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Bôcher, Osgood, and the
Ascendance of American
Mathematics at Harvard
Steve Batterson
The year 1888 is notable to members of the American Mathematical Society (AMS) for the founding of their organization under the name The New York Mathematical Society. In this same year Maxime Bôcher received his A.B. in mathematics from Harvard. The university also awarded Bôcher a fellowship that enabledhim to travel to Göttingen for graduate study. At the time, knowledgeable American mathematics students with means went to Germany to pursue a Ph.D. Opportunities for course work and thesis direction in the United States were vastly inferior. The country’s only significant mathematical scholars were the nonacademically employed George William Hill, the part-time professor Simon Newcomb, and thereclusive scientist J. Willard Gibbs. Over the 1890–1894 interval just two American universities would confer more than two mathematics Ph.D.’s [1], and neither of these programs was on a favorable trajectory. Johns Hopkins was in a decline that had begun with the recent departure of J. J. Sylvester. Clark University, after a promising first three years, underwent devastating turmoil and lost manyof its best staff [2], [3].
Yet by 1913 the American mathematical brand was appreciated in Europe. E. H. Moore, Maxime Bôcher, W. F. Osgood, Leonard Dickson, and G. D. Birkhoff were internationally respected mathematicians. Graduate programs at Chicago, Harvard, and Princeton offered European-level training that had been unavailable in the United States when Bôcher completed his undergraduatestudies a quarter century earlier. The advancement on American campuses began in the early 1890s.
Steve Batterson is associate professor of mathematics and computer science at Emory University. His email address is sb@mathcs.emory.edu.
Most significant was the opening of the University of Chicago in 1892. Under the leadership of E. H. Moore, Chicago recruited European emigrés to implement ahigh-level mathematics curriculum [2]. A steady stream of talented American students thrived in the scholarly environment. Moore’s Ph.D. students Dickson (1896), Oswald Veblen (1903), and Birkhoff (1907) would each go on to deliver plenary addresses to the International Congress of Mathematicians.
Compare the Chicago ascendance with contemporaneous developments at Harvard [4], [5], [2]. After obtainingtheir Ph.D.’s in Germany, Osgood and Bôcher became Harvard instructors in 1890 and 1891 respectively. None of their departmental colleagues were engaged in mathematical research. Together Bôcher and Osgood steadily changed the culture, publishing their scholarly work and invigorating the graduate program. Birkhoff joined the Harvard faculty in 1912 and then discovered his famous proof ofPoincaré’s Geometric Theorem. With Bôcher, Osgood, and Birkhoff, Harvard was the strongest department in the United States. Given the 1890 state of American mathematics, the rise of Harvard was remarkable, even if overshadowed by the more rapid advances at Chicago. This article traces these developments, focusing on the vital roles of Bôcher, Osgood, and the Harvard traveling fellowships.
Mathematics atHarvard Prior to 1880
In 1636 Harvard became the first college to be established in the North American British colonies.
To fulfill its mission of providing the educational essentials to prospective Puritan ministers, the curriculum featured Latin, Greek, Hebrew, rhetoric, and philosophy. The small presence of mathematics was restricted to some arithmetic and geometry in the final year. DuringHarvard’s first century mathematics was often taught by minimally trained instructors who held the title of tutor [6], [7].
The year 1727 marked the endowment of the Hollis Professorship of Mathematics and Natural Philosophy. The first holder was Isaac Greenwood. Greenwood, being knowledgeable in Newton, substantially elevated the Harvard faculty’s level of scientific competence. Unfortunately...
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