Damodar Dharmananda Kosambi
Damodar Dharmananda Kosambi (31 July 1907 – 29 June 1966) was an Indian polymath with interests in mathematics, statistics, philology, history, and genetics. He contributed to genetics by introducing the "Kosambi map function". In statistics, he was the first person to develop orthogonal infinite series expressions for stochastic processes via the Kosambi–Karhunen–Loève theorem. He is also well known 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. He was also a Marxist historian specialising in ancient India who employed the historical materialist approach in his work. He is particularly known for his classic work "An Introduction to the Study of Indian History". He is described as "the patriarch of the Marxist school of Indian historiography". 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 Communist Revolution and its ideals, and was  a leading activist in the world peace movement. Early life. Damodar Dharmananda Kosambi was born at Kosben in Portuguese Goa to the Buddhist scholar Dharmananda Damodar Kosambi. After a few years of schooling in India, in 1918, Damodar and his elder sister, Manik travelled to Cambridge, Massachusetts with their father, who had taken up a teaching position at the Cambridge Latin School. Their father 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, the young Damodar spent  a year in a 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 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 "". He was also granted  membership to the esteemed Phi Beta Kappa Society, the oldest undergraduate honours organisation in the United States. He returned to India soon after. 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 from the wealthy 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. 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. Mathematics. In 1932, he joined the Deccan Education Society's Fergusson College in Pune, where he taught mathematics for 14 years. In 1935, his eldest daughter, Maya was born, while in 1939, the  youngest, Meera. 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 map function. According to his equation, genetic map distance (w) is related to recombination fraction (θ) in the following way: formula_1 or, put in another way, formula_2 Kosambi's mapping function adjusts the map distance based on interference which changes the proportion of double crossovers.(To know more about this you can explore the given website https://www.academia.edu/665254/Kosambi_and_the_genetic_mapping_function (edit: Bhaskarlal Datta) 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 utilise the POD method. In recent years though, some authors have indeed referred to it as the Kosambi-Karhunen-Loeve decomposition. Historical studies. Until 1939, Kosambi was almost exclusively focused on mathematical research, but later, he gradually started foraying into social sciences. It was his studies in numismatics that initiated him into the field of historical research. He did extensive research in difficult science of numismatics. His evaluation of data was by modern statistical methods. For example, he statistically analyzed the weight of thousands of punch-marked coins from different Indian museums to establish their chronological sequence  and put forward his theories about the economic conditions under which these coins could have been minted. Sanskrit. He made a thorough study of Sanskrit and ancient literature, and he started his classic work on the ancient poet Bhartṛhari. He published exemplary critical editions of Bhartrihari's Śatakatraya and Subhashitas during 1945–1948. Activism. 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 the 1940s, Homi  J. Bhabha invited Kosambi to join the Tata Institute of Fundamental Research (TIFR). Kosambi joined TIFR as chair for mathematics in 1946, and held the position for the next 16 years. He continued to live in his own house in Pune, and commute to Mumbai every day by the Deccan Queen train. After independence, in 1948–49 he was sent to England and to the US as a UNESCO Fellow to study the theoretical and technical aspects of computing machines. In London, he started his long-lasting friendship with Indologist and historian A.L. Basham. In the spring semester of 1949, he  was a visiting professor of geometry in the Mathematics Department at the University of Chicago, where his colleague from his Harvard days, Marshall Harvey Stone, was the chair. In April–May 1949, he spent nearly two months at the Institute for Advanced Study in Princeton, New Jersey, discussing with such illustrious physicists and mathematicians as J. Robert Oppenheimer, Hermann Weyl, John von Neumann, Marston Morse, Oswald Veblen and Carl Ludwig Siegel amongst others. 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 1952–62 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. Post-TIFR days. His exit from the TIFR gave Kosambi the opportunity to concentrate on his research in ancient Indian history culminating in 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. Kosambi died of myocardial infarction in the early hours of 29 June 1966, after being declared generally fit by his family doctor on the previous day. 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 well-known indologist, wrote in his obituary: Kosambi's historiography. Although Kosambi was not a practising historian, he wrote four books and sixty articles on history: these works had a significant impact on the field of Indian historiography. He understood history in terms  of the dynamics of socio-economic 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: 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." 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." In his obituary of Kosambi published in "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." Legacy. Kosambi is an inspiration to many across the world, especially to Sanskrit philologists and Marxist scholars. He deeply influenced Indian historiography. The Government of Goa has instituted the annual D.D. Kosambi Festival of Ideas since February 2008 to commemorate his birth centenary. Historian Irfan Habib said, "D. D.  Kosambi and R.S. Sharma, together with Daniel Thorner, brought peasants into the study of Indian history for the first time." Kosambi was an atheist. India Post issued a commemorative postage stamp on 31 July 2008 to honour Kosambi. Mathematical and scientific publications. In addition to the papers listed below, Kosambi wrote two books in mathematics, the manuscripts of which have not been traced. The first was a book on path geometry that was submitted to Marston Morse in the mid-1940s and the second was on prime numbers, submitted shortly before his death. Unfortunately, neither book was published. The list of  articles below is complete but does not include his essays on science and scientists, some of which have appeared in the collection "Science, Society, and Peace" (People's Publishing House, 1995). Four articles (between 1962 and 1965) are written under the pseudonym S. Ducray. References. Bibliography. A collection entitled "Science, Society And Peace" of Prof DD Kosambi's essays has been published in the 1980s [exact year to be mentioned...] by Academy of Political & Social Studies, Akshay, 216, Narayan Peth,Pune 411030. Republished by People's Publishing House, New Delhi in 1995]