A History of Mathematics in the United States and Canada: Volume 2: 1900-1941

David Zitarelli (1941–2018) was an ardent promoter of the history of mathematics whose contributions included co-organizing conference sessions, preparing numerous well-received articles and books, and encouraging younger scholars. He was especially interested in the history of American mathematics and taught a unique course on the subject for a decade at Temple University, his home throughout a 42-year career. When Zitarelli died unexpectedly in December 2018, he was working on what was then envisioned as a three-volume account, covering 1492 to 2000, that had developed from his course notes. His family and the MAA Press imprint of the AMS Book Program agreed to complete as much as of the book as possible. Volume 1 (1492–1900) appeared in 2019, thanks to the copyediting efforts of MAA Press Acquisitions Editor Stephen F. Kennedy and AMS production editor Jennifer Wright Sharp. The MAA Review is by Scott Guthery; I have also written about it for Notes of the Canadian Mathematical Society and Mathematical Reviews (MR4306766).

The files for what became Volume 2 (1900–1941) were significantly more unfinished, so Kennedy teamed up with University of Richmond historian of mathematics Della Dumbaugh to clean up and rewrite Zitarelli’s draft as needed. (The notes for the years 1941–2000 were entirely preliminary and will remain unpublished, although readers can get some idea of what Zitarelli intended from the files on his personal website.) Like Volume 1, the book is generally organized chronologically, with seven chapters spread across two parts: “Consolidation and Growth, 1900–1930,” and “Internationalization, 1930–1941.” A “Transition 1930” section at the end of the first part evokes the similar sections in Volume 1, while an “Afterword” added by the editors brings the story of the two volumes to a close. A number of stylistic changes further distinguish the two volumes. Most notably, names are no longer set in boldface on first mention, a choice that provoked thoughts about Zitarelli’s methodology to which I will return below. Additionally, the endnotes of Volume 1 have been converted into footnotes and parenthetical references citing a numbered bibliography in Volume 2, decisions that I suspect will help many readers more easily connect Zitarelli’s evidence to his primary and secondary sources.

The narrative begins by returning to the E. H. “Moore Mob” at the University of Chicago, particularly Oswald Veblen, R. L. Moore, and George Birkhoff. The rest of the first chapter is largely a tour of institutions (Missouri, Washington University, Princeton, Harvard, Yale) interspersed with discussions of major national and international meetings, as mathematical research and higher education both grew steadily. Zitarelli notes the presence of several women. The second chapter considers the founding of the MAA, mathematics during World War I, and the arrival of international students in American graduate programs. Two chapters trace institutional developments during the 1920s, the experiences of Black mathematicians, increasing government support for research, and growth within the AMS. Mathematics in Canada finally makes a substantive appearance in the fourth chapter with an account of J. C. Fields and the 1924 ICM and other meetings. The final three chapters look at the Institute for Advanced Study, émigré mathematicians, and advances in fields such as algebra and logic.

Zitarelli was known for a people-centered methodology that employed storytelling to humanize mathematics and that emphasized communities and “rank-and-file” mathematicians. The use of boldfaced names and an overall structure as a series of mini-biographies made Volume 1 a very explicit presentation of Zitarelli’s preferred emphases. Volume 2 is less direct in its style and approach, but the focus remains on the individuals who comprise communities, institutions, and organizations. Indeed, sometimes the lists of names come at the reader so rapidly that those without some background in the history of American mathematics may experience information overload. Although there are still paragraphs and runs of several paragraphs devoted to biographies of a single person, Zitarelli’s method and interpretations feel sober in comparison to the exuberance of Volume 1. I suspect a key difference between the volumes is the considerably greater complexity of the 20th century, with networks and communities numbering in the hundreds rather than the dozens of earlier periods, as well as ever-deeper theories and results in mathematics itself. The quantity of mathematicians offers readers an opportunity to reflect on the constructs of great and “everyday” mathematicians, to use the term employed by Kennedy and Dumbaugh in the Afterword. Every accomplishment listed in the text sounded historically significant to me; the editors argue that the labors described by Zitarelli demonstrate that every mathematician (including the readers of this book) contributes to the discipline of mathematics. I think our assessments are not contradictory.

While this book contains more mathematical statements than Volume 1 did, it probably will not be assigned by instructors who want to concentrate on teaching mathematics in history of mathematics courses. Those who take a narrative approach may also find the volume more useful as a resource for teachers than as required reading for every student, although an electronic version opens the possibility of assigning excerpts. AMS in fact suggests a readership of “graduate students and researchers interested in the history of American mathematics,” but I recommend it also for any research or teaching mathematician in the United States and, perhaps, Canada, who wants to know the origins of the contexts in which they think about mathematics. The authors have done an impressive job of shaping Zitarelli’s historical research into a one-volume snapshot of a time and place that represent a rapidly-growing area of scholarship—besides the substantial literature included in the bibliography, valuable new works such as Karen Hunger Parshall’s The New Era in American Mathematics are continuing to adjust our understanding of the 20th century.

Amy Ackerberg-Hastings (aackerbe@verizon.net) co-edits MAA Convergence with Janet Heine Barnett and the CSHPM Notes column in Notes of the Canadian Mathematical Society with Hardy Grant. Multiple conversations with David Zitarelli enhanced her growth as a historian of 19th-century American mathematics education.