science, 10, 372774.
 1941 Pathequations admitting the Lorenz group  II, J. Indian Math. Soc., 5(2), 6272.
 1942 On the zeros and closure of orthogonal functions, J. Indian Math. Soc., 6(1), 1624.
 1943 Statistics in function space, J. Indian Math. Soc., 7, 7688.
 1944 The estimation of map distance from recombination values, Annals of Eugenics, 12(3), 172175.
 1944 Direct derivation of series spectra, Current Science, 13, 71.
 1944 The geometric method in mathematical statistics, Amer. Math. Monthly, 51(7), 382389.
 1945 Parallelism in the tensor analysis of partial differential equations, Bull. Amer. Math. Soc., 51, 293296.
 1946 The law of large numbers, Mathematics Student, 14, 1419.
 1946 Sur la differentiation covariante, Comptes rendus, 222, 211213.
 1947 An extension of the leastsquares method for statistical estimation, Annals of Eugenics, 18, 257261.
 1947 Les invariants differentials d'un tenseur covariant a deux indices, Comptes rendus, 225, 790792.
 1948 Systems of partial differential equations of the second order, Quarterly J. Math. (Oxford Series), 19(76), 204219.
 1949 Characteristic properties of series distributions, Proc. Nat. Inst. Science of India, 15(3), 109113.
 1949 The differential invariants of a twoindex tensor, Bull. Amer. Math. Soc., 55(1:2), 9094.
 1951 Seasonal variation in the Indian birth rate, (coauthored with S. Raghavachari), Annals of Eugenics, 16(2), 165192.
 1951 Series expansions of continuous groups, Quarterly J. Math. (Oxford Series 2), 2(8), 244257.
 1952 Pathspaces admitting collineations, Quarterly J. Math. (Oxford Series 2), 3(9), 111.
 1952 Pathgeometry and continuous groups, Quarterly J. Math. (Oxford Series 2), 3(19), 307320.
 1954 The metric in pathspace, Tensor (New Series), 3, 6774.
 1954 Seasonal variation in the Indian death rate, (coauthored with S. Raghavachari), Annals of Human Genetics, 19(2), 100119.
 1958 Classical Tauberian theorems, J. Indian Soc. Agricultural Statistics, 10, 141149.
 1958 The efficiency of randomization by card shuffling (coauthored with U.V. Ramamohana Rao), J. Royal Stat. Soc., Series A (General), 121(2), 223233.
 1959 The method of least squares, J. Indian Soc. Agricultural Statistics, 12, 4957.
 1959 An application of stochastic convergence, J. Indian Soc. Agricultural Statistics, 12, 5872.
 1963 The sampling distribution of primes, Proc. Nat. Acad. Sciences U.S.A., 49, 2023.
 1966 Scientific numismatics, Scientific American, February, 102111.
See also
Notes
 ^ ^{a} ^{b} Sreedharan, E. (2004). A Textbook of Historiography: 500 BC to AD 2000. Orient Blackswan. p. 469. ISBN 9788125026570.
 ^ Habib, Irfan (Seventh reprint 2007). Essays in Indian History. Tulika. p. 381 (at p 109). ISBN 9788185229003.
 ^ Weil, Andre. The Apprenticeship of a Mathematician. Berlin and Boston: Birkhauser. 1994.
 ^ http://etd.lib.fsu.edu/theses/available/etd07062009230217/unrestricted/Steward_J_Thesis_2009r.pdf
 ^ A.L. Basham, "Baba: A Personal Tribute"
 ^ An Introduction to the Study of Indian History, pp.1
 ^ A.L. Basham, op cit
 ^ "'Not a question of bias'". Frontline. Volume 17  Issue 05, Mar. 04  17, 2000. http://www.hinduonnet.com/thehindu/fline/fl1705/17050260.htm. Retrieved 20090623.
References
 R.S. Sharma and Vivekanand Jha, Indian Society, Historical Probings (in memory of D. D. Kosambi), People's Publishing House, New Delhi, 1974.
 J.D.Bernal: obituary D.D.Kosambi. Nature, 1966 Sept.3; 211: 1024.
External links
 The making of an Indologist (Review article in Frontline magazine)
 The Hindu online 22 April 2003
 Oxford University Press
 This site includes pdf copies of Kosambi's historical works
 Contains works on and of D.D. Kosambi
 A new site on D.D.Kosambi
 Biography of Kosambi by C.D. Deshmukh
 Blog on DD Kosambi
 Biography of Kosambi by Jyotsna Kamat
Categories: Goans in science and technology
 1907 births
 1966 deaths
 Harvard University alumni
 Historians of South Asia
 Indian Marxist historians
 Indian mathematicians
 Marathilanguage writers
 Numismatists
 People from Goa
 Sanskrit scholars
 20thcentury mathematicians
 Aligarh Muslim University faculty
 Banaras Hindu University faculty
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