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Bôcher, Osgood, and the Ascendance of American Mathematics at Harvard Steve Batterson

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Bôcher, Osgood, and the Ascendance of American Mathematics at Harvard Steve Batterson Bôcher, Osgood, and the Ascendance of American Mathematics at Harvard Steve Batterson he year 1888 is notable to members Bôcher, W. F. Osgood, Leonard Dickson, and G. D. of the American Mathematical Society Birkhoff were internationally respected mathema- (AMS) for the founding of their organi- ticians. Graduate programs at Chicago, Harvard, zation under the name The New York and Princeton offered European-level training TMathematical Society. In this same year that had been unavailable in the United States Maxime Bôcher received his A.B. in mathematics when Bôcher completed his undergraduate stud- from Harvard. The university also awarded Bôcher ies a quarter century earlier. The advancement on a fellowship that enabled him to travel to Göttin- American campuses began in the early 1890s. gen for graduate study. At the time, knowledge- Most significant was the opening of the Univer- able American mathematics students with means sity of Chicago in 1892. Under the leadership of went to Germany to pursue a Ph.D. Opportuni- E. H. Moore, Chicago recruited European emigrés ties for course work and thesis direction in the to implement a high-level mathematics curriculum United States were vastly inferior. The country’s [2]. A steady stream of talented American students only significant mathematical scholars were the thrived in the scholarly environment. Moore’s Ph.D. nonacademically employed George William Hill, students Dickson (1896), Oswald Veblen (1903), the part-time professor Simon Newcomb, and and Birkhoff (1907) would each go on to deliver the reclusive scientist J. Willard Gibbs. Over the plenary addresses to the International Congress 1890–1894 interval just two American universities of Mathematicians. would confer more than two mathematics Ph.D.’s Compare the Chicago ascendance with contem- [1], and neither of these programs was on a favor- poraneous developments at Harvard [4], [5], [2]. able trajectory. Johns Hopkins was in a decline After obtaining their Ph.D.’s in Germany, Osgood that had begun with the recent departure of J. J. and Bôcher became Harvard instructors in 1890 Sylvester. Clark University, after a promising first and 1891 respectively. None of their departmental three years, underwent devastating turmoil and colleagues were engaged in mathematical research. lost many of its best staff [2], [3]. Together Bôcher and Osgood steadily changed the Yet by 1913 the American mathematical brand culture, publishing their scholarly work and invigo- was appreciated in Europe. E. H. Moore, Maxime rating the graduate program. Birkhoff joined the Harvard faculty in 1912 and then discovered his Steve Batterson is associate professor of mathematics and famous proof of Poincaré’s Geometric Theorem. computer science at Emory University. His email address is [email protected]. With Bôcher, Osgood, and Birkhoff, Harvard was the strongest department in the United States. The author is grateful to Don Sarason and Raghavan Narasimhan for clarifying historical points and to Michele Given the 1890 state of American mathematics, Benzi and Albert Lewis for suggestions on the manuscript. the rise of Harvard was remarkable, even if over- Unpublished material is quoted courtesy of the Harvard shadowed by the more rapid advances at Chicago. University Archives; MIT Archives; Library of Congress; This article traces these developments, focusing on and Niedersächsische Staats- und Universitätsbibliothek, the vital roles of Bôcher, Osgood, and the Harvard Göttingen. traveling fellowships. 916 NOTICES OF THE AMS VOLUME 56, NUMBER 8 Mathematics at Harvard Prior to 1880 the superior continental In 1636 Harvard became the first college to be mathematics to students established in the North American British colo- in the United States. In nies. To fulfill its mission of providing the educa- 1824 Harvard juniors tional essentials to prospective Puritan ministers, began studying Farrar’s the curriculum featured Latin, Greek, Hebrew, adaptation of Bezout’s rhetoric, and philosophy. The small presence of calculus [7]. mathematics was restricted to some arithmetic The following year and geometry in the final year. During Harvard’s a brilliant sixteen-year- first century mathematics was often taught by old freshman enrolled minimally trained instructors who held the title at Harvard. Benjamin of tutor [6], [7]. Peirce had already re- The year 1727 marked the endowment of the ceived mathematical Hollis Professorship of Mathematics and Natural training from Nathaniel Philosophy. The first holder was Isaac Greenwood. Bowditch, whose son, Greenwood, being knowledgeable in Newton, sub- Ingersoll, was Peirce’s stantially elevated the Harvard faculty’s level of classmate at the Salem scientific competence. Unfortunately his tenure Grammar School. Peirce ended prematurely when he was dismissed over supplemented his Har- repeated incidents of drunkenness. Greenwood’s vard studies by assist- Maxime Bôcher. successor was his former student John Winthrop. ing Bowditch with the Serving from 1738 to 1779, Winthrop covered Laplace translation. In the broad span of mathematics and the physical addition, Peirce was an sciences. Harvard historian Samuel Morison char- avid reader of The Math- acterized Winthrop as “the first important scien- ematical Diary, solving tist or productive scholar in the teaching staff of problems posed in this Harvard College” [6, page 92]. Winthrop took the early American journal then-novel initiative of setting up an experimental [8]. physics laboratory. His lectures included the topic Peirce completed his of electricity. Winthrop’s astronomical observa- A.B. in 1829. Despite tions of the solar system earned him membership his ample mathematical in the Royal Society. gifts, Peirce’s opportu- When the nineteenth century began, no Ameri- nities for further study can professors were doing mathematical research. were severely limited; At both Harvard and Yale, scholarship in the Ph.D. programs did not subject meant the production of textbooks. By then exist in the United this time mathematics was front loaded into the States. Over the prior Harvard curriculum. Tutors handled arithmetic decade several Harvard and geometry in the freshman year. Subsequent students had returned to topics included algebra, logarithms, trigonometry, campus from advanced surveying, and spherical geometry. work at Göttingen and W. F. Osgood. In 1806 the Hollis chair was offered to Nathaniel other European institu- Bowditch, the author of an important handbook tions [6]. Their presence offered evidence and on navigation. Possessing only a rudimentary for- testimony to the benefits of study abroad. Yet mal education, the self-taught Bowditch was an Peirce remained in Massachusetts to teach at a interesting choice. Following a maritime career, prep school. His biographer speculates that recent he had entered the insurance business, all the family financial reversals forced Peirce to forgo time studying mathematics on his own. Bowditch European study and begin earning an income [8, turned down the professorship but became an page 52]. influential member of the Harvard Corporation, Peirce taught at the prep school for just two which governed the university. Meanwhile, he took years. Then a mathematics tutorship opened up on the ambitious project of translating and elu- for him when Farrar’s health began to fail. The cidating Laplace’s multivolume work on celestial 1831 Harvard appointment of Peirce was the be- mechanics. Its successful completion was arguably ginning of an historic tenure for American science. the most impressive American mathematical ac- Within months he submitted an original theorem complishment up to that time. for publication in The Mathematical Diary. It was In place of Bowditch, the Hollis chair was filled known that if 2n +1 − 1 is prime, then (2n +1 − 1)2n by John Farrar. Farrar was a charismatic lecturer. is perfect. Peirce proved that if a perfect number His contribution to American mathematics was M does not have the above form, then M must to translate French textbooks and introduce have at least four distinct prime factors [9]. Later, SEPTEMBER 2009 NOTICES OF THE AMS 917 a posthumously published paper of Euler showed scholarly prominence placed the Lazzaroni in a po- that any even perfect number has the form stipu- sition to promote national science initiatives. Out lated above. Thus Peirce’s result established that of their efforts came the creation of the American any odd perfect number has at least four distinct Association for the Advancement of Science and prime factors. the National Academy of Sciences. It is unclear whether the Harvard administration Peirce himself continued to do research in had any appreciation for this worthy demonstra- astronomy and mathematics. His astronomical tion of mathematical scholarship. Shortly after- work gained him admission to the Royal Society. ward, however, President Josiah Quincy steered However, Peirce’s magnum opus, Linear Associa- Peirce in a more traditional direction, the writing tive Algebra, was in mathematics. Along the way of textbooks. Peirce sought a clarification of pri- he held key positions with two important govern- orities. He asked whether the Harvard Corpora- ment scientific agencies, The Coast Survey and The tion wanted him to “undertake a Nautical Almanac. task that must engross so much Peirce remained at Harvard until his death in time and is so elementary in its 1880. As a teacher Peirce was generally depicted as nature and so unworthy of one incomprehensible to ordinary
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