2001, VOLUME 20 - ISSUE 4, DECEMBER - Status of Mathematics Research in India in 1990 and 1994: An Analysis based on MathSci


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 20th 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]

No.

Language No. of Papers in 1990 and 1994
1990 1994 Total

1  

English  

1308  

1388  

2696

2  

Hindi  

11  

3  

14

  

Total  

1319  

1391  

2710

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

No. Document Type   No. of Papers in 1990 and 1994
1990 1994 Total

1  

Books  

9  

8  

17

2  

Journals

1232  

1314  

2546

3  

Journal -Translation  

0  

3  

3

4  

Proceedings Papers  

78  

66  

144

  

Total  

1319  

1391  

2710

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

No. Publication Year* No. of Papers Papers (%)
1990 1994 Total

1  

1989, 1990  

2

0

2

.0.08

2  

1990  

1270

0

1270

46.87

3  

1990. 1991  

47

0

47

1.73

4  

1991, 1992, 1993, 1994  

15

15

0.55

5  

1992, 1993, 1994, 1995?, 1996?

10

10 

0.36

6  

1993, 1994  

8

8

0.29

7  

1994  

0

1343

1343

49.57

8  

1994, 1995?  

0

15

15

0.55

  

Total  

1319

1391

2710

100.00 

*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]

No   Journal Title   IF   PC No. of Papers
1990 1994 Total

1  

Indian J Pure Appl Math  

0.049  

IN  

64  

47  

111

2  

Bull Calcutta Math Soc  

0.000  

IN  

44  

40  

64

3  

Acta Cienc Indica Math  

0.000  

IN  

38  

35  

73

4  

Comm Statist Theory Methods  

0.152  

US  

30  

15  

45

5  

J Math Anal Appl  

0.338  

US  

18  

17  

45

6  

Proc Indian Acad Sci Math Sci  

0.021  

IN  

21  

24  

45

7  

J Phys A  

1.779  

GB  

20  

20  

40

8  

Fuzzy Sets and Systems  

0.610  

NL  

13  

25  

38

9  

Math Ed (Siwan)  

0.000  

IN  

21  

17  

38

10  

J Indian Math Soc  

0.000  

IN  

13  

19  

32

11  

Calcutta Stat Assoc Bull  

0.000  

IN  

23  

8  

31

12  

J Indian Acad Math (NS)  

0.000  

IN  

13  

17  

30

13  

Modern Phys Lett A  

1.172  

SG  

12  

18  

30

14  

Phys Lett A  

1.228  

NL  

14  

13  

27

15  

Pure Math Manuscript  

0.000  

IN  

26  

0  

26

16  

Astrophys Space Sci  

0.310  

NL  

24  

1  

25

17  

Indian J Math  

0.000  

IN  

15  

9  

24

18  

J Math Phys Sci  

0.000  

IN  

17  

7  

24

19  

Math Student  

0.000  

IN  

8

16

24

20  

J Natur Phys Sci  

0.000  

IN  

8  

15  

23

21  

Proc Math Soc  

0.000  

IN  

13  

10  

23

22  

Internat J Math - Math Sci  

0.000  

US  

13  

9  

22

23  

Internat J Theoret Phys  

0.345  

US  

12

10

22

24  

Pure Appl Math Sci  

0.000  

IN  

11  

11  

22

25  

J Math Phys  

0.969  

US  

11  

10  

21

26  

J Nat Acad Math India  

0.000  

IN  

12  

9  

21

27  

J Statist Plann Interference  

0.145  

NL  

8  

13  

21

28  

J Fuzzy Math  

0.000  

US  

11  

10  

20

29-30  

2 Journals 19 Papers each  

 

 

19  

19  

38

31-34  

4 Journals 18 Papers each  

 

 

31  

41  

72

35-37  

3 Journals 17 Papers each  

 

 

28  

23  

51

38-41  

4 Journals 16 Papers each  

 

 

28  

36  

64

42-43  

2 Journals 15 Papers each  

 

 

15  

15  

30

44-46  

3 Journals 14 Papers each  

 

 

16  

26  

42

47-52  

6 Journals 13 Papers each  

 

 

35  

43  

78

53-57  

5 Journals 12 Papers each  

 

 

25  

35  

60

58-60  

3 Journals 11 Papers each  

 

 

18  

15  

33

61-66  

6 Journals 10 Papers each  

 

 

29  

31  

60

67-71  

5 Journals 9 Papers each  

 

 

34  

11  

45

72-79  

8 Journals 8 Papers each  

 

 

28  

36  

64

80-94  

15 Journals 7 Papers each  

 

 

47  

58  

105

95-108  

14 Journals 6 Papers each  

 

 

44  

40  

84

109-132  

24 Journals 5 Papers each  

 

 

57  

63  

120

133 167  

35 Journals 4 Papers each  

 

 

54  

86  

140

168-217  

50 Journals 3 Papers each  

 

 

71  

79  

150

218-293  

76 Journals 2 Papers each  

 

 

50  

102  

152

294-467  

174 Journals 1 Paper each  

 

 

81  

93  

174

  

Non-Journal Papers  

 

 

87  

74  

161

  

Total  

 

 

1319  

1391  

2710

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]

No. Sub-fields No. of Papers (India) Total No. of Papers (World) Total Activity Index
1990 1994 1990 1994 1990 1994

1  

Statistics  

157  

142  

297  

2982  

3203  

6185  

2.07  

1.69

2  

General Topology  

106  

110  

216  

1278  

1267  

2545  

3.27  

3.31

3  

Quantum Theory  

78  

97  

175  

4220  

4297  

8517  

0.72  

0.86

4  

Special Functions  

82  

46  

128  

612  

688  

1300  

5.28  

2.55

5  

Economics-Operations Res.  

53  

58  

111  

3360  

3090  

6450  

0.62  

  0.71

6  

Relativity & Gravitation  

67  

43  

110  

1409  

1459  

1599  

2.87  

1.12

7  

Differential Geometry  

36  

67  

103  

1596  

1626  

3222  

0.89  

1.57

8  

Operator Theory  

39  

49  

88  

2678  

2866  

5544  

0.57  

?

9  

Number Theory  

37  

50  

87  

2296  

2182  

4478  

0.63  

0.87

10  

Functions of a Complex Variable  

40  

42  

82  

1252  

1357  

2609  

1.26  

1.19 

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

No.   Sub-field   Activity Index Relative Specialisation Index
1990 1994 1990 1994

1  

Special Functions  

5.28  

2.55  

0.682  

0.437

2  

General Topology  

3.27  

3.31  

0.532  

0.536

3  

Integral Transforms; Operational Calculus  

3.23  

1.84  

0.527  

0.296

4  

Statistics  

2.07  

1.69  

0.349  

0.257

5  

Astronomy and Astrophysics  

1.92  

-  

0.315  

-

6  

Relativity & Gravitation  

1.87  

1.12  

0.303  

0.057

7  

Sequences, Series, Summability  

1.57  

3.18  

0.222  

0.522

8  

Fourier Analysis  

1.46  

0.89  

0.187  

-0.058

9  

Functions of a Complex Variable  

1.26  

1.18  

0.115  

0.083

10  

Associative Rings & Algebras  

1.13  

1.21  

0.061  

0.095

11  

Real Functions  

1.04  

1.49  

0.020  

0.197

12  

Integral Equations  

1.00  

0.69  

0.000  

-0.183

13  

Differential Geometry  

0.89  

1.57  

-0.058  

0.222

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]

No. Publication Country 1990 1994 Total % of Total
No. of Journals   No. of Papers   No. of Journals   No. of Papers  

1  

India  

48  

524  

51  

475  

999  

36.86

2  

United States  

69  

232  

87  

271  

503  

18.56

3  

Netherlands  

33  

129  

29  

125  

254  

9.37

4  

Great Britain  

27  

74  

29  

81  

155  

5.72

5  

Germany  

19  

37  

18  

49  

86  

3.17

6  

Singapore  

6  

21  

9  

41  

62  

2.29

7  

Italy  

14  

30  

10  

22  

52  

1.99

8  

Taiwan  

4  

20  

4  

24  

44  

1.62

9  

Switzerland  

8  

12  

13  

30  

42  

1.55

10  

Japan  

9  

14  

15  

25  

39  

1.44

11  

Hungary  

10  

19  

6  

17  

36  

1.33

12  

Romania  

7  

17  

7  

18  

35  

1.30

13  

Poland  

8  

21  

4  

11  

32  

1.18

14  

Australia  

4  

13  

5  

16  

29  

1.07

15  

Canada  

8  

17  

8  

12  

29  

1.07

16-46  

31 other Countries  

34  

52  

58  

100  

152  

5.6

  

Total  

308  

1232  

353  

1317  

2549  

94.16

  

Non-journal Papers  

 

87  

 

74  

161  

5.9

  

Total  

 

1319  

 

1391  

3710  

100.0 

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]

No. Journal Title No. of Papers
1990 1994 Total

1  

Indian J Pure Appl Math  

64  

47  

111

2  

Bull Calcutta Math Soc  

44  

40  

84

3  

Acta Cienc Indica Math  

38  

35  

73

4  

Proc Indian Acad Sci Math Sci  

21  

24  

45

5  

Math Ed (Siwan)  

21  

17  

38

6  

J Indian Math Soc  

13  

19  

32

7  

Calcutta Statist Assoc Bull  

23  

8  

31

8  

J Indian Acad Math  

13  

17  

30

9  

Pure Math Manuscript  

26  

0  

26

10  

Indian J Math  

15  

9  

24

11  

J Math Phys Sci  

17  

7  

24

12  

Math Student  

8  

16  

24

13  

J Natur Phys Sci  

8  

15  

23

14  

Proc Math Soc  

13  

10  

23

15  

Proc Appl Math Sci  

11  

11  

22

16  

J Nat Acad Math India  

12  

9  

21

17  

J Indian Soc Math Statist  

11  

8  

19

18  

Jnanabha  

9  

9  

18

19  

Ganita  

7  

10  

17

20  

Ganita Sandesh  

10  

7  

17

21  

Aligarh Bull Math  

7  

9  

16

22  

J Indian Statist Assoc  

8  

8  

16

23  

Prog Math (Varanasi)  

5  

11  

16

24  

J Ramanujan Math Soc  

4  

9  

13

25  

Opsearch  

4  

9  

13

26  

Proc Nat Acad Sci India Sect A  

6  

7  

13

27  

Sankhya Ser B  

8  

5  

13

28  

Vijnan Parishad Anusandhan Patrika  

10  

3  

13

29  

Math Today  

5  

7  

12

30  

IAPQR Trans  

8  

3  

11

31  

Ganita Bharati  

4  

6  

10

32  

Ultra Sci Phys Sci  

0  

10  

10

33-62  

30 other Journals  

71  

70  

141

  

Total  

524  

475  

999 

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]

IF Range No of Journals No. of Papers
1990 1994 Total

0.0 or unknown  

246  

656  

713  

1369

>0.0 -0.5  

130*  

369  

384  

753

>0.5 - 1.0  

50  

84  

104  

188

>1.0-1.5  

15  

34  

44  

78

>1.5 -2.0  

13  

39  

41  

80

>2.0 -2.5  

4  

12

5

17

>2.5 - 3.0  

1  

0  

2  

2

>3.0 - 3.5  

3  

19  

14  

33

>3.5 - 4.0  

3  

13  

8  

21

>6.0 -7.0  

2  

6  

2  

8

Total  

467  

1232  

1317  

2549

* 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]

No. Institution City No. of Papers
1990 1994 Total

1  

Tata Institute of Fundamental Research  

Bombay  

95  

77  

172

2  

University of Calcutta  

Calcutta  

75  

56  

131

3  

Indian Statistical Institute  

Calcutta  

55  

67  

132

4  

Indian Institute of Science  

Bangalore  

35  

60  

95

5  

Banaras Hindu University  

Varanasi  

47  

47  

94

6  

Indian Statistical Institute  

New Delhi  

33  

39  

72

7  

University of Delhi  

New Delhi  

30  

40  

70

8  

Indian Institute of Technology  

Madras  

26  

45  

71

9  

Jadavpur University  

Calcutta  

34  

34  

68

10  

University of Madras  

Madras  

27  

32  

59

11  

Aligarh Muslim University  

Aligarh  

17  

37  

54

12  

Indian Institute of Technology  

Kharagpur  

18  

32  

50

13  

Indian Institute of Technology  

Kanpur  

22  

27  

49

14  

Institute of Mathematical Sciences  

Madras  

15  

32  

47

15  

Panjab University  

Chandigarh  

18  

27  

45

16  

Indian Institute of Technology  

Bombay  

21  

24  

45

17  

University of Kalyani  

Kalyani  

22  

21  

43

18  

Lucknow University  

Lucknow  

16  

26  

42

19  

Indian Institute of Technology  

New Delhi  

20  

22  

42

20  

Dr Hari Singh Gour University  

Sagar  

22  

19  

41

21  

Marathwada University  

Aurangabad  

19  

19  

38

22  

University of Poona  

Pune  

18  

13  

31

23  

Cochin University of Science and Technology  

Cochin  

13  

15  

28

24  

Burdwan University  

Burdwan  

11  

17  

28

25  

Tata Institute of Fundamental Research   Bangalore  

23  

4  

27

26  

Indian Statistical Institute  

Bangalore  

13  

14  

27

27  

Jawahar Lal Nehru University  

New Delhi  

15  

11  

26

28  

University of Roorkee  

Roorkee  

13  

13  

26

29  

Kalyan Mahavidyalaya  

Bhilainagar  

17  

9  

26

30  

University of Jodhpur  

Jodhpur  

17  

8  

25

31  

University of Rajasthan  

Jaipur  

20  

5  

25

32  

Andhra University  

Waltair  

17  

8  

25

33  

University of Gorakhpur  

Gorakhpur  

11  

13  

24

34  

Vikram University  

Ujjain  

12  

10  

22

35  

Saha Institute of Nuclear Physics  

Calcutta  

8  

14  

22

36  

Gurukul Kangri Vishvavidyalaya  

Hardwar  

6  

14  

20

37 - 188  

152 other Institutions published each between 19 and 1 papers   

 

438  

440  

877

  

Total  

 

1313  

1391  

2710

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]

Organization Type 1990   1994   Total
Academic   1045   1080   2125

Research  

166

175

341

Central Ministries  

107  

130  

237

Private Bodies  

0  

6  

6

State Governments  

1  

0  

1

Total  

1319  

1391  

2710

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

No State No. of Papers
1990 1994 Total

1  

West Bengal  

261  

263  

524

2  

Uttar Pradesh  

197  

237  

434

3  

Maharashtra  

188  

159  

347

4  

Tamil Nadu  

99  

155  

254

5  

Delhi  

116  

135  

251

6  

Karnataka  

96  

127  

223

7  

Madhya Pradesh  

93  

72  

165

8  

Rajasthan  

50  

21  

71

9  

Andhra Pradesh  

39  

28  

57

10  

Orissa  

19  

43  

62

11  

Bihar  

33  

17  

50

12  

Kerala  

26  

22  

48

13  

Gujarat  

26  

20  

46

14  

Chandigarh  

18  

27  

45

15  

Assam  

14  

16  

30

16  

Haryana  

17  

9  

26

17  

Punjab  

8  

18  

26

18  

Jammu and Kashmir  

6  

14  

20

19  

Goa  

2  

4  

6

20  

Manipur  

6  

0  

6

21  

Meghalaya  

4  

0  

4

22  

Mizoram  

1  

2  

3

23  

Himachal Pradesh  

0  

2  

2

  

Total  

1319  

1391  

2710

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]

No City No. of Papers
1990 1994 Total

1  

Calcutta  

191  

185  

376

2  

New Delhi  

116  

135  

251

3  

Bombay  

131  

206  

237

4  

Madras  

78  

126  

204

5  

Bangalore  

78  

96  

174

6  

Varanasi  

47  

48  

95

7  

Aligarh  

19  

37  

56

8  

Kanpur  

25  

27  

52

9  

Kharagpur  

18  

32  

50

10  

Aurangabvad  

22  

24  

46

11  

Chandigarh  

18  

27  

45

12  

Kalyani  

22  

21  

43

13  

Lucknow  

16  

26  

42

14  

Sagar  

22  

19  

41

15  

Jaipur  

28  

8  

36

16  

Allahabad  

11  

22  

33

17  

Pune  

18  

14  

32

18  

Bhubaneswar  

7  

22  

29

19  

Gauhati  

13  

16  

29

20  

Burdwan  

11  

17  

28

21  

Cochin  

13  

15  

28

22  

Bhilainagar  

17  

9  

26

23  

Gorakhpur  

13  

13  

26

24  

Hyderabad  

13  

13  

26

25  

Roorkee  

13  

13  

26

26  

Jodhpur  

17  

8  

35

27  

Ujjain  

14  

11  

25

30  

Mysore  

6  

15  

21

31  

Ahmedabad  

13  

7  

20

32  

Hardwar  

6  

14  

20

33 - 110  

78 cities each contributed between 1 to 19 papers  

236  

195  

431

  

Total  

1319  

1391  

2710

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 MedlineCurrent 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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