The Rockefeller Foundation was established in 1913 with a broad philanthropic mission that did not explicitly include mathematics. As the Foundation evolved in the 1920s, however, mathematics made inroads into what was becoming the modern world of foundation — and later governmental — support for scientific research. These inroads stemmed from the Foundation's International Education Board (IEB), created in 1923 with a mission both to provide fellowships for young scientists internationally and to support the infrastructure of science through capital grants for building and maintaining research institutes. As mathematicians like George David Birkhoff and Oswald Veblen came increasingly to advise IEB officials, mathematics began to benefit from Rockefeller philanthropy. Moreover, given the international focus of the Board, this philanthropy contributed in complex ways to the internationalization of science in general and of mathematics in particular. It is precisely this thorny historical problem of the Foundation's role in the internationalization of mathematics between the two World Wars that Reinhard Siegmund-Schultze confronts in his meticulously researched and abundantly illustrated book.

The story begins in 1923 when Wickliffe Rose, originally a professor of philosophy and history but after 1910 a Rockefeller functionary, assumed the presidency of Rockefeller's General Education Board and insisted on the simultaneous foundation of an International Education Board. His wish was granted; he became head of both new boards; and he began the process of setting the agenda for the IEB. His white paper of April 1923, "Scheme for the Promotion of Science on an International Scale," focused first and foremost on fellowships and secondarily on institutional grants, but Rose recognized that ideas on paper were one thing, the actual needs of science internationally another. To inform himself more fully of the situation in Europe and to apprise the Europeans of the new Rockefeller initiative, Rose traveled to nineteen different countries between December 1923 and April 1924, talking with scientists of note and generally observing the state of science. Among the mathematicians he consulted at Birkhoff's suggestion were Émile Borel in France, G. H. Hardy in England, Tullio Levi-Civita in Italy, and Gösta-Mittag-Leffler in Sweden; Rose also spoke with Hermann Weyl, who was then in Zürich, about the state of mathematical affairs in Germany. His discussions with these and other mathematicians helped him not only formulate an international slate of potential fellowship candidates but also determine viable places for American mathematicians to further their studies abroad.

In his ongoing efforts to assess the international scientific scene, moreover, Rose continued to consult with specialists in the various fields. In mathematics those consultants were men like E. H. Moore at the University of Chicago and his two students, Veblen at Princeton and Birkhoff at Harvard. Rose asked them, among other things, to identify the leaders in the field internationally. From these lists submitted early in 1926, the IEB drafted a map of the "Relative Standing of Mathematical Centers of Europe and Numbers of Outstanding Men at Each," which showed Göttingen, Paris, and Rome of roughly equal strength [p. 44]. When Birkhoff toured Europe from February through September 1926 as a "traveling professor" funded by and reporting to the IEB, he submitted a somewhat different assessment: the top countries in mathematics internationally were, first, Germany, followed by the United States, France, Italy, and England, while the most important mathematical center was Paris followed by Rome and Göttingen. As Siegmund-Schultze remarks, "Birkhoff's report of September 1926 on his trip, as well as his assessments of European mathematics as of the mid-twenties reveal the growing independence and self-confidence of American mathematics" [p. 56]. The report — in addition to over a dozen revealing and previously unpublished archives — is reproduced in full in one of the book's seventeen appendices.

After setting the stage in Chapter 2 with the early history of the IEB and with an account of the involvement of mathematicians in setting its agenda, Siegmund-Schultze moves on to look more closely in Chapter 3 at the "General Ideological and Political Positions Underlying the IEB's Activities." A key Rockefeller operative in shaping these positions was the physicist, Augustus Trowbridge, the head of the IEB office in Paris that oversaw the IEB's activities in Europe. Trowbridge conceived of Europe in terms of scientifically advanced and scientifically backward countries and often found the IEB caught between the objectives of supporting the best science and helping the scientifically backward. Moreover, Trowbridge and other IEB officials also saw their mission as one of spreading, through their fellowship program, American values like energy, hard work, the equal treatment of workers, and the decentralization of science at the same time that they implemented new policies like the concept of matching funds. This sociological component of foundation support, Siegmund-Schultze argues, was one of several factors contributing to the internationalization — or perhaps to the Americanization — of mathematics between the wars.

Up to this point, the narrative focuses primarily on the Rockefeller institutions, their development and philosophy. In Chapter 4, the book's longest and most archivally driven chapter, the emphasis shifts to the people who actually held the fellowships. Through a painstaking reading of fellowship files, Siegmund-Schultze teases out the largely unwritten practice of the Rockefeller philanthropies in their support for mathematics. What were the selection criteria for choosing fellows? How did (or did) they differ for applicants from different countries? Were applicants from certain countries favored over applicants from other countries and, if so, why? What, if any, strings came attached to Rockefeller support? What, if any, mathematical areas or styles of mathematical research were favored in the selection process? How did (or did) the granting of Rockefeller fellowships in particular fields shape mathematics from a technical, cognitive point of view? How did (or did) their trips abroad affect the fellows' subsequent careers? What sorts of attitudes did the fellows encounter during their fellowship periods? What were the particular challenges faced by women fellows? These and other questions are explored in this rich but somewhat fragmented chapter, a chapter that might have benefitted from a more fully developed, more synthetic conclusion.

Although they formed the major focus of the IEB's activities, fellowships were not the only type of foundation funding. Chapter 5 looks closely at Rockefeller involvement in the late 1920s both in the building of the Mathematics Institute in Göttingen and in the construction of the Institut Henri Poincaré in Paris. These two projects were undertaken with different objectives in mind. In contributing to the institute in Germany, the IEB aimed to maintain (especially in the aftermath of World War I) the high mathematical standards that had been achieved there by the turn of the twentieth century, while it supported the Paris institute project in an effort to bring French mathematics into what was becoming the international mainstream.

Both of these institute projects reached completion just a few years prior to the seizure of power by the Nazis in Germany in 1933. The radically altered political situation in Europe reflected itself in waves of emigrés seeking asylum elsewhere. In his sixth and final chapter, Siegmund-Schultze examines the impact on mathematics of the Rockefeller Foundation's Emergency Program for placing displaced scholars. Much has been written on the topic of scientific and mathematical refugees, but Siegmund-Schultze keeps his focus on the Foundation, its attitudes, its policies, and its cooperation with the American mathematical community and leaders like Veblen and Roland G. D. Richardson. In particular, he uses the cases of the German statistician, Emil Gumbel, and of the French mathematician, André Weil, to explore some of the conflicting attitudes within the Rockefeller Foundation and within American society at large toward Jews and political dissenters.

The book closes with a mere three-page "Epilogue" that could rather have been a true concluding chapter to a book that raises so many fascinating and complex issues. Still, Siegmund-Schultze has provided us with a wealth of data, a bounty of archival material, and much to think about as we continue to grapple with the social history of mathematics in the twentieth century.

Karen Hunger Parshall is Professor of History and Mathematics at the University of Virginia. Together with Adrian C. Rice, she has recently coedited the book, Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945 (Providence: American Mathematical Society and London: London Mathematical Society, 2002).