The New Era in American Mathematics, 1920–1950

Karen Hunger Parshall

• Publisher: Princeton University Press
• Year: 2022
• ISBN:
  9780691233819
• Topic: Mathematics
• Subtopic: History & Philosophy of Mathematics
• Index: Mathematics

A meticulously researched history on the development of American mathematics in the three decades following World War I As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States.Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline.Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field.

PART I

1920–1929: “We are evidently on the verge of important steps forward.”

—Roland Richardson, undated but early 1926

1

Surveying the 1920s Research Landscape

In December 1918, Edward Van Vleck was “crazy to get back into real scientific work.”¹ The University of Wisconsin mathematician had turned fifty-four just months after the United States had entered World War I in 1917 and had engaged in the war effort as an instructor for the Student Army Training Corps (SATC) on his home campus in Madison. With his usual nine hours of teaching a week augmented by two additional four-hour classes of freshman algebra targeted at SATC students, his “war work,” not surprisingly, had “absorbed all of [his] spare time and energy.” He had been completely diverted from the research in analysis that he had been faithfully pursuing since his days in Göttingen as a doctoral student of Felix Klein.²

Van Vleck was, in some sense, a member of the “first generation” of research mathematicians in the United States.³ Although he had done graduate work at the Johns Hopkins University before earning his Göttingen degree, he, like many other American mathematical aspirants born in the 1860s, had recognized that the kind of training he sought was largely unavailable in the United States in the early 1890s. He thus went abroad and returned with a personal mathematical research agenda as well as a dual sense of his academic mission. He was a teacher of undergraduate as well as graduate students, but he was also an active researcher. After 1904 and thanks to its then president, the geologist Charles Van Hise, the University of Wisconsin to which Van Vleck had moved in 1906 was also coming to share this ethos. It was one of the state universities that had begun to respond to changes in American higher education under way at least since 1876 with the founding of Hopkins in Baltimore. In fits and starts, other institutions followed suit into the opening decades of the twentieth century.

In many ways, World War I had served as a wake-up call to those in academe but, perhaps more importantly, to others in newly created philanthropies as well as to some within the Federal government. They had begun to recognize the value of original research for the welfare of the nation; they increasingly saw the need to support research financially. Savvy university administrators witnessed and steadily responded to this trend over the course of the 1920s and 1930s. They followed the money. Maybe the philanthropies were on to something. Maybe research should be more vigorously encouraged within the universities. Maybe faculties should be formed and sustained on the basis of research productivity and graduate training, first, and undergraduate teaching, second.

The war had also served as a break in business as usual. In its aftermath, there was a sense within the scientific community more broadly, but within the mathematical community, in particular, of entering into “a new era in the development of our science.”⁴ “Every nerve should be strained to get our research back on its feet,” in Roland Richardson’s view.⁵ He was apparently not alone in this conviction. He and other American mathematicians poured themselves into their work in the 1920s, but what did that mean? What were their main research interests? Where were those interests fostered? What, in short, was the lay of the American mathematical research landscape in the 1920s?

FIGURE 1.1. Oswald Veblen (1880–1960) (ca. 1915). (Photo from Wikimedia Commons.)

Mathematicians in Colleges and Universities

“Mathematical research is done almost entirely by university and college teachers,” Princeton’s Oswald Veblen patiently explained in 1924 to Vernon Kellogg, an entomologist and the permanent secretary of the National Research Council (NRC).⁶ Yet, he continued, “[a] mathematics department in an American university has to deal with an enormous mass of freshmen, a very large number of sophomores, and with extremely small numbers of juniors, seniors and graduate students.” Veblen was certainly in a position to know.

His father had been a professor of mathematics and physics at the University of Iowa, where the young Veblen had pursued his undergraduate studies. After a year at Harvard to earn a second B.A.—and presumably to supplement the more limited offerings that had been available to him in Iowa City—he proceeded to the University of Chicago in 1900, where his uncle, the iconoclastic economist and sociologist, Thorstein Veblen, happened then to be on the faculty.⁷ As a graduate student, Veblen imbued an ethos of research, research, research under his doctoral advisor E. H. Moore. His 1903 Ph.D. was followed by two years at Chicago as an associate in mathematics and, in 1905, by a preceptorship at Princeton.⁸ All the while, he churned out new results in what was then his main field, geometry. Veblen had thus experienced firsthand American higher mathematics education at levels from the so-so to the very best and had fully embodied the teacher-researcher mindset.

Moreover, from his highly privileged position as President of the American Mathematical Society from January 1923 through December 1924, he had become “rather acutely conscious of the fact that the needs of mathematical research have not yet been brought to the attention of those,” like Kellogg, “whose position enables them to have a view of the strategy of Science.”⁹ But if Veblen laid blame for this state of affairs, it was at the feet of the mathematicians themselves, for they “have too easily assumed that an outside world which cannot understand the details of their work is not interested in its success.” In 1924, having embraced the role of mathematical leader in the research as well as in the political sense, Veblen had many reasons to reject that assumption (see the next chapter), but he also appreciated the need clearly to articulate how mathematicians, as distinct from other types of scientists, fit into the modern college and university.

Since the beginnings of higher education in the United States, mathematics had been a key, required component of the undergraduate, liberal arts curriculum.¹⁰ By the 1920s, however, America’s universities—as opposed to its four-year colleges—had produced a cadre of college and university professors who were trained to do original research but who were hired largely to teach undergraduates. They populated a wide array of institutions.

The colonial colleges—Harvard, Yale, Princeton, Columbia, Pennsylvania, Brown, and others—had, over the course of the final quarter of the nineteenth century and into the opening decades of the twentieth, begun to reorient themselves toward undergraduate and graduate instruction. Owing to their relatively long histories and to their traditionally collegiate focus, some of these schools experienced more difficulty than others in redefining themselves as actual universities in which faculties were expected actively to engage in research and publication. The same was true of some of the state-supported schools—like the Universities of Michigan, Iowa, Wisconsin, Kansas, Texas, and California at Los Angeles. After the 1862 Morrill Act provided funding for them, moreover, the Federal land-grant universities—such as the University of California in Berkeley, the University of Illinois, the Massachusetts Institute of Technology (MIT), and the Ohio State University—realized their more practical orientation at both the undergraduate and graduate levels. These types of schools were supplemented, in the so-called Gilded Age that followed the U.S. Civil War, by privately endowed women’s colleges—especially Pennsylvania’s Bryn Mawr—and other institutions—such as Hopkins, Clark University, and the University of Chicago—that set new standards particularly for graduate education and the production of original research.¹¹ Faculty members at both colleges and universities were coming to define themselves in terms of teaching and research.

For American mathematicians, this dual personality was both like and unlike that of their European counterparts. American and European mathematicians strove to do research and to publish the fruits of their labors, but in Europe—and especially in Germany and France where a system of Gymnasien and lycées, respectively, provided instruction at the freshman and sophomore levels—mathematicians were not involved in more introductory teaching.¹² Yet, in the United States, as Veblen explained to Kellogg, “[a] man with good mathematical gifts and normal personal qualities has little trouble in obtaining as good a position as is available under our system,” “[b]ut when he obtains it he has a teaching schedule of from nine to fifteen hours a week as compared with three hours a week for his colleague in the Collège de France.”¹³ “Moreover,” Veblen went on, “he becomes tremendously interested in this teaching; he sees the manifold ways in which it could be improved, and he plays his part in the committees and other administrative devices which are trying to do the obvious tasks of the university in a better way.” The American mathematician was thus able to spend only a relatively “small fraction” of time on research, given that a certain “sense of res...