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Subbiah Arunachalam*, K Umarani

M S Swaminathan Research Foundation
Third Cross Street, Taramani Institutional Area, Chennai-600113
* Address for correspondence: arun[at]mssrf[dot]res[dot]in; Fax: 91 44 2541319

ABSTRACT

Mathematics research in India, as reflected by papers indexed in MathSci 1990 and 1994, is quantified and mapped. There were 1,319 papers originating in India and indexed in the1990 disc of MathSci CD-ROM version, and 1,391 papers indexed in 1994. Of these 2,710 papers; 2,549 appeared in 467 journals, 221 of which were indexed in Journal Citation Reports 1994. In these two years, Indian researchers published 999 papers in 62 Indian journals, 503 papers in 108 US journals, 254 papers in 40 Dutch journals, and 155 papers in 42 British journals. One hundred and eighty-eight institutions located in 110 cities/towns and 23 states/union territories contributed to India's research output indexed in MathSci, although only three have contributed more than a hundred papers in the two years, and another nine had contributed 50 or more papers. Academic institutions published 87% of all papers and central government-funded research councils and departments accounted for 12.6%. Four cities, viz. Calcutta, New Delhi, Bombay, and Madras published more than 200 papers each in the two years. Five states, i.e.. West Bengal, Uttar Pradesh, Maharashtra, Tamil Nadu, and Delhi published more than 250 papers each. More than 53% of journal papers were published in journals not indexed in Journal Citation Reports. Only 81 papers appeared in journals of impact factor greater than 2.000, and these are mostly physics journals. Of the 61 sub-fields in MathSci, Indian researchers were most active in statistics, general topology, quantum theory, and special functions. India has a high activity index for special functions and general topology and a moderately high activity index for statistics; integral transforms and operational calculus; and sequences, series and summability. The activity is low in partial differential equations; ordinary differential equations, numerical analysis, K-theory, and computer science. The future of mathematics in India seems to rest with DAE, TIFR and ISI. Universities seem to be losing momentum.

KEYWORDS: India; Mathematics research; Scientometric study.

INTRODUCTION

Mathematics is the basis of modern civilization, although much of the pursuit of mathematics is without any inkling to the real world, says Basil Gordon of the University of California at Los Angeles [1]. Indeed, there is something for everybody to gain from the universal language of mathematics. Today, it is virtually impossible to do advanced level work in any branch of science or engineering or some areas of economics and social sciences without the application of mathematics.

India has a very long tradition of excellence in mathematics and astronomy, dating back to antiquity. In modern times, India has produced much work in both pure and applied mathematics as well as in the related areas of operations research, statistics, computer science and theoretical physics. According to Basil Gordon [1], Russia and the USA are the top contributors to the literature of mathematics, followed by England, France, Germany and then India and China. The 20th century has transformed mathematics from a cottage industry run by a few semi-amateurs into a worldwide industry run by an army of professionals, says Michael Atiyah [2] in his preface to Mathematics: Frontiers and Perspectives, brought out by the American Mathematical Society on behalf of the International Mathematical Union as part of the celebration of the Year of Mathematics. A part of the army lives and works in India. Today, Indian mathematicians, statisticians and computer scientists are welcome everywhere. Virtually every major university in North America has one or more Indian mathematicians, statisticians or computer scientists on its faculty.

There are a few accounts of mathematics research in 20th century India. Notable among them are those by Varadarajan [3], Narasimhan [4], and Seshadri [5], all outstanding mathematicians. They have written from the perspective of professional researchers trying to look at achievements of Indian mathematics, both of individuals and institutions. In contrast, this report is written from the perspective of scientometricians trying to map mathematics research in India by analysing the published literature. There is another difference: While the three eminent mathematicians have covered several decades, we have analysed the research output over two selected years, 1990 and 1994.

The words "Indian mathematics" evoke in the minds of most people the images of Ramanujan and the well-known mathematicians of ancient India such as Aryabhata, Bhaskara and Brahmagupta. But what about more recent times? Narasimhan [4] has chronicled the work of Indian mathematicians in the first half of the 20^th century, who under very difficult circumstances kept mathematical traditions alive in India. He singles out Calcutta and Madras as the two most important centres and has paid handsome tributes to K Anand Rau, R Vaidyanathaswamy, T Vijayaraghavan, S S Pillai and S Minakshisundaram of the Madras school, Syamdas Mukhopadhyay, Nikhilranjan Sen, Rabindranath Sen, P C Mahalanobis [founder of Indian Statistical Institute (ISI), Calcutta], and R C Bose of the Calcutta school, and Komaravolu Chandrasekharan [who founded the school of mathematics at Tata Institute of Fundamental Research (TIFR), Bombay] and C T Rajagopal (Ramanujan Institute, Madras). Narasimhan [4] pays glowing tributes to C P Ramanujam with the words, "certainly one of the most powerful mathematical minds to emerge in India since the mid-fifties" and "in many ways, a singular figure."

Varadarajan [3] and Seshadri [5] have written brief accounts of mathematics in post-Independent India. Both of them highlight the very important role played by TIFR, largely thanks to the initial leadership of K Chandrasekharan, and ISI, Calcutta, where C Radhakrishna Rao played a crucial role. Among those who made a mark in this period are C P Ramanujam and V K Patodi, both of whom died in the prime of their creative life, C S Seshadri, M S Narasimhan, M S Raghunathan, S Ramanan, K Ramachandra (all of TIFR), C R Rao, S R S Varadhan, V S Varadarajan (all three now in the USA), K R Parthasarathy, and R Ranga Rao (all of ISI, Calcutta). Mention must also be made of certain foreigners such as the Jesuit priest Fr Racine of France and F W Levi of Germany, both of whom had worked in India and helped many young aspiring Indian mathematicians.

In what follows, we have attempted to map India's contribution to the literature of mathematics and related fields as seen from two years (1990 and 1994) of MathSci database on CD-ROM. We have identified the institutions active in publishing, the journals used and their impact factors, the sub-fields in which different institutions are active, etc. We have not extended the analysis to the contributions made by individuals. This study is in continuation of a series of studies on mapping India's contribution to different fields such as physics [6], biology [7], agriculture [8], medicine [9,10], materials science [11], science as a whole (based on data from Science Citation Index) [12], and mathematics [13, 15-16].

METHODOLOGY

The techniques used for data collection and analysis are largely similar to our earlier studies [6-11]. Bibliographic data on documents originating from Indian institutions were downloaded from the MathSci CD-ROM database, giving "(6-*" as the search command under `IN' (for institution) for the disc years 1990 and 1994. This search picks up all entries having an Indian address in the byline irrespective of whether it is the address of the first author, second author or the last author.

Unlike with some other bibliographic databases on CD-ROM, downloading such data from MathSci database is simple and straightforward. The fields downloaded are: AU (author), PY (publication year), JN (journal title), LA (language), PC (subject descriptor), DT (document type), and IN (institution name).

The MathSci database has 61 sections covering such diverse sub-fields as History and Biography; Information and Communication, Circuits, and Functions of a Complex Variable. While most sub-fields are part of mainstream mathematics, some sub-fields are closely related to mathematics, such as Statistics; Computer Science; Astronomy and Astrophysics; Geophysics; Quantum Theory; and Economics, Operations Research, Programming, Games.

Impact factor values for journals were noted from Journal Citation Reports 1994. Not all journals indexed in MathSci are indexed in Science Citation Index, and those journals not indexed in SCI are not assigned any impact factor. The data was analysed using programs generated in-house using FoxPro, Excel and Access.

FINDINGS

MathSci has indexed 1,319 publications from India in 1990 and 1391 in 1994. But for 14 of these papers written in Hindi, all the rest were in English [Table 1]. In Table 2, we have classified the documents by document type, as given in the database. Journal papers account for 93.4% of all publications in 1990 and 94.5% in 1994. The publication years of papers indexed in the two disc years are given in Table 3. For some reason, the database lists more than one publication year in some entries.

Table 1: Indian Papers covered by MathSci in 1990 and 1994
[Classified by Language]

Table 2: Indian Papers covered by MathSci in 1990 and 1994
[Classified by Document Type]

Table 3: Number of Papers Published in Various Years as seen from MathSci 1990 and 1994

*In some entries more than one year in mentioned against publication year.
? It is not clear how 1995 and 1996 as publication years have figured in MathSci of 1994!    

Journals Often Used

Indian researchers have used 467 journals in these two years to publish 2,549 papers in the area of mathematics and related fields [Table 4] for an average of 5.5 papers per journal in two years. Apart from the title of the journal, we have listed in this table, the country of publication of the journal and the impact factors of the journals as seen from Journal Citation Reports. As not all journals are listed in JCR, we have shown zero impact factor for all non-JCR journals. The three journals that have published the largest number of papers from India are Indian journals. The next two are American journals, one of them is a statistics journal. Thirteen of the twenty journals often used by Indian mathematicians to publish their work are Indian journals. India has published more than ten papers in the two years in 66 journals and more than 20 papers in 27 journals. At the other extreme, India has published just one paper each in 174 journals and two papers each in 76 journals. Only 221 journals have an impact factor; all the 246 others are not indexed in SCI and JCR.

Distribution by Sub-fields

Table 5 gives the distribution of the papers by sub-fields. In all, there are 61 sub-fields, but Indians are really active only in about half of them. The fields in which Indian researchers have published large number of papers are: Statistics (299), General Topology (276), Quantum Theory (175), Special Functions (128), Economics and Operations Research (111), Relativity and Gravitation (110), and Differential Geometry (103). We have calculated the activity index (AI) for each sub-field for both 1990 and 1994 using the formula [14]:

            The world share of the given country in publication in the given field
AI =    -----------------------------------------------------------------
            The overall world share of the given country in publications

or

            The share of the given field in the publication of the given country
AI =    -----------------------------------------------------------------
            The share of the given field in the world total of publications

We have also calculated the relative specialization index (RSI) (Table 6), using the formula

RSI = (AI - 1) / (AI +1)

Table 4: Journals Used by Indian Researchers for Publishing their Papers as recorded in MathSci 1990 and 1994
[Arranged in Descending Order of Papers]

NB: Abbreviations used in the Table 4. GB - Great Britain, IF - Impact factor, IN - India, NL - Netherlands, PC - Publication Country.
- Impact factor values taken from JCR 1994.
- Impact factors of journals not covered by JCR has been shown as 0.000 which may not be correct in all cases. - Ed.

Table 5: Distribution of Indian Mathematics Papers according to Sub-fields with Activity Index
[First 10 most productive sub-fields]

Table 6: Activity Index and Relative Specialisation Index for Various Sub-fields
[First 13 Sub-fields with High Activity Index]

Both special functions and integral transforms have recorded a reasonably high activity index in 1990 and a lower value in 1994. In contrast, in general topology, India has recorded a reasonably high activity index in both 1990 and 1994 (Table 5 and 6). There are fields like Statistics and Associative rings, where the activity index has remained at a moderate level and within a small range in both 1990 and 1994. In the case of sub-field, Sequences, Series and Summability, the activity index has risen sharply from 1.57 in 1990 to 3.18 in 1994. In many sub-fields the activity is less than 1.0, meaning that the activity in those fields are below the country's overall average. Table 6 lists the relative specialization indices for the different sub-fields in 1990 and 1994. It should be remembered that no country (or organization) can have positive RSIs for all sub-fields.

Distribution by Journal Country

The distribution of papers by country of publication of journal is shown in Table 7.

Table 7: Indian Mathematics Papers arranged by Country of Publication of Journals
[As recorded in MathSci 1990-1994]

Apart from Indian journals, Indian researchers publish their work often in US journals and to a lesser extent in journals published from the Netherlands, UK and Germany. In all, in these two years, Indian works have appeared in journals published from more than 40 countries. The 62 Indian journals in which Indian mathematics papers have appeared are listed in Table 8.

Table 8: Indian Journals covered by MathSci 1990 and 1994
[Arranged in Descending order of Number of Papers]

About 42.5% of journal papers in 1990 and 36.1% of journal papers in 1994 were published in Indian journals. This figure has come down to about 20% in 1998 [13]. Of the 2,549 journal papers, 1,369 (nearly 54%) have been published in journals not listed in JCR, and 753 (less than 30%) in journals whose impact factor is less than 0.5 (Table 9).

Table 9: Distribution of Indian Mathematics Papers by Impact Factor Range
[based on JCR 1994 data]

* The five Indian journals which have an impact factor >0 are in this range.

Only 62 papers have appeared in journals with an impact factor greater than 3.0, and only 29 in journals with impact factor greater than 3.5. It may be noted that many of these higher impact journals are in the area of physics. Most mathematics journals have low impact factors.

Distribution by Institution

Table 10 lists the 188 Indian institutions that have published papers which have been indexed in MathSci in 1990 and/or 1994. Well-known mathematics research centers such as the Tata Institute of Fundamental Research, University of Calcutta, Indian Statistical Institute, top the list. Please note that we have not clubbed different centers of Indian Statistical Institute into one entry in this table. While TIFR and University of Calcutta have published fewer papers in 1994 than in 1990, ISI and Indian Institute of Science, Bangalore, have published a larger number of papers in 1994 than in 1990. 

Table 10: Institution-wise Distribution of Indian Papers on Mathematics in Descending Order
[As recorded in MathSci 1990, 1994]

Table 11 provides a breakup of papers by institutional type. Academic institutions perform the bulk of mathematics research in India. This is despite the fact that we have assigned ISI to the Ministry of Planning.

Table 11: Distributions of Papers as per Types of Organizations
[As recorded in MathSci 1990, 1994]

Table 12: Statewise Distribution of Indian Mathematics Papers
[As recorded in MathSci 1990, 1994]

Distribution by State and City

Table 12 lists the number of publications that have come out of different states and union territories and Table 13 lists the number of publications from different cities and towns.

Table 13: Citywise Distribution of Indian Mathematics Papers
[As recorded in MathSci 1990, 1994]

Papers have come from 110 cities/ towns. Calcutta, New Delhi, Mumbai (Bombay), Chennai (Madras), Bangalore, Varanasi and Aligarh lead the rest of India as do West Bengal, Uttar Pradesh, Maharashtra, Tamil Nadu and Delhi among states.

Others

The Report also includes distribution of papers by types of institution and also deals with institutional strength and journals preferred.

CONCLUSION

This is a macroscopic study and we have analysed up to the institutional level and not gone to the departmental or individual level. There had been a slight increase in the number of publications in 1994, but as another study by us had shown there had been a considerable decline in 1998. Calcutta, New Delhi, Bombay, Madras, and Bangalore are the major centers of research. TIFR, ISI, and University of Calcutta are the leading institutions. Universities seem to be doing less and less, and publishing in low impact journals [14]. That is not a good sign. Statistics, general topology and quantum theory are the sub-fields in which Indian researchers publish large number of papers.

REFERENCES

1. Gordon B. Personal Communication.

2. Arnold Vi, Atiya M, Lax P, Mazur B, eds. Mathematics: Frontiers and Perspectives. Washington, DC: American Mathematical Society, 2000. 459p.

3. Varadarajan V.S. Mathematics in and out of Indian universities, The Mathematical Intelligencer 1983; 5:38-42.

4. Narasimhan R. The coming age of mathematics in India. In: Hilton P, Hirzebruch F, Remmert R, eds. Miscellanaea Mathematica, Berlin: Springer _ Verlag, 1991: 235-258.

5. Seshadri C S. Mathematics in India during the last fifty years, talk delivered at the Indo-French Seminar on History of Development of Science in India and in France, Madras, October 1992.

6. Arunachalam S, Dhawan M. Physics Research in India: An Analysis based on Physics Abstracts 1992. Report submitted to NSTMIS, Department of Science and Technology, New Delhi. 1996.

7. Arunachalam S. Mapping life sciences research in India: A profile based on BIOSIS 1992 _1994. Current Science 1999; 76: 1191-1203.

8. Arunachalam, S. Agricultural Research in India _ A Profile Based on CAB Abstracts 1990 _ 1994. Report submitted to NISSAT, DSIR, New Delhi, 1998.

9. Arunachalam S. How relevant is medical research done in India? _ A study based on Medline. Current Science 1997; 72: 912-922.

10. Arunachalam S. Does India perform medical research in areas where it is most needed? National Medical Journal of India 1998; 11: 27-34.

11. Arunachalam S. Meyyappan N, Sridhar G S. India's Contribution to the Literature of Materials Science and Related Fields: An Analysis Based on Materials Science Citation Index 1991 _ 1994. Report submitted to NSTMIS-DST, New Delhi, March 1998.

12. Arunachalam S, Srinivasan R. Science in India: A Profile based on India's Publications as covered by Science Citation Index 1989 _ 1992, Report submitted to NSTMIS-DST, New Delhi, March 1998.

13. Arunachalam S. India's Contribution to the Literature of Mathematics and Rrelated Fields: An Analysis Based on MathSci 1988 _ mid-1995. Report submitted to NSTMIS-DST, New Delhi, March 1998.

14. European Commission, EUR 17639 - Second European Report on S&T Indicators 1997. Luxembourg: Office of the Official Publications of the European Communities. December 1997. Appendix, p. M-23.

15 Arunachalam S, Rino S. I. Mathematical Research in India in 1998: An Analysis based on MathSci, Report submitted to NISSAT-DSIR, October 2001.

16 Arunachalam S. Mathematics research in India today: What does the literature reveal? Scientometrics 2001; 52:235-259.

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The paper is a summary of the Report prepared under the National Mapping of Science Project, sponsored by NISSAT and does not include all the tables and figures.

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Information Today & Tomorrow, Vol. 20, No. 4, December 2001, p.23-p.30
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