The Game of Cipher Beads

Comparison between the various impact factors of a few Russian journals demonstrates the deficiencies of the popular citation indices. DOI: 10.1134/S1990478909030065 Since recently there has been much ado invoked in science by incessant attempts at replacing expertise with numerical manipulations. Of especial relevance to the Russian mathematical community are the following indices: • MCQ, the Mathematical Citation Quotient of the American Mathematical Society which utilizes the database of Mathematical Reviews (abbreviated to MR); • IF or ISI, the classical impact factor of the Institute for Scientific Information which is a part of the Thomson Reuters Corporation; • RISC, the Russian Index of Scientific Citation (cp. [1]) which rests upon the database of the Scientific Electronic Library ; • MNRU, the impact factor of the All-Russia Mathematical Portal Math-Net.Ru which uses its own database (cp. [2]). These indices are calculated for each journal one by one. Let QN,k be the number of citations in year N of the articles published in the journal in year N − k. By PN we denote the number of the articles published by the journal under study in year N . Note in passing that N is the number of a year in the Gregorian calendar, and so N is at least six since N is greater than thousand. In this notation MCQN , the MCQ of the journal in year N , is calculated as follows: MCQN = QN,1 + QN,2 + · · · + QN,5 PN−1 + PN−2 + · · · + PN−5 . Denote the impact factor in year N by IFN . By definition, IFN = QN,1 + QN,2 PN−1 + PN−2 . Thus, MCQ and IF are defined by the same scheme covering the different time spans of the relevant databases (cp. [3]). The first takes the citations of the previous five years; whereas the second, of the last two years. The RISC and MNRU impact factors are calculated by the classical two-year formula for IF suggested by Eu. Garfield, the founder of the Institute for Scientific Information (cp. [4]). It is worth observing that all four indices use the different although intersecting databases. Let us assume that all articles in some journal are of the same high quality and have the same number of citations. Assume further that the number of articles in any volume is the same every year. In other words, suppose that QN,k and PN are independent of N and k. In this model case, the MCQ and IF of the journal must coincide with one another as well as with the remaining two indices. Some fluctuations are The text was submitted by the author in English. E-mail: [email protected]