Vital Statistics on the Numbers Game

Vital Statistics on the Numbers Game

hile unable to determine how many of the minds involved are actually beautiful (although most are, no doubt, perfectly presentable), Science Watch offers here a survey of mathematics research over the last 10 years. Highly cited institutions (on the next page) are ranked both by citations (left column) and citation impact (that is, citations per paper, at right). Highly cited authors also appear on the next page. The most-cited journals appear below.

These rankings are from ISI Essential Science Indicators Web product, a Thomson/ISI web-based evaluation tool, and are based on papers published and cited in more than 300 ISI-indexed journals of mathematics and statistics between 1991 and December 2001.

Highly Cited Journals in Mathematics, 1991-2001
(Ranked by citations to papers published and cited between 1991 and December 2001)

Rank	Journal	Citations
1	J. Amer. Statist. Assn.	16,457
2	Biometrics	10,854
3	J. Math. Analysis	9,845
4	Annals of Statistics	9,702
5	Proc. Amer. Math Soc.	9,237
6	C.R. Acad. Sci. Ser. I Math.	9,153
7	Trans. Amer. Math. Soc.	8,586
8	Journal of Algebra	8,531
9	J. Functional Analysis	7,999
10	Biometrika	7,911
11	SIAM J. Numer. Anal.	7,383
12	Inventiones Mathmaticae	7,382
13	J. Roy. Stat. Soc. Ser. B Meth.	6,575
14	Mathemat. Programming	6,444
15	Linear Algebra Appl.	6,112

SOURCE: ISI Essential Science Indicators Web product, 1991-2001

By the measure of total citations, the University of Paris 6 took the top spot, with more than 7,500 collective citations to 2,271 mathematics papers over the last decade. The most-cited of these is "Semiclassical quantization of multidimensional systems," by E.B. Bogomolny, Nonlinearity, 5(4):805-66, 1992, with 121 citations to date. "Representations of quantum algebras," by H.H. Andersen and colleagues (Invent. Math., 104[1]:1-59, 1991), was the second-most-cited paper featuring authors affiliated with University of Paris 6; this paper has been cited roughly 70 times.

In citations-per-paper influence, the University of Washington scored the highest number (of those institutions that produced at least 500 mathematics papers during the last decade), with an average of 8.24 citations. The most-cited mathematics paper from the University of Washington, in fact, turned out to be the most-cited paper in this survey: "Performing the exact test of Hardy-Weinberg proportion for multiple alleles," by Sun-Wei Guo and Elizabeth A. Thompson, Biometrics, 489(2):361-72, 1992. This paper has now been cited more than 650 times, clearly demonstrating the extent to which biomedicine has benefited from algorithmic analysis and other mathematical techniques for exploring and interpreting genetic data. Both of the papers authors, not suprisingly, wound up among the decades most-cited mathematics researchers as determined by ISI Essential Science Indicators Web product. Guo and Thompson are just two of the eight representatives in the ranking from the field of biostatistics. Another University of Washington biostatistician, Norman E. Breslow, contributed to the surveys second-most-cited paper, "Approximate inference in generalized linear mixed models," J. Amer Stat. Assn., 88(421):9-25, 1993, with more than 420 citations. Breslow and coauthor Douglas G. Clayton, of the MRC Biostatistics Unit in Cambridge, U.K., also appear among the decades most-cited authors.

Another standout among institutions was Stanford University, which scored second in both the total-citations and impact rankings. Stanfords most-cited paper was "Multivariate adaptive regression splines," by J.H. Friedman, (Ann. Statist., 19[1]:1-67, 1991), with approximately 350 citations. Stanfords next-most-cited paper, "Ideal spatial adaptation by wavelet shrinkage," (Biometrika, 81[3]:425-55, 1994), with 300 citations, was written by two more of this surveys featured authors, Stanford colleagues David L. Donoho and Iain M. Johnstone.

As Donoho explains in a commentary written for in-cites, the online editorial component of ISI Essential Science Indicators Web product, the "wavelet shrinkage" that he and Johnstone discuss is a technique for removing noise from "signals, images, and other sorts of data." Wavelets, Donoho notes, have been a popular and broadly applicable topic in statistics over the last two decades. (Donohos comments can be read at http://in-cites.com/scientists/DrDavidDonoho.html).

Of all the authors in this survey, none was more highly cited than Pierre-Louis Lions of the University of Paris 9, whose research has included work on nonlinear partial differential equations. Lionss most-cited paper in this survey, "Users guide to viscosity solutions of second-order partial differential equations" (with M.G. Crandall and H. Ishii, Bull. Amer. Math. Soc., 27[1]:1-67, 1992), has been cited more than 315 times. Lions was awarded the Fields Medal, the highest prize in mathematics, in 1994.

Continued on the following page: Mathematics Research: Institutions Ranked by Citations and Citation Impact and Highly Cited Authors in Mathematics, 1991-2001.

Science Watch^Ž, May/June 2002, Vol. 13, No. 3
Citing URL: http://www.sciencewatch.com/may-june2002/sw_may-june2002_page1.htm