Are There Research Teams in a “ Little Science ” Discipline such as Mathematics ?

The objective of this paper is to analyse the role of collaboration in Mathematics, which has been described as one of the less collaborative disciplines within the hard sciences. Scientific production of Spain in the area of Mathematics, years 1996-2001, was downloaded from SCI database, to which MathSci thematic codes were added. Trends in the collaboration between authors and centres in the area are analysed at the discipline level and differences between thematic specialities in behaviour and visibility are shown. A steady increase in the different collaboration indicators is observed in the area, although below that described for all areas combined. At the micro level research teams are identified through co-authorship analysis and an in-depth study of the most productive teams is developed. Individual and collective research coexists in the area. An exploratory study of the relationship between variables through multivariate analysis shows that the number of publications tends to increase with team size, while productivity tends to decrease; large teams are more likely to collaborate both at the national and at the international level; and national collaboration fosters interdisciplinarity. Expected impact is enhanced by international collaboration. Some conclusions with science policy implications might be drawn. Introduction Different reasons have been put forward to explain the increasing role of collaboration in research. Since research is becoming increasingly complex, collaboration between specialists in different disciplines is necessary to solve scientific inquiries and understand nature. Moreover, collaboration is a source of interdisciplinarity, which has emerged as a decisive factor in the production of new knowledge and has lead to the greatest scientific advances as a result of the cross-fertilization process that occurs among disciplines. Numerous studies on collaboration from different points of view have been published in the last years (see for example Newman, 2004; Melin, 2000; Katz, 1997). The trend to collaborate varies according to the disciplines. It is the norm in “big science”, in which large teams work in the development of sophisticated research projects (i.e. particle physics), while it is less frequent in certain “little science” areas such as Mathematics and especially in different disciplines of Social Sciences and Humanities. The fact that research in the latter needs neither large teams nor sophisticated laboratory techniques is the underlying reason for its low collaboration. However, collaboration tends to increase also in these traditionally low-collaborative areas, which are also learning to take advantage of the benefits of the interactions among scientists. The objective of this paper is to analyse the role of collaboration in Mathematics, which has been described as one of the less collaborative disciplines within the hard sciences (Newman 2004). The following questions are addressed: • Is collaboration increasing also in this area during the last years? • Are we able to distinguish occasional collaboration from the more sustained collaboration that occurs within a research team? Are there research teams in the area? • Are there differences in the trend towards collaboration of the different disciplines within the Mathematics area? 1 This work was financed by the Spanish Plan Nacional de I+D+I (BFF2001-4415-E). We would like to thank Manuel de Leon and David Martin for their valuable contribution as experts in the field of Mathematics. María Bordons, María Teresa Fernández, Fernanda Morillo and Isabel Gómez 306 • Is there any sign of positive effects of collaboration upon scientific research? Does it increase productivity? Does it increase impact of research? Does it foster interdisciplinarity? Methodology Scientific production of Spain in the area of Mathematics, years 1996-2001, was downloaded from the Science Citation Index (SCI) (CD-ROM edition). For the field delimitation the ISI classification of journals into categories was used and the following subfields were considered: Mathematics, Applied Mathematics, Mathematics-miscellaneous, Operations Research-Management Science, Statistics & Probability, Mathematical Physics, Social Sciences-Mathematical Methods. All types of documents were included in the study. Bibliographic data obtained from SCI were standardised. Institutions were codified following the codification scheme developed at our centre. Author names were also normalised since the same scientist can be registered through several different names in SCI. To enable the study of research topics thematic codes describing the content of each document were obtained from the specialised database MathSci, produced by the American Mathematical Society. It uses the “Mathematics Subject Classification” (MSC) to index documents. This classification includes more than 5000 terms sorted in a hierarchical structure with five levels of aggregation. For our analysis we have worked at the two-digit level, in which 59 different codes are distinguished. Documents published by Spanish authors in MathSci were retrieved and matched with documents downloaded from the SCI. MathSci thematic codes were added to SCI records. For the study of collaboration different levels of analysis were established: 1. Collaboration between centres: • collaboration rate (percentage of documents with at least 2 centres) • national collaboration rate (% of documents with at least 2 domestic centres) • international collaboration rate (% of documents with at least 1 foreign centre) • average number of centres per document 2. Collaboration between authors • average number of authors per document • study of research teams Research teams were obtained according to co-author analysis. The most productive author within a group is named “team leader”, although he/she is not necessarily the intellectual leader of the group. All authors sharing at least 50% of their production with a leader were considered as pertaining to his/her group. The structure of teams was checked by experts in the area. An in-depth analysis was conducted for the most productive teams selected for fitting at least one of the following criteria: high production of the team leader, high production of the team or high team productivity. Results A total of 4940 documents were published by Spanish scientists in Mathematics journals during the period 1996-2001. Spain shows a certain specialisation in Mathematics, since it is responsible for 3.5% of the world production in the area, while its contribution to all the areas is around 2.5%. Moreover, the growth rate in the number of publications in the area has been higher that that corresponding to all topics. In fact, this is the area with the highest increasing trend in Spain during the last years. The most productive subfield is Mathematics (41%), followed by Applied Mathematics (37%) and Mathematical Physics (23%). The categories of Applied Mathematics, Operations Res.-Manag. Sci. and Mathematical Methods-Social Sci. showed a growth rate above the average (table 1). In relation to the international visibility of the publications, the trend to publish in high impact factor journals (journals in the first quartile of the journal ranking in descending order of impact factor, by Are There Research Teams in a “Little Science” Discipline such as Mathematics? 307 disciplines) remained quite stable over the years. It was around 20% in most categories, being remarkable the high value in Mathematical Physics (60%). Table 1. Publications of Spanish authors in Mathematics Category 1996 2001 Total 1996-2001 % Doc. 1996-2001 Growth rate (%) % Doc. Q1 Mathematics 263 401 2009 40.67 52 20.51 Applied Mathematics 199 416 1810 36.64 109 21.19 Mathematical Physics 155 234 1139 23.06 51 60.79 Statistics & Probability 54 89 444 8.99 65 25.00 Oper. Res.-Manag.Sci. 32 62 279 5.65 94 24.46 Mathematics, miscel. 25 25 184 3.72 0 20.33 Math.Meth. -Social Sci. 15 41 173 3.50 173 9.76 Total 597 1011 4940 69 %Doc.Q1= % documents in journals located in the first quartile Collaboration at the field level An increasing trend in scientific collaboration was observed by means of different indicators: number of authors per document, number of centres per document and number of documents with more than one centre, although the values obtained are clearly below the average described for the whole country (table 2). Table 2. Collaboration in Mathematical publications Mathematics All Areas Collaboration indicators 1996 2001 1996 2001 Av.No.Authors/doc. 2.34 2.50 5.70 5.73 Av.No.Centres/doc. 1.78 1.94 2.30 2.56 % Doc. with more than 1 author 79% 81% 92% 94% % Doc. with more than 1 centre 53% 58% 55% 63% % Doc. with more than 1 national centre 22% 24% 33% 37% % Doc. with at least 1 international centre 37% 40% 29% 36% Total number of documents 597 1,011 18,454 21,086 The percentage of documents with more than one centre in Mathematics during 1996-2001 was quite similar to that of all areas (57% vs 60%), but a higher percentage of international collaborative documents (39% vs. 32%) and a lower percentage of national collaborative documents (24% vs. 35%) was observed. On the other hand, documents in collaboration in Mathematics increased quicker than those signed by just one centre (86% vs 50%), being the growth rate of national and international collaboration similar and quite above that corresponding to the whole country in all areas. Spanish scientists in Mathematics collaborated mainly with scientists in the European Union, followed by North America and Latin American countries. The highest increase corresponded to collaboration with Latin American countries (170%), which in a lower rate was also described for all areas combined. The highest collaboration was found in Mathematical Physics, which shows the highest percentage of documents in collaboration (68%) and especially, in international collaboration (47%) (table 3). It