This is alarming, and casts further doubt on the "Shanghai Rankings," which focus only on the natural and social sciences, and are heavily dependent on dubious citation data:
Mathematics, an open-access journal produced by the Multidisciplinary Digital Publishing Institute, published more than 4,763 articles in 2023, making up 9.3 percent of all publications in the field, according to the Web of Science. It has an impact factor of 2.4 and an article-influence measure of just 0.37, but, crucially, it is indexed with Clarivate’s Web of Science, Elsevier’s Scopus, and other indexers, which means its citations count toward a variety of professional metrics. (By contrast, the Annals of Mathematics, published by Princeton University, contained 22 articles last year, and has an impact factor of 4.9 and an article-influence measure of 8.3.)
One important citation metric targeted for citational gamesmanship is Clarivate’s prestigious “Highly Cited Researchers” list....The Highly Cited Researchers list also feeds into one indicator in the Shanghai Ranking, an academic ranking of world universities....
In 2023 a network of around 100 researchers [in mathematics] managed to co-author 17 papers — and get those papers cited 396 times from 2023 to early 2024. That is a remarkable citation rate. All 17 papers are on Clarivate’s “Highly Cited Papers” list for mathematics in 2023.
An intriguing pattern emerges when examining the articles that reference those 17 papers: The total number of citing articles is 84, 75 of which are either self-citations or co-author citations. That tight collaboration suggests a closely knit network of authors with potential biases in the citation patterns, casting doubt on the actual influence of the scholarship. Moreover, the average number of references to the 17 Highly Cited Papers is close to five, with several articles garnering more than five citations. Typical individual mathematicians would have received just one scholarly reference to their 2023 publications from other work in the field.
Let us focus on one of the citing articles, to see the peculiar way some targeted references appear:
"For future research directions, we hope to do some related work on singularity theory and symmetry (see [13–20])."
References 13 to 20 are papers with the same first author and an editor of an open-access journal where four of the 17 highly cited papers published by the network in 2023 appeared, along with 21 of the network’s 75 citing articles.
In another of those 75 citing articles, we find 10 self-citations within the network — nine of the references (Nos. 15 to 23) again to papers from within the network with the same first author. Those nine are lumped as follows in the text, right after an appropriate reference (No. 14):
"… studied the timelike circular surfaces in Minkowski 3-space from the viewpoint of singularity theory. They presented singularities and symmetry properties of timelike circular surfaces in Minkowski 3-space [14]. Moreover, some of the latest connected studies about symmetry and singularity can be seen in [15–23]."
That way of artificially acknowledging someone else’s work is not the result of the well-known Matthew effect, the “enhancement of the position of already eminent scientists who are given disproportionate credit in cases of collaboration.” Instead, it results from a concerted group effort to elevate one scholar at the top of its pyramid. The network we uncovered has produced 75 inconspicuous papers, primarily published in mega-journals, within a short time frame. The journals do not command the same level of attention and scrutiny as established venues, and so there is generally little recognition of the network’s research. But that lack of scrutiny serves the citation ring’s interests — less-scrupulous citation standards allow it to cite and thus elevate work published in the same types of journals.
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