Looking Back at 60 Volumes of SIAM Review
By Nicholas Higham
SIAM was founded in 1952 to promote applied mathematics research and facilitate the exchange of ideas between mathematicians and others in science and industry [3]. Its initial publications were SIAM Newsletter, glossy and in U.S. half letter format, and the Journal of the Society for Industrial and Applied Mathematics — both of which began in 1953. The newsletter included news about SIAM and the applied mathematics community, book reviews, and adverts. It also contained technical articles of broad interest under the heading “SIAM Notes.”
The January 1958 newsletter featured a frontpage article announcing a new journal called SIAM REVUE,^{1} which promised expository papers, book reviews, articles on education and policy, and a problems section.
The first issue of SIAM Review appeared in January 1959. Among the articles in early issues were reprints of “SIAM Notes,” the first being Thomas N.E. Greville’s “The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear Equations.” Pseudoinverses proved to be a popular topic in the journal for many years to come.
Beginning with volume 2 of SIAM Review, a “News and Notices” section (later renamed “Chronicle”) appeared in each issue, intending to “report to the membership the activities of the Society, and news and meeting notices of interest to the applied mathematician.” This section took over the role of SIAM Newsletter, which was later rejuvenated as SIAM News and gradually adopted the task of providing news about SIAM. View archives of SIAM Review.
SIAM Review’s first issue of 1960 contained a report by Donald Thomsen, Jr. (IBM)—who had just completed his term as SIAM President—on SIAM activities in the preceding year. It described the establishment of a committee to expand SIAM’s conference program and the intention to start a SIAM monograph series. The report tallied membership at 1,626, with 47 institutional members and 14 sections. Other officer reports appeared from time to time, including annual reports from the treasurer that from 1986 to 1998 shared much interesting information about SIAM, financial and otherwise. Until 1998, each issue published a list of new members.
Cartoon created by mathematician John de Pillis.
In its early years, SIAM Review sometimes printed reports of various types of meetings. A 1964 article provides a transcript of a panel discussion on mathematical publishing at the previous year’s SIAM fall meeting [4]. It is striking that many of today’s issues were also of concern 54 years ago, such as the proliferation of journals, the quality of writing in mathematical papers, and the ways in which editors and referees maintain standards of accepted papers. The comprehensive survey articles for which SIAM Review is renowned were not a feature of every issue in the early years, but became more common in the 1970s.
In the July 1975 issue of SIAM Review, the editors announced a new section titled “Classroom Notes in Applied Mathematics” consisting of “brief notes (one to four printed pages), which are essentially selfcontained applications of mathematics that can be used in the classroom.” They stated that the intention was to eventually collect these notes into a book. This happened in 1987, with the publication of Mathematical Modelling: Classroom Notes in Applied Mathematics [7], edited by Murray Klamkin. The same author, who edited the problems section from 1959 to 1993, later published a selection of problems and solutions from the journal [8]. The December 1986 issue featured a paper typeset in TeX that author Layne Watson, an early adopter of TeX, had delivered as cameraready hard copy [15]. It was not until 1990 that submission instructions mentioned the possibility of authors providing TeX sources for their accepted papers.
The last issue of 1996 announced a major redesign of SIAM Review. It arose from recommendations of a 1994 ad hoc committee appointed by the SIAM president to evaluate all SIAM journals. The March 1999 issue was the first to be published in the new format, and a preface from editorinchief Margaret Wright explained the changes. A glossy dark blue cover, shiny paper, and a page design unique to the journal were part of the new look. It contained four sections—titled “Survey and Review,” “Problems and Techniques,” “Education,” and “Book Reviews”—with autonomous section editors, along with a “SIGEST” section that reprinted a notable paper of broad interest from another SIAM journal. The previous “Problems and Solutions” section became electronic only. Each section featured an introduction by the relevant section editor that put the articles into context; nowadays these introductions are also posted on SIAM News Online. This format remains essentially unchanged today, though the second section was renamed “Expository Research Papers” in 2010 and “Research Spotlights” in 2012.
Book reviews have always been a popular component of SIAM Review, with expert reviewers providing insight into relevant fields and offering due praise and criticism. The redesign introduced “Featured Reviews,” in which a reviewer assesses several books on a particular topic. These are especially useful for instructors searching for a suitable classroom text. For example, “PDE Books, Present and Future” by J. David Logan in the September 2000 issue and “Two New Books on Partial Differential Equations” by Ronald B. Guenther and Enrique A. Thomann in the March 2005 issue remain useful guides to textbooks available at those times for a PDE course.
Another recent feature of SIAM Review is the publication of reports on educational matters, such as the influential 2001 report on graduate education in computational science and engineering (CSE) [12] (complemented by [16]), which was followed a decade later by a report on undergraduate education [13]. A report on challenges, opportunities, and directions for CSE research and education for the next decade will appear later this year [11].
In preparing this article, I had a lot of fun browsing through the back issues of SIAM Review. Here are a few observations. The second mostcited^{2} article from the 1960s is actually a halfpage problem [14] that introduced a novel application of the orthogonal Procrustes problem. I have even cited it myself. As far as I know, only one paper has had the honor of appearing in SIAM Review twice: the famous “nineteen dubious ways” paper on the matrix exponential by Cleve Moler and Charles Van Loan [9]. It was reprinted in 2003 as part of SIAM’s 50th birthday celebrations, with new material to bring it up to date [10]. It is interesting to note that some of SIAM Review’s mostcited papers have appeared in the Education section, including [2] and [6]. Indeed, six of the 10 mostdownloaded papers (see the chart on page 9) appeared in the Education section. Papers with a pedagogic slant can clearly still garner many citations from the research literature. The longest paper I could find (based on some Emacs and MATLAB hacking of the SIAM Review BibTeX file in the TeX User Group bibliography archive) is [1], which at 107 pages is longer than some SIAM books. Back issues of SIAM Review contain gems that one might not expect to find. One of my favorites is the delightful glimpse into the life of Leonhard Euler by Walter Gautschi [5].
Two measures of SIAM Review’s influence are its citations and its impact factor. SIAM Review is consistently among the topranked journals in applied mathematics by impact factor, and often holds the leading position. Many of its papers boast thousands of citations. Table 1 shows the five mostcited papers as of January 2018, according to Google Scholar.
Table 1. The five mostcited papers in SIAM Review per Google Scholar, as of January 2018.
The mix of older and more recent papers in the table shows that SIAM Review not only covers enduring topics but also identifies new and emerging areas. Indeed, the June 2018 issue will present a survey on the very timely topic of optimization methods for machine learning.
SIAM Review’s first 60 volumes are a microcosm of applied mathematics and computational science from 1959 until now. As such, they provide a valuable historical record, both in the technical content and the news items about early SIAM activities. However SIAM Review evolves over the next several decades, it will remain a mustread for those who want to keep up with innovations in research and education in our field.
^{1} This spelling, which suggests a rather different sort of publication, was only used once in the article and was presumably a typo.
^{2} All citations are from Google Scholar.
References
[1] Asch, M., Kohler, W., Papanicolaou, G., Postel, M., & White, B. (1991). Frequency Content of Randomly Scattered Signals. SIAM Rev., 33(4), 519625.
[2] Berrut, J.P., & Trefethen, L.N. (2004). Barycentric Lagrange Interpolation. SIAM Rev., 46(3), 501517.
[3] Block, I.E. (1973). SIAM — Its First Three Years. SIAM Rev., 15(2), vix.
[4] Block, I.E., & Drenick, R.F. (Eds.). (1964). A Symposium on the Publication of Mathematical Literature. SIAM Rev., 6(4), 431454.
[5] Gautschi, W. (2008). Leonhard Euler: His Life, the Man, and His Works. SIAM Rev., 50(1), 333.
[6] Higham, D.J. (2001). An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. SIAM Rev., 43(3), 525546.
[7] Klamkin, M.S. (Ed.). (1987). Mathematical Modelling: Classroom Notes in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics.
[8] Klamkin, M.S. (Ed). (1990). Problems in Applied Mathematics: Selections from SIAM Review. Philadelphia, PA: Society for Industrial and Applied Mathematics.
[9] Moler, C.B., & Van Loan, C. (1978). Nineteen Dubious Ways to Compute the Exponential of a Matrix. SIAM Rev., 20(4), 801836.
[10] Moler, C.B., & Van Loan, C. (2003). Nineteen Dubious Ways to Compute the Exponential of a Matrix, TwentyFive years Later. SIAM Rev., 45(1), 349.
[11] Rüde, U., Willcox, K., McInnes, L.C., De Sterck, H., Biros, G., Bungartz, H.,…,Woodward, C.S. (2018). Research and Education in Computational Science and Engineering. To appear in SIAM Rev., 16(2).
[12] SIAM Working Group on CSE Education. (2001). Graduate Education in Computational Science and Engineering. SIAM Rev., 43(1), 163177.
[13] SIAM Working Group on CSE Undergraduate Education. (2011). Undergraduate Computational Science and Engineering Education. SIAM Rev., 53(3), 561574.
[14] Wahba, G. (1965). Problem 651, A Least Squares Estimate of Satellite Attitude. SIAM Rev., 7(3), 409.
[15] Watson, L.T. (1986). Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods. SIAM Rev., 28(4), 529545.
[16] Yasar, O., & Landau, R.H. (2003). Elements of Computational Science and Engineering Education. SIAM Rev., 45(4), 787805.

Nicholas Higham is Royal Society Research Professor and Richardson Professor of Applied Mathematics at The University of Manchester. He is the current president of SIAM. 