Wonders beyond numbers: A brief history of all things mathematical, by Johnny Ball

Abstract

reorienting toward research, while EliakimHastings Moore built an active department at Chicago, which was research-driven from the start. Batterson’s fourth and fifth chapters describe Osgood’s, Bôcher’s and Moore’s efforts to conduct and promote mathematical research in the USA, including the important role all three (especially Moore) played in the growth of the American Mathematical Society and the training of the next generation of Americanmathematical researchers. The remaining two chapters follow the development of the mathematics department at Princeton University in the first decade of the twentieth century, as well as the movement and accomplishments of George David Birkhoff and other freshly minted American mathematical researchers. The text’s institutional focus accounts for its emphasis on university presidents, especially Charles William Eliot at Harvard and Daniel Coit Gilman at Hopkins, but also William Rainey Harper at Chicago and Thomas Woodrow Wilson at Princeton. In Batterson’s discussion of the institutional landscape crafted by these men are glimpses of cultural considerations as well, both in terms of the broader cultural landscape of the Progressive Era United States and the more local cultures of mathematics departments themselves. The former is hinted at, for example, in Batterson’s mention of the public backlash in response to Gilman’s prioritization of advanced research and graduate education at Hopkins. And the latter is suggested by Batterson’s description of the ‘magic’ of Klein’s lectures at Göttingen (p 8) and the ‘magical environment’ created by Moore, Bolza, and Maschke at Chicago (p 169). Batterson’s book is smoothly written and well researched, drawing from over a dozen archival collections at almost a dozen different institutions. Included are appendices that show the 1849–50 Yale course catalogue as well as the 1905–06 list of graduate mathematics courses at Harvard and Chicago. Along with a handful of expository descriptions of important mathematical results, readers will find awell-crafted account of departments, careers, training and administration during a crucial period in American mathematics.