Indian Journal of History of Science, 50.3 (2015) 521-532 DOI: 10.16943/ijhs/2015/v50i4/48321 Features of Mathematical Sciences in India during the Second World War* Jagdish N Sinha** (Received 23 November 2014) Abstract This study is focused on the development of mathematical sciences in India during the Second World War with reference particularly to India’s indigenous tradition in mathematics, the ongoing freedom struggle in the country, and the crosscurrents of influences coming from all over the world. The subject acquires significance all the more as an entirely new branch of mathematics——Operational Research— came into being during this period, and revolutionary progress was made in other areas like artificial intelligence and computer science, and statistics. Since India was crucially involved in the war as a part of the British Empire, a look at the developments here may prove valuable, especially in the light of her own rich tradition in mathematics and its application in the postwar reconstruction. For, as the war escalated and postwar reconstruction became a national urgency in many countries, especially the Allied and the Axis powers, research in these areas unveiled their potentialities for peacetime development, too. What was the scenario in India? How and how far could the mathematical sciences develop during the war here, especially in comparison to the developed countries? Did the indigenous knowledge and talent prove of any help both with respect to the global war and post-war reconstruction? Key words: Artificial Intelligence, India, Mathematics, Operational Research, Statistics, World War. 1. INTRODUCTION crucially involved in the war as a part of the British Wars have universally catalysed science Empire (Voigt, 1987), a look at the developments and technology throughout history; and the latter here may prove insightful, especially in the light have shaped the means and methods of war. The of her own rich tradition in the field of greatest of them, the two World Wars (I: 1914-18, mathematics (Sen, 1971, pp.136-212). Globally, II: 1939-45), promoted science and technology, research in these new areas had initially started including mathematics, on an unprecedented scale. for different purposes and in different perspectives; This study is focused on and around the Second but the crisis of the Second World War streamlined World War with reference to the mathematical their focus and increased their pace. As the war sciences in India. For, during this war, an entirely escalated and post war reconstruction became a new branch of mathematics—Operational national urgency in many countries, research in Research—came into being, and revolutionary these areas unveiled their potentialities for progress was made in other emerging areas like peacetime development. As such, these new fields computer science, and statistics1. Since India was of science attracted attention as much of * This is a fully revised version of my paper presented at the National Meet on History of Mathematical Sciences, 7-9 January 2010, organised by the Department of History, University of Delhi, Delhi. The author is beholden to its organisers for their encouragement and support. **Associate Professor of History, Rajdhani College, University of Delhi, Raja Garden, New Delhi 110015; Email: [email protected]. Mailing Address: 38- Uttaranchal Apts., 5- I.P. Extension, Delhi 110092. 1 See J.D. Bernal, Science in History, Vol. 3: The Natural Sciences in Our Times, Harmondsworth, 1954, especially pp. 831-48, and other pages; also see Vol. 4: The Social Sciences: Conclusion, esp. pp. 1139-44. 522 INDIAN JOURNAL OF HISTORY OF SCIENCE economists, politicians and the defence experts as endeavours, like war and developmental activities, of mathematicians. These developments took seem to have gained currency in the world much place in the developed countries like the UK, the later, probably from the nineteenth century.2 USA and Germany and some activities were India did have a very long and rich experienced in those allied with them, too (Bernal, tradition of mathematics as a scholastic discipline. 1954). A survey of its early mathematics has been made What was the scenario in India? What were by BB Datta, SN Sen and others. Some of the great the main factors responsible for the rise of names of the period are Āryabhaa I (b. 476 AD), mathematical sciences, and the problems they Bhāskara I (c. 600 AD), Brahmagupta (c. 598 AD), addressed, here? How and how far could they Mahāvīracārya (c. 850), Āryabhaa II (950 AD), develop under the impact of the war, especially in Śridharacārya (c. 991 AD), Śripati (c. 1000), comparison to the developed countries? Did the Bhāskara II (c. 1114 AD), Nārāyaa (c. 1350), indigenous knowledge and talent prove of any help Mādhava (c. 1400), Nīlkaha (1500) and during the war, and what was the latter’s impact Jyehadeva (1550). ‘The Medieval period on it? Here, it may be noted that under the colonial witnessed the growth of a sizable mathematical conditions, it is important not only to find out what literature in Arabic and Persian and presented an happened in the past but also what did not. This opportunity for cross-fertilization of the efforts of study is essentially concerned with the social two distinct cultures.’3 From ancient times, the aspects of the subject, in the background especially knowledge of Indian mathematics travelled to the of imperialism, nationalism, and indigenous West through the Middle East; and the concept of tradition and response. zero and place-value left their mark there, the Unfortunately, the official secrecy influence of which may be noticed even in the maintained in the colonial policy concerning European Renaissance of the sixteenth century various aspects of life during the war and after, (Gunatilake, 1999). This interaction influenced the makes the task of the historian difficult (Sinha, developments in India, too (Gunatilake, 1999). By 2008, pp.12-14). The fact that India did have a long the eighteenth century, the astronomical tradition of mathematics, which did not disappear knowledge of the West had started influencing the totally by this time (Sen, 1939-1950), makes it all indigenous thinking on the subject. Sawai Jai the more meaningful to find out if the British made Singh II evinced considerable interest in the use of it, or of the new branches of mathematics, developments in this area in the West (Ghori, 1980, mentioned above, in their post-war reconstruction Rahman, 1989). programme here. If not, why and how? And in With the rise and expansion of the that case, how did the Indian mathematicians react European imperialism in the East, Western to that? mathematics reached India in different ways— through trade, state-supported Western Education 2. THE BACKGROUND and science, Surveys, etc. The establishment of The conscious application of mathematics the European, especially the British, rule in the on organised level for collective human Indian subcontinent led to the crumbling of the 2 J.D. Bernal, Science in History, 1954, provides an excellent general view of developments. 3 S.N. Sen, ‘Mathematics’, 1971, p. 136. For contemporary sources, see A. Rahman, ed., Science, Technology in Medieval India: A Bibliography of Source Materials in Sanskrit, Arabic and Persian, New Delhi, 1982; also his Trimurti: Science, Technology and Society, New Delhi, 1972, esp. pp.235-39. HISTORICAL NOTE: FEATURES OF MATHEMATICAL SCIENCES IN INDIA 523 indigenous institutions of learning with the fall of subjects in the academics, including mathematics, the native states which patronised them. This lost priority to the urgent necessities of the war. cleared the road for the expansion of the Western Nothing significant seems to have been done by science in India (Kumar, 1991). Yet, millions of the government to promote pure mathematics.4 people used the traditional mathematics in their Yet, the Indian mathematicians continued to do day-to-day life, as they used the traditional appreciable work in several branches of measurements of weight, space, time and celestial mathematics. Some of them were K Anand Rau activities which are still in vogue to an extent in (1893-1966), S S Pillai (1901-1950), S Chowla India (Dharampal, 1971). Not long ago from the (1907-1995), T Vijayaraghavan (1902-1955), K period of this study, India produced a mathematical Chandrashekharan (1920-1995), and S genius in Srinivasa Ramanujan (1887-1920); Minakshisundaram (1913-1968) (Seth, 1963). (Kanigel, 1991) and there were scores of others Whereas only 27 doctorates had been awarded in who were impressively grounded in mathematics the 30 years between 1910 and 1940, the number when the Second World War broke out (Seth, 1963, rose to 42 in just 10 years between 1940 and 1950 Jaggi, 1984, pp119-32). S Ramanujan was deeply (Jaggi, 1984, p.127). Why the colonial indifference rooted in India’s philosophical tradition and to basic sciences could not deter Indians from working in this field merits some explanation. A spiritualism, and P C Mahalanobis (1893-1972), close observation of the trend seems to suggest a physicists-turned-statistician, returned to that their drive sprang essentially from their Sāmkhya and the Jain philosophy of Sadyvād for nationalistic urge to measure up their talent and his intellectual mooring just on the eve of the capabilities with their masters who always Second World War and worked through it (Rudra, underestimated their talent and discriminated with 1996) to which we would return later for more them. The indigenous interest and achievements discussion. The process was deeply influenced by in mathematics in the past must have fuelled their the consequences of the colonial rule; and the urge additionally. The palpable spurt in Second World War added new factors to impact mathematical research during the Second World it. War may be ascribed to their awareness to the global developments to which the Indian scientists 3.