(31 July 1907-29 June 1966)
V. V. GOKHALE
Death overtook Professor D. D. Kosambi in his bed in the early hours of 29 June 1966 prematurely and almost surreptitiously, after he had been declared generally fit on the previous day by his family doctor. It was a case of myocardial infract. A glance at, the accompanying list of his publications will bring home to us the serious loss the world of progressive and talented writers has suffered and the void his death has left among the leading savants of renascent India.
Born at Kosben in Goa, then under the rule of the Portuguese colonialists, Damodar Kosambi was brought up in a family known for its rigorous standards of learning and social behaviour. He had inherited from his father, the renowned Buddhist scholar Dharmanand Kosambi, an insatiable spirit of inquiry, a love of wandering and a sharp, versatile intellect, which took him quickly ahead of his co- workers and gave his views a rare sense of originality. After some schooling in India, his father, who had accepted a teaching assignment at Harvard (USA), took him to the Cambridge Latin School, where as a boy of eleven he dedicated himself to a student's hard life until after about eight years we see him emerging as a brilliant young graduate of the Harvard University in Mathematics, History and Languages. On returning to India he worked for a few years at the Banaras Hindu University and then at the Aligarh Muslim University before he decided to settle down in Poona in 1932 as Professor of Mathematics at the Fergusson College--a college known for its pioneering services in the field of national education and where his father had taught for many years and laid the foundations of Buddhist Studies in western India. It was during the crucial period of fourteen years he spent at this college:, which be in lighter vein characterized as "Rama's exile into the wilderness", that Professor Kosambi carried on an incessant struggle for mastery in various fields of knowledge and laid the foundations of his greatness as a scholar and a thinker .
Endowed with a powerful and far-reaching imagination and an outstanding mathematical ability, Kosambi, who had concentrated his mind almost exclusively upon mathematical research up to 1939, was gradually led to use his abstract methods for obtaining new results in various branches of social sciences. He began by applying statistical methods to Indian numismatics. He was seen weighing with the utmost precision and unremitting zeal thousands of punch-marked coins obtained from different museums in the country and thrashing out his data until he could establish their chronological sequence, forward convincing arguments regarding the economic conditions under which they could bave been minted, and discover facts about the dynastic history of the pre-Mauryan period, based upon a wide study of the ancient literary sources and his new metrological findings. The more he examined the productive spirit working behind the panorama of Indian history, the more charmed he was by the manifold aspects of Indian. culture, the past as well as the present. While giving mathematical precision to his ideas in the various branches of humanities, he turned almost instinctively to his Sanskrit inheritance. His frank and scholarly estimate of Bhartrhari's aphorisms and later of Vidyakara's anthology, Subhasitaratnakosa, was a standing testimony to his versatile genius and quick mastery of the latest advances in literary criti- cism. In these and other Indological shldies covering a wide range of subjects from the Vedic and the Epic to the classical literature of India he owed as much to Sukthankaros prolegomena to the critical edition of the Mahabharata as to the most modern standards of criticism in the West.
Being deeply preoccupied with the entire field of knowledge as it were, it was no wonder that his mathematical lectures in the Fergusson College seemed to go well over the heads of the postgraduate candidates. That as a result of this Kosambi had to leave the college ought to open our eyes to the dangers involved in our borrowing an examination- ridden system and uninspiring standards of education in this country. The width of his comprehension and his penetrating researches, however, had been making their mark among the scientific circles of India and abroad. It was not long before he was offered the Chair for Mathematics in the Tata Institute of Fundamental Research. of Bombay in 1946, which he held for the next sixteen years. The new position offered him opportunities of developing closer contacts with scholars of his own calibre all over the world and of meeting his financial responsibilities better than before. Kosambi, however, could not relish the conditions under which he had to work. Living in his own house in the BORI Colony, Poona, he had to march every morning to the railway station and make the "Deccan Queen" his second home in order to attend to his duties in Bombay. Besides, a man of his temperament, solely dedicated to the pursuit of knowledge and social enlightenment, was entitled, he thought, to a freedom of thought and action, such as we hardly expect to meet with in an emergent society struggling for its economic independence. All the same, he was able now not only to give a final shape to some of his earlier studies, but also to launch upon new orientations in the fields of Biology, Ethnology, Archaeology and Prehistory. And every now and then we see him turning back from his study of the social sciences to the development of his research in the comparatively abstract or pure fields of science: the last book he sent out for publication dealt with Prime Numbers. His last major work, The Culture and Civilisation of Ancient India in Historical Outline (London, 1965) , which has now come to be translated into several European and Asian languages, set the seal of recognition on his vast erudition, his ability to discover basic motives of human civilization and his brilliant powers of exposition.
It is not for us to estimate the scientific advances made by Professor Kosambi in the fields of Genetics, Statistics and Mathematics or the part played by him in various other spheres of activity, e.g., in his capacity as Member of the World Peace Council visiting the socialist countries of the East and the West. He believed in the Marxist method of interpreting and changing the human society, but did not hesitate to revise the data of Marx himself in the light of modern research. As an independent thinker with a passionate devotion to scientific research, he seemed to be almost exclusively preoccupied with his own intellectual pursuits. As such, he was sometimes accused of brusqueness and intolerance, but he had obviously no use, nor time for all the sophistications of our normal social life, nor could he afford to waste his energies on empty rituals and ceremonies, except for treating them as objects or his anthropological studies. And yet, whenever he found some time to relax, his childlike simplicity and sparkling wit were most refreshing even to those who were nearest to him and he spread laughter and sunshine around him. Towards his friends he was generous to a fault, his inner life was marked by an unmistakable streak of asceticism, while his ethical standards were unusually high and severe. Professor D. D. Kosambi deserves to be remembered as one of the highly gifted and versatile scientific workers and indefatigable scholars of modern India for whom a relentless search for the highest human values was the only natural way of life.
(Reprinted from the .4nnals of the Bhan4arkar Oriental Research Institute, xlvii (Poona, 1967),118-30. )
BOOKS AND ARTICLES BY D. D. KOSAMBI
(Based on his notes )
I. Books
1. An Introduction to the Study of Indian History (Popular Book Depot, Bombay, 1956).
2. Exasperating Essays: Exercise in the Dialectical Method (People's Book House, Poona, 1957) .
3. Myth and Reality: Studies in the Formation of Indian Culture (Popular Prakashail, Bombay, 1962).
4. The Culture and Civilisation of Ancient India in Historical Outline (Routledge & Kegan Paul, London, 1965) .
II. Edited Works
1. The Satakatrayam of Bhartrhari with the Comm. of Ramarsi, edited in collaboration with Pt. K. V. Krishnamoorthi Sharma (Anandasrama Sanskrit Series, No.127, Poona, 1945), pp. 2+140+6+1.
2. The Southern Archetype of Epigrams Ascribed to Bhartrhari (Bharatiya Vidya Series 9, Bombay, 1946), pp. 176+ 13+8. (First critical edition of a Bhartrhari recension.)
3. The Epigrams Attributed to Bhartrhari (Singhi Jain Series 23, Bombay, 1948), pp. viii+82+240. (Comprehensive edition of the poet's work remarkable for rigorous standards of text criticism.)
4. The Subhasitaratnakosa of Vidyakara, edited in collaboration with V.V. Gokhale (Harvard Oriental Series 42, 1957)
5. The Cintamani-saranika of Dasabala; Supplement to Journal of Oriental Research, xix, pt, II (Madras, 1952) . viii+15, (A Sanskrit astronomical work which shows that King Bhoja of Dhara died in 1055-56.)
III. Arlicles
- "Precessions of an Elliptical Orbit", The Indian Journal of Physics, v, pt. III ( 1930) , 359-64.
- "On a Generalization of the Second Theorem of Bourbaki", Proceedings of the Academy of Sciences, UP, i ( 1931 ) ( 3 pages).
- "Modem Differential Geometries", The Indian Journal of Physics, vii, pt. II (1932), 159-64.
- "On the Existence of a Metric and the Inverse Variational Problem", Proceedings of the Academy of Sciences, UP, ii (1932), 17-28.
- "Geometrie Differentielle et Calcul des Variations", Rendiconti della R. Accademia Nazionale Dei Lincei, xvi, Series 6 ( 1932) , 410-15.
- "On Differential Equations with the Group Property", Journal of the Indian Mathematical Society, xix (1932), 215-19.
- "Affin-geometrische Grundlagen der Einheitlichen Feld- theorie", Sitzungsberichten der Preuss B. Akademic der Wissenschaften, Physikalisch-mathematische Klasse, xxviii (1932), 342-45.
- "The Classification of Integers", Journal of the University of Bolnbay, ii, pt. II (1933), 18-20.
- "The Problem of Differential Invariants", Journal of the Indian Mathematical Society, xx (1933), 185-88.
- "Parallelism and Path-spaces", Mathemati8che Zeitschrift, xxxvii (1933), 608-18.
- "Collineations in Path-space", Journal of the Indian Mathematical Society, i ( 1934) , 69-72.
- "Continuous Groups and Two Theorems of Euler", The Mathematics Student, ii (1934), 94-100.
- "The Maximum Modulus Theorem", Journal of the University of Bombay, iii, pt. II (1934), 11-12.
- "Systems of Differential Equations of the Second Order", The Quarterly Jourllal of Mathematics, vi (Oxford, 1935), 1-12.
- "Homogeneous Metrics", Proceedings of the Indian Academy of Science, i (1935), 952-54.
- "An Affine Calculus of Variations", Ibid. ii ( 1935) , 333- 35.
- "Differential Geometry of the Laplace Equation", Journal of the Indian Mathematical Society', ii (1936), 141-43.
- "Path-spaces of Higher Order", The Quarterly Journal of Mathematics, vii (Oxford, 1936), 97-104.
- "Path-geometry and Cosmogony", Ibid. pp. 290-293.
- "Les metriques homogenes dans les espaces cosmogoniques", Comptes Rendus, ccvi (Paris, 1938) , 1086-88.
- "Les espacts des paths generalises qu'on peut associer avec un espace de Finsler", Ibid. pp. 1538-41.
- "The Tensor Analysis of Partial Differential Equations", Journal of the Indian Matlrematical Society, iii ( 1939) , 249-53.
- "
A Note on the Trial of Sokrates", Fergusson College Magazine (1939), pp. 1-6 (Sokrates and the class war of his day); Reprinted in Exasperating Essays.
- "The Emergence of National Characteristics among Three Indo- European Peoples", Annals of the Bhandarkar Oriental Research Institute, xx, . pt. II (Poona, 1940), 195-206. (Trial speculation on Indology.)
- (a) "The Function of Leadership in a Mass Movement";
(b) "The Cawnpore Road", Fergusson College Maga- zine (1939-40), pp. 1-7 (A critique of dialectical- materialistic social theory; a story published under the pseudonym "Ahriman"); Reprinted in Exasperating Essays.
- (a) "Revolution and the Progress of Science", New Age, v, 320-25. (A survey of the effects of the Revolution, upon Mathematics in the USSR);
(b) "Science Learns the Goose-step", Ibid. pages unknown, as the Journal was suppressed soon after
- "Path-equations Admitting the Lorentz (Group-I)", Journal of the London Mathematical Society, xv (1940), 86-91.
- "
A Statistical Study of the Weights of the Old Indian Punch-marked Coins", Current Science, ix (1940), 312- 14.
- "A Note on Two Hoards of Punch-marked Coins Found at Taxila", New Indian Antiquary, iii (1940), 156-57.
- "The Concept of Isotropy in Generalized Path-spaces", Journal of Indian Mathematical Society, iv (1940), 80-88. 31 ."
- A Note on Frequency Distribution in Series", The Mathematics Student, viii (1940) , 151-55.
- "On the Study and Metrology of Silver Punch-marked Coins", New Indian Antiquary, iv (1941), 1-35 and 49-76 (Numismatics as a science, with an application to its most difficult problem) ; (b) Additions and Corrections, Ibid. v (1942).
- "A Bivariate Extension of Fisher's Z Test", Current Science, x (1941), 191-92.
- "Correlation and Time Series", Ibid. pp. 372-74. 35 .
- "The Quality of Renunciation in Bhartihari's Poetry". Fergusson College Magazine (1941). (A Study in Comparative Literature) .Republished with changes in Bharatiya Vidya (1946), pp. 49-62. Reprinted in Exasperating Essays.
- "Path-equations Admitting the Lorentz (Group-II)", Journal of the Indian Mathematical Society, v (1941), 62-72.
- "On the Origin and Development of Silver Coinage in India", Current Science, x (1941), 395-400. (Shows that the punch-marked coinage system developed from Mohenjodaro cut silver pieces.)
- "On Valid Tests of Linguistic Hypotheses", New Indian Antiquary, v (1942), 21-24.
- "Zeros and Closure of Orthogonal Functions", Journol of the Indian Mathematical Society, vi (1942), 16-24.
- "The Effect of Circulation upon the Weight of Metallic Currency", Current Science, xi (1942), 227-31.
- "A Test of Significance for Multiple Observations", Ibid. pp. 271-74.
- "Progress in the Production and Consumption of Textile Goods in India", Journal of Indian Merchants' Chamber (Bombay, 1943) , pp. 11-15. Published as by "Vidyarthi" and Miss Sushila Gokhale.
- "Race and Immunity in India", New Indian Antiquary, vi (1943), 29-33.
- "Statistics in Function Space", JournaJ of the Indian Mathematical Society, vii ( 1943) , 76-88.
- "Soviet Victory and the World Revolution", Indo-Soviet lournal, ii (7 November 1943), 6, (Shows that the theory of world revolution had not been abandoned by the USSR, as of that date. )
- "The Estimation of Map Distance from Recombination Values", Annalsof Eugenics, xii, pt. III ( 1944) , 172- 75.
- "George David Birkhoff : 1884-1944" ( Obituary) , The Mathematics Student, xii ( 1944 }, 116-20.
- "Direct Derivation of Series, Spectra", Current Science, xiii (March 1944), 71.
- "The Geometric Method in Mathematical Statistics", American Mathematical Monthly li (1944). 382-89.
- "The Change in the Soviet Constitution", Indo-Sovjet Journal, ii, no.9 (1944).
- "Caste and Oass in India", Science and Society, viii ( 1944) , 243-49. (Comment on an article by P. Rosas on the subject.) .
- "Soviet Science: What Can It Teach Us?", Indo-Soviet Journal, 11-13 (22 June 1944).
- "Parallelism in the Tensor Analysis of Partial Differential Equations", Bulletin of the American Mathematical Society, ti ( 1945) , 293-96.
- "The Raman Effect" (Anonymous, as by an "Indian Scientist") , People's Age (22 July 1945) .
- "Some Extant Versions of Bharatihari's Satakas", Journal of the Bombay Branch of the Royal Asiatic Society, xxi (1945),17-32.
- "The Law of Large Numbers", The Mathematics Student, xiv (1946), 14-19.
- "The Parvasamgraha of the Mahabharata", Journal of the American Oriental Society', lxvi, no.2 (Baltimore, 1946) , 110-17; followed by the counts of E. D. Kulkarni, Ibid. 118-44. (First complete discussion of the problem and of V. S. Sukthankar's concept of a "fluid text".)
- "On the Authorship of the Satakatrayi", Journal of Oriental Research, xv (Madras, 1946) , 64- 77.
- "Sur la Differentiation Covariante", Comptes Rendu.v, ccxxii (Paris, 1946), 211-13.
- "Silver Punch-marked Coins with special reference to the East Khandesh Hoard", Journal of the Numismatic Society of India, viii ( 1946) , 63-66.
- "Early Stages of the Caste System in Northern India", Journal of the Bombay Branch of the Royal Asiatic Society, New Series, xxii ( 1946) , 33-48.
- "The Village Community in the 'Old Conquests' of Goa", Journal of the University of Bombay, xv, no.4 (1947),63-78
- " An Extension of the Last-squares Method of Statistical Estimation", Annals of Eugenics, xiii (1947), 257-61.
- "Some Applications of the Functional Calculus", Presidential Address to the Mathematics Section of the Indian Science Congress (Delhi, 1947). (Completely ruined in printing; no proof shown to the author.)
- "Les Invariants Differentiels d'un Tenseur Covariant a deux Indices", Comptes Rendus, ccxxv (Paris, 1947) , 790-92.
- "Early Brahmins and Brahminism", Journal of the Bombay Branch of the Royal Asiatic Society, xxiii (1947), 39-46.
- "Systems of Partial Differential Equations of the Second Order", Quarterly Journal of Mathematics, xix (Oxford, 1948), 204-19.
- "Chronological Order of Punch-marked Coins- I: A Re-examination of the Older Taxila Hoard", Journal of the Bombay Branch of the Royal Asiatic Society, xxiv.:xxv (1948-49), 33-47.
- "The Avatara Syncretism and Possible Sources of the Bhagvad-Gita", Third. pp. 121-34.
- "Characteristic Properties of Series Distributions", Proceedings of the National Institute of Science of India, xv (1949), 109-13.
- "Lie Rings in Path-space", Proceedings of the National Academy of Science, USA, xxxv (1949), 389-94.
- "Marxism and Ancient Indian Culture" (Asverse review of S. A. Dange's India from Primitive Communism to Slavery), Annals of the Bhandarkar Oriental Research Institute, xxix (Poona, 1949), 271-77.
- "Differential Invariants of a Two-index Tensor", Bulletin of the American Mathematical Society, Iv,no. 2 (1949), 90-94.
- "On the Origin of Brahmin Gotras", Journal of the Bombay Branch of the Royal Asiatic Society, xxvi ( 1950) , 21-80.
- "Series Expansions of Continuous Groups", Quarterly Journal of Mathematics, ii, no.2 (Oxford, 1951), 244-57.
- "Chronological Order of Punch-marked Coins-lI: The Bodenayakanur Hoard", Journal of the Bombay Branch of the Royal Asiatic Society, xxvi (1951), 214-18.
- "Urvasi and Puniravas", Journal of the Bombay Branch of the Royal Asiatic Society, xxvii ( 1951) , 1-30. Reprinted in Indian Studies: Past & Present, i, no.1 (Calcutta, 1959), 141-75, and in Myth and Reality.
- "On a Marxist Approach to Indian Chronology", Annals of the Bhandarkar Oriental Research Institute, xxxi (Poona, 1951), 258-66.
- "Seasonal Variations in the Indian Birth-rate" (in collaboration with S. Raghavachari) A nnals of Eugenics, xvi (1951), 165-92.
- "Imperialism and Peace", Monthly Review, iii (1951), 45-49.
- "Parvasamgraha figures for the Bhisma Parvan" (in collaboration with E. D. Kulkarni), Journal of the American Oriental Society, Ixxi (Baltimore, 1951) , 21-25.
- "Path-spaces Admitting Collineations", Quaterly Journal of Mathematics, ii, no.3 (Oxford, 1952), 1-11.
- "The Sanskrit Equivalents of Two Pali Words",Annals of the Bhandarkar Oriental Research Jnst:tute, xxxii (Poona, 1952), 53-60 (Gives the correct derivation of sammapaso and vassakara.)
- "Path-Geometry and Continuous Groups", Quarterly Journal of Mathematics, ii, no.3 (Oxford, 1952), 307-20.
- "Ancient Kosala and Magadha", Journal of the Bombay Branch of the Royal Asiatic Society, xxvii (1952), 180-213.
- "Science and Freedom", Monthly Review , iv ( 1952) , 200-05.
- "Geldner's Rgveda", Journal of Oriental Research (Madras, 1952) , pp. 291-95 (Essay review with special attention to words like ibhya) .
- "Chronological Order of Punch-marked Coins- III: The Paila Hoard", Journal of the Bombay Branch of the Royal Asiatic Society, xxvii (1952), 261-71,
- "Brahmin Clans", Journal of the American Oriental Society. Ixxiii (Baltimore, 1953), 202-8. (Review and critique of J. Brough's book, The Early Brahmanical System of Gotra ancl Pravara. Cambridge, 1953. Mistaken for a polemic.)
- "Seasonal Variations in the Indian Death- rate" (in collaboration with S. Raghavachari), Annals of Human Genetics. xix (1954), 100-19.
- "The Periodization of Indian History", ISCUS, i ( 1954) , 40-55. (Arbitrarily changed by the editors, without consulting the author.)
- "Notes on the Class Structure of India", Monthly Review, vi ( 1954) , 205-13. Reprinted in Exasperating Essays.
- "The Metric in Path-space", Tensor, New Series, iii (1954), 67-74.
- "What Constitutes Indian History ?", Annals of the Bhandarkar Oriental Research Institute, xxxv (Poona., 1955), 194-201. (Essay review of the first three volumes of the Bhartiya Vidya. Bhavan's The History and Culture of the Indian People.)
- "The Basis of Ancient Indian History-I", Journal of the American Oriental Society, lxxv, no.1 (Baltimore, 1955),35-45.
- "The Basis of Ancient lndian History-II", Ibid. no.4 (1955),226-37.
- "The Working Class in the Amarakosa, Journal of Oriental Research. xxiv (Madras, 1955), 57-69. (Shows the existence of a hierarchical principle in the Amarakosa classification. )
- "On the Development of Feudalism in India", Annals of the Bhandarkar Oriental Research Institute, xxxvi, pts. III-IV (Poona, 1956), 258-69. (Adverse critique of Soviet Professor K. A. Antonova's theories.)
- "Origins of Feudalism in Kashmir", Journal of the Bombay Branch of the Royal Asiatic Society. (The Sardhasatabdi Commemoration Volume, 1804-1954, Bombay, 1956-57), pp. 108-20.
- "Dhenukakata", Journal of the Bombay Branch of the Royal Asiatic Society, xxx, pt. II (1957), 50-71. (Identification of the ancient Greek colony in Maharashtra. Also, complete text and translation of all known Brahmi inscriptions in Maval caves, including one from Karle hitherto unpublished. The first photograph of the Sphinx on a Karle pillar.)
- "The Basis of Despotism", Economic Weekly (Bombay, 2 November 1957), pp. 1417-19. (Review of K. A. Wittfogel's Oriental Despotism.)
- "Indo-Ariiskii Nosovoi Ukazatel", Sovetskaya Etnografia (Ak. Nauk. USSR), no.1 (1958), 39-57. (Demonstrates the unreliability of nasal-index data in theorizing about Indian racial groups. )
- "Classical Tauberian Theorems", Journal of the Indian Saciety of Agricultural Statistics, x, nos. 1-2 ( 1958) , 141-49.
- "The Efficiency of Randomization by Card Shuffling" (in collaboration with U.V.R. Rao), Journal of Royal Statistics Society, cxxi, no.2 (1958), 223-33. (Analysis of statistical defects underlying para-psychological experiments.)
- "The Text of the Arthashstra", Journal of the American Oriental Society, Ixxviii, no.3 (Baltimore, 1958), 169-73. (Shows that about a quarter of the original work is lost, but more or less uniformly over the whole text.)
- "The Method of Least Squares", Journal of the lndian Society of Agricultural Statistics, xi, nos. 1-2 (1959), 49-57.
- "Notes on the Kandahar Edict of Asoka", Journal of the Economic and Social HiStory of the Orient, ii (Leiden, 1959), 204-06.
- "China's Communes", Monthly Review, x ( 1959) , 425-29. 109.
- "Primitive Communism", New Age (Monthly), viii, no.2 (February 1959), 26-39. (First treatment of "Communism" in primitive society, without idealisation of ethnographic data. )
- "Indian Feudal Trade Charters", Journal of the Economic and Soda! History of the Orient, ii, pt. III (Leiden, 1959), 281-93. (Special treatment of the Visnusena Charter of A.D. 592, correcting D. C. Sircar's gruesome mistakes.)
- "An Application of Stochastic Convergence", Journal of the Indian Society of Agricultural Statistics, xi ( 1959) , 58-72.
- "At the Cross-roads: Mother Goddess Cult Sites in Ancient India", Journal of the Royal Asiatic Society (London, 1960),17-31; 135-44.
- "Social and Economic Aspects of the Bhagvad-Gita", Journalof the Economic and Social History of the Orient, iv, pt. II (Leiden, 1961), 198-224. (Revision of an anticle originally published in Enquiry, ii (1959), 1-20. Reprinted in Myth and Reality.)
- "Kaniska and the Saka Era", Marg (April 1962); also Journal of the Bombay Branch of the Royal Asiatic Society, xxxv (1962), 36-37, (Identifies Kaniska I with Soter Megas and Kaniska II with the king of the coins. )
- "Pierced Microliths from the Western Deccan Plateau", MAN (January 1962), nQte 4, pp. 10-12. (Apparently the first announcement of such microliths.)
- "Megaliths in the Poona District", MAN (May 1962), note 108, pp. 65-67+plate.
- "The Sampling Distribution of Primes", Proceedings of the National Academy of Sciences (USA), xlix (1963), 20-23.
- "Combined Methods in Indology", Indo- Iranian Journal, vi (1963), 177-202. (By special invitation of the editors; shows that philology, history, archaeology and anthropology have to be combined to get valid results in any one of these fields, which treated in isolation, leads to wrong conclusions otherwise.)
- "Prehistoric Rock Engravings near Poona", MAN (1963), note 60, pp. 57-58.
- "Staple Grains' in the Western Deccan", MAN (1963), note 156, pp. 30-31.
- "The Beginning of the Iron Age in India", Jurnal of the Economic and Social History of the Orient. vi, pt. III (Leiden, 1963), 309-18 (Places this irtlportant change at about 800-700 B.C.. much earlier than D. H. Gordon and Mortimer Wheeler would have it.)
- "The Autochthonous Element in the Mahabharata' Journal of the American Oriental Society. lx.xxiv (Balti- more, 1964), 31-44.
- "The Historical Krishna", Times of India Annual (1965), pp. 27-36.
- "Numismatics as a Science", Scientific American (February 1966), pp. 102-11.
- "Living Prehistory in India", Ibid. (February 1967). Re-. printed in The American Review ( October 1967) .
- "Adventure into the Unknown", Current Trends in Indian Philosophy. ed. K. S. Murty and K. R. Rao (Asia Publishing House, Bombay, 1972), pp. 152-67. (A note on the writer's personal philosophy as a scientist and research worker. )
- "Prime Numbers", Monograph completed a few days before the author's death.