An Outline of the History of Mathematics in the U

The Hilbert American Colony This file provides more biographical details on the Hilbert American colony than are given in the Transition_1900 section. Table 1 lists the 13 American students who earned doctorates under the direction of David Hilbert at Göttingen, in chronological order. Only one finished before the turn of the 20th century. One of the next two was Hilbert’s first female student. Rather than describing the lives and careers of the remaining eleven members of Hilbert’s American colony in chronological order, they appear according to their rankings published in the first three editions of American Men of Science (AMoS), which appeared in 1906, 1910 and 1921. In each of the three lists, scientists regarded as the most eminent in their field were asked to rank others in the field, with the top 1000 awarded stars beside their name. Eighty mathematicians were starred, and the numbers in the AMoS column in Table 1 designate the edition in which they were listed (if at all): 1 for 1906, 2 for 1910, and 3 for 1921. Name Year AMoS Legh Wilber Reid 1899 Anne Lucy Bosworth 1900 Edgar Jerome Townsend 1900 3 Earle Raymond Hedrick 1901 1, 2, 3 Charles Albert Noble 1901 Oliver Dimon Kellogg 1902 2, 3 Charles Max Mason 1903 2, 3 Wilhelmus David Westfall 1905 David Clinton Gillespie 1906 William DeWeese Cairns 1907 Arthur Robert Crathorne 1907 Charles Haseman 1907 Wallie Hurwitz 1910 3 Table 1: Hilbert’s American student Legh Wilber Reid (1867-1961) was the only American to complete requirements for a doctorate before 1900. For inexplicable reasons—perhaps due to an unusual first name that does not automatically suggest an American—he is sometimes omitted from listings of Hilbert’s students, but the authoritative biography Hilbert by the late Constance Reid (1918-2010; no relation to Legh) asserts rather plainly, “When Legh Reid, one of his former American students, wrote a book on the subject, Hilbert endorsed it with enthusiasm.”1 Indeed, Reid is an authentic American (born in Alexandria, VA) who obtained a doctorate under Hilbert in 1899. Earlier he had received two bachelor’s degrees, one from Virginia Military Institute in 1887 and another from Johns Hopkins University two years later. He worked 1889-1893 as a human computer for the U.S. Bureau of the Census and the U. S. Coast and Geodetic Survey. Reid was appointed instructor at Princeton University in 1893, a position that allowed him to take graduate courses. He obtained a master’s degree from Princeton in 1896 and then sailed abroad to study in Göttingen. Recall that Princeton faculty members Henry Fine and Henry Thompson had obtained their doctorates under Felix Klein at Leipzig Göttingen in 1885 and 1892, respectively. Reid, however, did his doctoral work under David Hilbert, obtaining his doctorate in 1899 for the dissertation “Tafel der Klassenanzahlen für kubische Zahlkörper.” He published that work in English in 1901 in the American Journal as “A table of class numbers for cubic number fields.” Its major results lean heavily on a technical lemma due to Hilbert’s close friend and later colleague, Hermann Minkowski. Legh Reid spent the rest of his career at Haverford College (all-male until 1980), from his appointment as instructor in 1900 to his retirement as professor emeritus in 1934. His major contribution to mathematics was his book The Elements of the Theory of Algebraic Numbers, published by Macmillan Company in 1910 and containing an introduction by David Hilbert. According to a faculty memorial written about Reid upon his death at age 93, the book “is still used in graduate schools throughout the country although it was published fifty-one years ago.”2 Reid exerted a considerable influence on Haverford students in academics (maintaining the Phi Beta Kappa chapter during his tenure) and athletics (in 1925 he established the Virginia Tennis Cup that was described as “a decided stimulus to tennis interest”3 at the college). Until quite recently, Anne Lucy Bosworth Focke (1868-1907) was a complete stranger. Her omission from most sources on women in American mathematics is somewhat surprising since she was known to be one of Hilbert’s students, but nothing else was known about her family or professional life. The breakthrough occurred only in 2005 when Sarina Wyant, an archivist at the University of Rhode Island (URI), asked a graduate student to search archival material on Bosworth at URI to satisfy a genealogical request. The portrait that follows has been pieced together from that material as well as additional searches. Anne Lucy Bosworth was born in Woonsocket, RI, most likely in 1868. She entered Wellesley College in 1886 and graduated four years later with a B.S. degree. Two other members of that class, Grace Andrews and Clara Bacon, would also earn Ph.D.s in mathematics at Columbia (in 1901) and at Johns Hopkins (1911), respectively. Anne Bosworth then taught in high school for two years. In 1892 she was appointed the first professor of mathematics and physics at the fledgling Rhode Island College of Agriculture and Mechanic Arts (now URI), which had been founded in 1888 under a different name four years earlier with funds from the Morrill Act. Because Bosworth was the sole member of the department and the college offered postsecondary-level courses for the first time, her duties were quite broad, requiring her to develop the curriculum, initiate a book collection, and teach courses in algebra, geometry, calculus, and various physics offerings, including one on electricity, which she called “this still mysterious force.” Bosworth was one of the many college teachers who attended courses during summer quarters at the University of Chicago, enrolling in 1894, 1896, and 1897. In April 1898, she was granted a leave of absence from URI to study abroad. The student yearbook from 1898, The Grist, was dedicated to her and records the students’ warm affection: “To Miss Bosworth, our professor and classmate, we, who honor her ability and value her friendship, respectfully dedicate this volume.” One year later their beloved professor returned home with a doctorate from one of the world’s leading figures. The genesis of the awarding of this degree is rather curious because Bosworth was caught completely unaware. After all, her only intention in going abroad was to attend courses at Göttingen, not to seek a degree. So, in the summer of 1898 she attended a series of lectures on mechanics by Felix Klein in a class that included two Bryn Mawr graduates who had spent the previous year in Göttingen. In the fall, she took courses from Arthur Schoenflies, Issai Schur, and Woldemar Voigt. But it was David Hilbert’s lectures on Euclidean geometry that turned out to be critical. In the spring of 1899 he summoned her to tea and asked when she planned to take her doctoral exams. She replied that she had not even given thought to a dissertation topic and therefore had no such intention. In characteristic Hilbert manner, he blurted out, “But your dissertation is finished!” Apparently, Hilbert judged her solution to a special exercise he had posed in the class to be worthy of a thesis. So much for her plans to travel throughout Europe that summer—instead she devoted her time to writing the dissertation. She took her oral exam that July, a little over one year after arriving in Göttingen. When the degree was formally awarded in 1900 Anne Bosworth became David Hilbert’s first female doctoral student based on the dissertation “Begründung einer vom Parallelenaziome unabhängigen Streckenrechnung.” George Halsted described the thesis as “a beautiful piece of non-Euclidean geometry [that] is, so far as I know, the first feminine contribution to our fascinating subject.”4 We do not know who advised Bosworth to make such a plucky move abroad. We wonder, for instance, if the success of Mary Winston, Isabel Maddison, or Annie MacKinnon with Felix Klein played a role. But we do know that Bosworth joined the AMS in February 1900, the year after she returned from Germany, where she had been escorted by her mother the whole time. More importantly, she had probably met Theodore Moses Focke (1871-1949) on the initial leg of her sojourn to Göttingen. Focke had been a tutor in physics and chemistry at Oberlin College 1893-1896 before traveling abroad to pursue a graduate degree in physics at Göttingen. He received his doctorate in 1898 for a dissertation on the thermal conductivity of various kinds of glass. However, instead of heading back to the U.S. right away, he joined two friends on a 2000- mile bike ride to the Mediterranean coast and back, climbing the Alps on the return trip. Focke and Bosworth most likely met during the time between his return to Göttingen and his departure for the position he had accepted as instructor in mathematics at the Case School of Applied Science in Cleveland (now Case-Western Reserve University). Meanwhile, Bosworth had returned to URI in the fall of 1899. However, she left the college after her marriage to Focke in August 1901. When her resignation became official the next year the school’s president wrote, “It is with regret that the institution loses Miss Bosworth from the faculty. Her conscientious work has been, from the beginning, highly appreciated by every member of the institution.”5 The first six years of marriage reflected the culture of the time and were very productive for both newlyweds, though in quite different ways. Theodore Focke was promoted to assistant professor in 1902, when their first child, Helen, was born. Two sons, Arthur Eldridge Focke and Alfred Bosworth Focke followed in arithmetic progression, in 1904 and 1906, and both would be successful, AE as a metallurgist and AB as a physicist.

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