American Mathematics 1890–1913: Catching Up to Europe

In 1994, David Rowe and I published The Emergence of the American Mathematical Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore. There, we detailed the institutional and mathematical developments that had resulted, by 1900, in a free-standing mathematical research community in the United States. We opened our book with a chapter that set the stage by briefly surveying the contours of the American mathematical landscape over the course of the first three quarters of the nineteenth century, and we closed by briefly sketching developments up to World War II. Both of these book-end chapters were intended to suggest lines of future research, and it is the latter chapter that seems to have served as a particular point of departure for Steve Batterson in his new book on American Mathematics 1890–1913: Catching Up to Europe. Indeed, Batterson acknowledges that he “learned a lot” from our book and that “[r]eaders familiar with” it “will undoubtedly recognize its impact on” his own text (p. 200).

In particular, Batterson fleshes out, in more detail than we were able to in our final chapter — given our principal timeframe of 1876 to 1900 — the pictures of Princeton and Harvard in the first decade of the twentieth century. In the case of the former, he delves, in his sixth chapter (of seven), into the preceptorial program instituted by Woodrow Wilson in 1905 in an effort both to enhance undergraduate education and to augment the Princeton faculty with talented, more research-oriented instructors. Oswald Veblen, Luther Eisenhart, and Joseph Wedderburn all got their Princeton starts as preceptors. Veblen and Eisenhart went on to be especially influential in building a strong mathematics program there in the 1920s and 1930s, capitalizing particularly on such external developments as the inauguration, late in 1923, of National Research Council Fellowships in mathematics. Relative to Harvard, Batterson looks closely, in his seventh chapter, at the negotiations that, in 1912, brought George Birkhoff from his Princeton preceptorship to the Harvard professorship that he would hold until his death in 1944. He also sheds some new light, in his fourth chapter, on the subsequent Harvard careers of William Osgood and Maxime Bôcher, two of the Americans who had gravitated to the seminars of Felix Klein in Göttingen in the late 1880s.

In perhaps the most original part of the book, Batterson nicely uses the papers of astronomer Simon Newcomb and mathematician Henry White to detail, in his fifth chapter, the interesting sequence of discussions between the American Mathematical Society (AMS) and the Johns Hopkins University at the end of the 1890s. The English mathematician and first Hopkins professor of mathematics, J. J. Sylvester, had founded the American Journal of Mathematics in 1878. In short order, it had become the publication outlet for America’s growing cadre of research-oriented mathematicians. By the late 1890s, however, the perception was that the journal’s editorial standards had fallen and that steps needed to be taken. (Sylvester had returned to England to assume the Savilian Professorship of Geometry late in 1883 and his student, Thomas Craig, had largely taken over editorial control with less than rousing success.) Might it be possible for the AMS to take over the American Journal and give it those higher editorial standards? In the end, the answer was a resounding “no,” but the situation ultimately resulted in the founding of a new research-oriented journal, the Transactions of the American Mathematical Society, and Batterson tells this tale compellingly.

The other chapters of Batterson’s book, however, contain less that is new. His first chapter largely revisits, with few new insights, the so-called “American colony” of students centered primarily on Felix Klein in Göttingen in the 1880s. His second chapter represents an archivally based digression, ostensibly on “19th-century American notions of scholarship,” that focuses on Benjamin Peirce at Harvard and Hubert Newton at Yale, while largely ignoring the vast literature on the history of higher education in the nineteenth century. Chapter three centers on the academic institution-building of Charles Eliot, the President of Harvard from 1869 to 1909, and Daniel Gilman, the President of Johns Hopkins from its founding in 1876 to 1901, and, especially relative to Gilman at Hopkins, covers ground that has already been well-trod using many of the same archival sources. Chapter four looks at mathematics at Harvard and the University of Chicago in the 1890s, and, again, especially relative to the latter, offers few new insights.

This book aimed to show that “American mathematics had earned standing by the beginning of the first World War, rather than the second” (p. xi). What, however, does “standing” mean and how exactly is it measured? These key questions are never explicitly addressed nor does any kind of sustained argument unite the various chapters of the book toward the book’s stated goal. In the unfocused and rather rambling concluding chapter seven, the argument would seem to be that the United States had “caught up” with Europe by 1913 because: (1) in 1912, William Osgood and Maxime Bôcher gave plenary lectures at the International Congress of Mathematicians in Cambridge, England (p. 188) (although decades-long American-based Simon Newcomb had done so in Rome four years earlier in 1908); (2) in 1913, George Birkhoff published his “Proof of Poincaré’s Geometric Theorem” in the Transactions of the American Mathematical Society and, in Constance Reid’s estimation, “for the first time in [Richard] Courant’s memory, the Göttingers looked with admiration across the ocean” (p. 184; the reference is to Constance Reid, Courant in Göttingen and New York: The Story of an Improbable Mathematician, p. 46. Reid gives no actual attribution here to Courant himself.) (although, and Courant was too young to remember this, E. H. Moore had been awarded an honorary doctorate from Göttingen as early as 1899); and (3)–(5):

[Dunham] Jackson’s thesis had just opened up the field of quantitative approximation theory. The work of Veblen and Alexander was crucial to launching the rapid development of algebraic topology that took place over the following decades. [Leonard] Dickson was a major force in many aspects of algebra. Thus cutting-edge research was taking place at the three American mathematical centers of Harvard, Princeton, and Chicago (p. 184).

Perhaps with twenty-twenty hindsight, these things may be seen as harbingers of “catching up to Europe,” but in order actually to demonstrate the “catching up” and “standing” of the American mathematical community in the eyes of the Europeans, one would have to assess the attitudes and opinions of the contemporaneous Europeans themselves relative to the Americans and their work. This would require delving into their writings, both published and unpublished.

Moreover, even Batterson seems to realize that being on “the verge of parity with European nations” (p. 197) cannot be pinpointed as sharply as 1913. In the passage quoted above, he notes that Jackson’s work “had just opened up” a new field, and he acknowledges that the advances in algebraic topology spurred by the work of Veblen and Alexander “took place over the following decades.” Indeed, attitudes do not tend to change overnight, and it would arguably not be until the 1930s, that is, closer to World War II than to 1913, that nearer “parity” with Europe would be attained. It was, after all, in the 1930s that refugees from Nazism found and settled into an American mathematical community that, the teaching of undergraduates aside, they found little different in quality and vibrancy from what they had left behind in Europe.

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Karen Hunger Parshall is Commonwealth Professor of History and Mathematics at the University of Virginia. Her research focuses on the 19th and 20th centuries and explores both the technical developments of algebra — the theory of algebras, group theory, algebraic invariant theory — and more thematic issues such as the development of national mathematical research communities (specifically in the United States and Great Britain) and the internationalization of mathematics. Her most recent books are Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century (co-authored with Victor Katz) (Princeton: Princeton University Press, 2014) and Bridging Traditions: Alchemy, Chemistry, and Paracelsian Practices in the Early Modern Era: Essays in Honor of Allen G. Debus (co-edited with Michael T. Walton and Bruce Moran) (Kirksville: Truman State University Press, 2015).