Providence Reporter

American Mathematical Society recently issued the following announcement.

In the historic Old West Side of Ann Arbor, Michigan sits a four-story brick building with unusually sloped hallways and a labyrinthine arrangement of staircases. These peculiarities convey memories of the edifice’s past as a brewery—but fermentation vats and bottling lines gave way decades ago to bookshelves and offices. Since 1984, the site has brewed and distributed mathematical knowledge as the home of the AMS’s Mathematical Reviews (MR).

Founded in 1940 by Otto Neugebauer, MR began as a monthly publication reviewing the latest mathematics papers. In 1996, the AMS launched MathSciNet, the online version of MR, which has ballooned into a “ginormous database that indexes literally millions of mathematical items,” said Heather Jordon, an associate editor at MR. In a typical year, 24,000 mathematicians from around the world review a total of 42,000 mathematics publications to help fellow researchers stay abreast of new developments—and every single review is solicited and edited by associate editors like Jordon.

A combinatorist, Jordon initially followed a traditional academic career path in mathematics. She joined the faculty of Illinois State University in 2002 and became a full professor in 2010. But soon she found herself ready for a major career shift. Jordon took a position at MR to provide a different service to the discipline.

And what a vital service it is: With MathSciNet, mathematicians can quickly determine what’s been done already on the problems they’re pondering, evaluate the relevance of a multitude of papers, and follow threads of inquiry through the literature. All of this is made possible by a dedicated team of mathematicians, copy editors, catalogers, programmers, and others working diligently behind the scenes. While serving as an associate editor is a possibility that mathematicians do not often consider, Jordon and her colleagues find it a fulfilling role.

From published paper to review in MathSciNet

Throughout its more than 80-year history, MR has evolved along with technology. The last print issue of Mathematical Reviews arrived in libraries and mailboxes in 2012; since then, MathSciNet has continued expanding in content and features. Meanwhile, intimidating piles of print journals, once omnipresent in the MR office, are now almost entirely supplanted by online versions. Nevertheless, the process by which a new review appears still follows the same core steps as it did decades ago.

The 16 associate editors—all PhD mathematicians—each oversee a set of Mathematics Subject Classifications (MSCs) as well as a related set of journals. As an editor combs through journals in the “prescanning” phase (with the help of specialized software), they determine which papers to include in MathSciNet under which MSCs. At the same time, "for each of the papers, you decide [whether] this is a paper that we're just going to index, or we're going to assign to it the author summary, or we're going to send [it] out for an external review," explained associate editor Andrés Eduardo Caicedo. Meanwhile, cataloguers make sure that the paper’s authors are matched to the correct profiles in MathSciNet.

Caicedo, who has worked at MR since 2015, first encountered the “big orange volumes” of Mathematical Reviews as an undergraduate at the University of the Andes in Colombia. At MR, he handles mainly mathematical logic and foundations (MSC 03) and computer science (68), plus two smaller areas: general algebraic systems (08) and order, lattices, and ordered algebraic structures (06). Matching a paper to a reviewer is “a bit of an art,” Caicedo said. “We have a big database, but in the end it's a bit subjective.” MR editors try to find a reviewer who isn’t a close colleague of the authors, yet whose expertise relates to the topic of the paper.

When the draft of a review comes in, the staff of Reviewer Data Services checks the TeX, and a copy editor cleans up the language and citations. Then, the assigning editor uncaps their (now metaphorical) green pen to closely examine the review’s content. "I'm reading it for grammar, style, making sure the math is correct, making sure that the way that things are phrased is going to be understandable to another mathematician," said Jordon, who manages combinatorics (MSC 05) and information and communication theory (94).

As users of MathSciNet know, reviews range widely in length. Michael Atiyah, for example, had a knack for writing crystal-clear single-paragraph reviews. Other reviews dive into more detail and thus are much more time-consuming to edit.

"In logic, for instance, a lot of the reviews tend to be a bit long,” Caicedo said. “So even if at the end, there aren't that many reviews, [one review] might require that you go and consult references, and it might take an hour or more to go through."

When the first editor is satisfied, the review passes to the desk of a second editor (who first-edits different MSCs). From there a copy editor does a final check before the review is posted to MathSciNet, thus completing the journey. All in all, at least five people, two of them mathematicians, have pored over the review to ensure that it meets MR’s high standards for accuracy and clarity and appropriately links to other items within the database.

Original source can be found here.