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Home , Earle Raymond Hedrick, Isabel Maddison, Oliver Dimon Kellogg

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 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 1901 1, 2, 3 Charles Albert Noble 1901 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 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 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 (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. But tragedy struck in 1907 when Anne Bosworth Focke came down with pneumonia and died at age 38, leaving behind children aged five, three, and one. She never did revise her dissertation for publication in the U.S. Theodore Focke himself was promoted to full professor the next year, and appointed Kerr Professor of mathematics and head of the department. Ten years later, in 1918, he became Case’s first dean, serving in that position as well as chair of the department until his retirement in 1944. Why has Anne Bosworth remained unknown to historians of mathematics? After all, being the first female doctoral student of someone as internationally recognized as David Hilbert is a major accomplishment in any time period, let alone one in which women were prevented from

enrolling in most graduate programs. When searching for biographical material on scientists from this era, a generally reliable volume is American Men of Science, which first appeared in 1906. But it contains no entry under “Bosworth,” and not just because of the second word in the title of this volume. Indeed, she can be found there. At that time, an entry for a married woman was subsumed under the last name of her husband, hence a later listing in the volume reads, “Focke, Mrs. Theo. M. (Anne Bosworth).” This might explain why she is missing from all histories of women mathematicians up to the groundbreaking book by Judy Green and Jeanne LaDuke in 2009, whose genealogical inquiry sparked the Rhode Island archival search. The remainder of this file describes the lives and careers of the remaining eleven members of the Hilbert colony according to rankings published in the first three volumes of American Men of Science. Five of Hilbert’s dozen American students were starred in the first three volumes, with Earle Raymond Hedrick (1876-1943) the only one listed in all three. Born in Indiana, with roots reaching back to Pennsylvania settlers from the 1670s, Hedrick received his undergraduate education at Michigan, culminating with an AB degree in 1896. After teaching high school for a year in the Wisconsin town with the melodic name Sheboygan—and a serene location along Lake Michigan—he enrolled in the graduate program at Harvard, where he excelled under Maxime Bôcher and William Osgood for two years. Hedrick was then awarded a Parker Fellowship for study abroad, which he used to go directly to Göttingen to study with Felix Klein and David Hilbert. (Chapter 5 and the Transition Section to Part III provide details about these traveling fellowships, and the role they played in the development of mathematics in America. Recall that Bôcher and Osgood had both studied with Klein in Göttingen on Parker fellowships, though Osgood ended up taking his doctorate at Erlangen.) Hedrick completed his dissertation on differential equations, “Über den analytischen Charakter der Lösungen von Differentialgleichungen,” in two years. Harvard then extended his scholarship to cover a third year, which he used for additional studies in Paris with Emile Picard, Édouard Goursat, and , among others. Upon returning to the U.S. Hedrick accepted a position at the Sheffield Scientific School at Yale where, after a brief stint, he left in 1903 to become professor and head of the department of mathematics at the . He remained in this position until 1924 except for a period of service during World War I, in this case for six months as director of the mathematical educational corps with the American expeditionary force in France. During his time at Missouri,

he helped found the third section of the AMS, the Southwestern Section, in 1906 and served as chair of the organizational meeting. He also translated (with Otto Dunkel) Goursat’s famous Cours d’Analyse into English, a book that was “widely used thereafter in all college circles.”6 In 1924 Hedrick left Missouri to become professor and department head at the at Los Angeles (UCLA). Five years later he was elected to a two-year term as president of the AMS. A signal change in Hedrick’s life occurred in 1937 when he left academia for administration, becoming one of two provosts and vice-presidents for the entire University of California system. When he retired five years later at age 65, a memo from the UCLA faculty expressed appreciation for his efforts on the university’s behalf: “By performing manifold duties on the Los Angeles campus with wisdom and foresight, Dr. Hedrick exercised a great influence throughout the University and … [with] his expert analysis of complex administrative matters.”7 [Certain terms have been italicized to suggest that the anonymous author was likely a mathematician.] Like many mathematicians, Hedrick did not abandon his subject upon retirement, but returned to his earlier interest in applications of mathematics. He had published one paper on Hooke’s law and another on the transmission of heat in boilers; he was also a member of three societies for electrical and mechanical engineering. Because of this experience, Hedrick was offered the opportunity to develop the Program of Advanced Instruction and Research in Mechanics at . So, he departed the left side of the country for the right, geographically speaking, to become Visiting Professor and to help inaugurate the Quarterly of Applied Mathematics, the journal proposed to be sponsored by the Program. However, Hedrick became ill shortly after arriving in Providence and died a few months later, in February 1943, the year the Quarterly was launched. His editorial work had been extraordinary; he was editor of the Monthly 1913-1915, Editor-in-Chief of the Bulletin 1921-1937 (Volume 44 (1938) was dedicated to him), editor for 34 volumes of the Engineering Record, and editor for 35 volumes in the Series of Mathematical Texts. Closely aligned with Earle Hedrick at the beginning of their careers is Oliver Dimon Kellogg (1878-1932), who was strongly influenced to study mathematics while an undergraduate at Princeton by Henry Fine from the time he entered the university as a freshman in 1895. Recall that Fine was the only person ever to write a doctoral dissertation in English under Felix Klein (or, in fact, in any language other than German). Apparently, Fine’s lectures stoked mathematical flames in Kellogg so strongly that upon his 1899 graduation he remained on

campus another year to get a master’s degree. That background was sufficient for a successful program at Göttingen under the direction of David Hilbert, with funds supplied by a John S. Kennedy Fellowship. Kellogg received his doctorate in January 1903 for a dissertation on integral equations and the very difficult Dirichlet Problem, which he solved for a particular case, but by the time the degree was officially awarded he had already returned to Princeton as an instructor. Over the next few years he published two papers that pointed out, and then corrected, flaws that he had found in his dissertation, “Zur Theorie der Integralgleichungen und des Dirichlet’schen Prinzips.” Oliver Kellogg was recruited to the University of Missouri in 1905 by the aforementioned Earle Hedrick. It is unknown why Kellogg departed Princeton at that time because Dean Henry Fine had just begun the historic upgrading of the Princeton faculty with the addition of preceptors that in mathematics included and Gilbert Bliss. In fact, Kellogg and Bliss essentially traded places. Certainly, Kellogg prospered despite heavy teaching loads and administrative duties in what was then the Southwest region of the country, initially publishing impressive papers on potential theory, three in 1908 alone (two in the Transactions and the other in the Annals). During this time, he also wrote a series of articles on the teaching of mathematics, and then in 1909 teamed up with Hedrick to write the textbook Applications of Calculus to Mechanics. But it was his 1912 Transactions paper “Harmonic functions and Green’s integral,” that brought him acclaim for what is called today the “Kellogg Theorem” on harmonic and Green’s functions. Like many mathematicians of his generation, Kellogg’s career was disrupted by war service when he was assigned to work on the design of devices to detect submarines for the U.S. Coast Guard Academy one year after Maxime Bôcher died suddenly just before the start of the 1918- 1919 academic year. At the end of that first year, Kellogg was appointed to a permanent position at Harvard with the rank of associate professor, and was promoted to full professor seven years later, in 1927. During that time Kellogg produced his only doctoral student, Arthur H. Copeland, whose dissertation “Studies on the gyroscope” was submitted in 1926. Copeland then spent a distinguished career at the . Just three years earlier, Kellogg published a related paper in the Transactions on this very topic, studying the gyroscope as an application of properties of spherical curves. Perhaps Kellogg’s most important mathematical achievement, however, was the joint paper “Invariant points in function space” he published in 1922 with George Birkhoff containing the

celebrated Birkhoff-Kellogg Theorem, which is a generalization of the famous Brouwer Fixed Point Theorem. Clearly Birkhoff and Kellogg were working at a level unprecedented in the U.S. up to that time. Kellogg’s name has come down to us today in another hyphenated result, the Kellogg-Evans Lemma, which he proved and included for the first time in his classic 1929 text, Foundations of Potential Theory. A recent analysis of this book concluded, 8 Accessible to both advanced undergraduates and beginning graduate students, it was noteworthy for its rigour and felicitous style. While not specifically mentioned, many of the proofs in the volume—even of well-known results—are original and due to Kellogg, himself. Four years later Griffith C. Evans, the driving force behind the elevation of the University of California at Berkeley to the highest level of research mathematics, proved the lemma in greater generality, hence the hyphenated form of its name. At the time of Kellogg’s death in 1932 he was working on an advanced volume to supplement his already famous 1929 book. Overall, Earle Hedrick and Oliver Kellogg are known for different types of contributions. For Hedrick, it was administrative leadership, especially at UCLA but also with the AMS and MAA, as well as editorial positions with journals in both organizations. For Kellogg, however, it was research, either with published papers in the most important American journals of the day or as influential books. Arguably the most accomplished American scientist in the Hilbert colony is Charles Max Mason (1877-1961), who was always called by his middle name and was not even aware that it was not his first name until he saw it on his college diploma. During the year 1898-1899 Mason taught high school, and modern historian Patti W. Hunter summed up his versatility by noting that he also “coached the track team, led the school orchestra, and trained the debating team.”9 Mason had just graduated from the University of Wisconsin after having been influenced by mathematics professor Charles Sumner Slichter to switch from engineering. While an undergraduate he not only was a champion high-jumper (hence the stint as a track coach), but he sailed, canoed, skated, and played the violin (hence the orchestral activity). But mathematics became his passion, and, after one semester of what he later referred to as “so-called graduate work”10 at Wisconsin, he went to Germany in 1900 to study with Hilbert at Göttingen even though he was seemingly ill-prepared for such study. But by dint of hard work Mason excelled and Hilbert soon gave him a problem to solve. The good news is that the aspiring mathematician solved the problem in short order; the bad news is that his elegant solution required only two pages. While the length of dissertations in mathematics might be shorter than those in most

other subjects, none is that short, so Hilbert handed Mason a second problem, one whose solution required several months of intense investigation—abetted by a productive dream one night—that led to the considerably expanded 1903 dissertation on differential equations “Randwertaufgaben bei gewöhnlichen Differentialgleichungen.” This work was so substantial and impressive that Mason graduated with highest distinction in a class that included the well- known Japanese mathematician Teiji Takagi (1875-1960). Max Mason set about an academic career as soon as he returned from Europe, teaching for one year at MIT followed by four at Yale. He was especially productive between 1904 and 1910, publishing eight papers in pure mathematics—one in the Annals in 1906 and seven in the Transactions. He spent the next 17 years, 1908-1925, at his alma mater, the University of Wisconsin, where George Birkhoff was a colleague the first year and Arnold Dresden the entire time. However, Mason’s primary interest in his first years there changed from mathematics to physics, and he never wrote another paper in pure mathematics. Nonetheless, because of his earlier work, he was invited to present a series of AMS colloquium lectures at a summer meeting held at Yale. In the preceding chapter, we saw that the first such colloquium had been held at the AMS summer meeting in Buffalo in 1896 and that the texts of the lectures from the fourth colloquium in 1903 were the first to be published. Max Mason was one of three speakers invited to deliver the fifth Colloquium at the 1906 summer meeting at Yale, along with E.H. Moore and E.J. Wilczynski. AMS historian R. C. Archibald stated that this Colloquium11 set a high standard of excellence. Through the kind offices of Prof. Pierpont, Yale U. assumed the responsibility for the publication of these lectures. The fact that Moore was such a distinguished alumnus of Yale was doubtless a determining factor in effecting the arrangement. The fact that Mason was a rising star on the Yale faculty could not have hurt the cause either! The series of three sets of lectures, including the one by Mason titled “Selected topics in the theory of boundary value problems of differential equations,” was published in 1910. To recapitulate, Max Mason received his doctorate under Hilbert in 1903 and then taught at MIT, Yale, and Wisconsin. Like Kellogg, Mason took a leave of absence from Wisconsin during World War I for two years to manage a large research team at the National Research Council working on submarine warfare. During this time, 1917-1919, he invented a submarine detection device known as the “M-V tube” (for Multiple-Variable), which “allowed the crew to determine the location of a submarine or other ship producing the noise.”12 Mason’s inspirational mathematics professor Dean L.B. Slichter wrote that his “contributions were critical

in all aspects of these problems, in acoustical theory, and in mechanical and naval engineering.”13 Mason’s experience of successfully administering a group of scientists led the University of Chicago to offer him the presidency in 1925; he thereby became the first person to hold that office who was not one of the original faculty members from 1892. The entire Chicago faculty, not just the mathematics department, was delighted with his performance and expected him to enjoy a long tenure, but when Mason’s first wife died in 1928 (he would marry a third time after the death of his second wife), he left academia for good, moving to New York as director of the Natural Sciences Division of the Rockefeller Foundation. This position too proved to be short lived, only one year, because in 1929 he was promoted to president of the Foundation upon the death of the previous office holder. Mason held this position for a seven-year period that turned out to be critical for funding in mathematics. He left the Rockefeller Foundation in 1936 for California to direct a team that was constructing the Palomar Observatory. Overall, we view Max Mason as the most distinguished member of Hilbert’s American colony because of his research accomplishments, administrative record, and influence in funding mathematics research. Edgar Jerome Townsend (1864-1955) received his undergraduate education at tiny Albion College in Michigan, earning a bachelor’s degree in 1890. He then enrolled at the University of Michigan for a year, obtaining a master’s degree and accepting an instructorship at the Chicago Manual Training School. The location in the Windy City turned out to be serendipitous because while attending the Chicago Congress in August 1893 he was offered a position at the University of Illinois, where he spent the rest of his career until retirement in 1929. Townsend was one of 28 mathematicians who signed the circular announcing a conference to form the Chicago Section of the AMS in December 1896, and one of 17 members who attended that gathering. He served one term as chair of the Section 1904-1905, and was an active member of a committee that considered the question of the mathematics curriculum in technical schools and in technical departments at colleges and universities, an appointment probably based on a long paper he wrote in 1902 in The School Review offering an “Analysis of the failures in freshman mathematics.” He was also elected to the AMS council for a three-year term 1906-1908. Townsend took a two-year leave of absence 1898-1900 to study under Hilbert at Göttingen, where he obtained his doctorate in 1900 for a dissertation titled “Über den Begriff und die Anwendung des Doppellimes.” At Illinois, he directed two Ph.D. dissertations, the first in 1903

and the other nine years later. He also served as Dean of the College of Science at the university 1905-1912. One of Edgar Townsend’s greatest accomplishments at Illinois was the collection of models he assembled after returning home from Göttingen in 1900. Even before going abroad he had been exposed to the impressive display of models made by the famous Brill firm at the Chicago Congress, so once he got settled back at Illinois he set about extending his university’s collection. By 1911 this endeavor assumed such prime importance that Dean Townsend hired the mathematician Arnold Emch to expand the collection, resulting in the largest such exhibition on public display in the country. Many of the models constructed by Emch were not available anywhere else in the world at the time. The influence of Hilbert on his American students was great, as one sees in Townsend’s 1902 translation of the Göttingen giant’s classic work Grundlagen der Geometrie from 1899. The resulting book The Foundations of Geometry is officially titled an “authorized translation,” yet one reviewer was definitely not a fan. The review in the Monthly soon after the book appeared groused, 14 Readers of the American Mathematical Monthly may consult a technical review of this translation in Science, … where in the interest of merest justice are pointed out some few among the blemishes in what Professor Townsend puts forth as a translation of Hilbert’s beautiful “Festschrift.” The review in Science is devastating, using such phrases as “stupendous blunder” and “still more ludicrous” as well as the criticism that the translation of a particular axiom “is so bungled as to be worse than meaningless, actually false.”15 Who is the Science reviewer? The same as the Monthly critic, George Bruce Halsted, who 25 years earlier was forced to leave Johns Hopkins while still a graduate student because of the brouhaha he instigated between J. J. Sylvester and C. S. Peirce. Well, Halsted’s purple prose in a different entry in Science would land him in hot water again later in the year, when his nasty description of the Board of Regents at the University of Texas, where he was head of the mathematics department, caused his dismissal. While the criticism of Townsend caused no such dismissive problem, it could not have been received too kindly in Illinois. On the other hand, Townsend’s three textbooks were reviewed much more favorably. His First Course in Calculus (1909) was “accorded very high rank,”16 Functions of a Complex Variable (1917) was “carefully and well written … [and] will undoubtedly be well received by both teachers and students … There are but few errors … that … should be of no

serious trouble even to a beginner,”17 and the companion volume Functions of Real Variables (1929) “will be welcomed by teachers and students alike.”18 The last of Hilbert’s quintet of those starred in the American Men of Science, Wallie Abraham Hurwitz (1886-1958), was the son of Jewish-German parents. He was born and raised in Missouri, to where his parents had emigrated about 1870. He graduated from Mizzou in 1906 with two bachelor’s degrees, as president of the class, and with a master’s degree for the thesis titled, “Definition of improper groups by means of axioms.” Moreover, in his senior year he was an assistant in mathematics. Just how talented Hurwitz was can be seen in a passage describing his success in a Mizzou course taught by Gilbert Bliss: “W.A. Hurwitz was an extraordinarily able and precocious student in one of his classes.”19 After graduating from the University of Missouri, Wallie Hurwitz matriculated in the graduate program at Harvard 1906-1909 before traveling abroad on a Sheldon Fellowship to study under David Hilbert. In one year, he earned a doctorate that was awarded in 1910 for a dissertation on linear partial differential equations of the first order. Upon receiving the degree, he returned to the U.S. as assistant professor at Cornell, where he remained for the rest of his career (except for the year 1941-1942 at the Institute for Advanced Study). Throughout his career Hurwitz was active with the AMS, beginning as cooperating editor of the Transactions, a position he held 1915-1926. During that time, he also was a member of Council 1919-1921 and served on the Committee of Publication for the Bulletin 1921-1923. In 1921, when the AMS first began the practice of inviting speakers to deliver lectures at meetings, he was the first one so chosen; he also delivered an invited lecture eleven years later, both given at meetings held in New York City.20 Moreover, he served as an AMS consultant on cryptanalysis for the War Preparedness Board before the outbreak of World War II. Hurwitz was a charter member of the MAA and edited the Monthly column “Questions and Discussions” from 1919 through 1921. Curiously, he gave up research at age 52, although he continued to teach advanced courses and attend meetings after that. Two colleagues attempted unsuccessfully to engage him in collaborative efforts after that but he resisted. As Mark Kac commented, “A shame. He had an excellent mind and was very knowledgeable.”21 Hurwitz had lifetime affection for the stock market and was apparently quite successful with investments. He acquired a sizable estate that he donated to three universities—Missouri, Harvard, and Cornell.

None of the remaining Hilbert figures was starred in AMoS, yet all pursued successful careers. We begin with Wilhelmus David Allen Westfall (1879-1951) because of his close connection with Earle Hedrick and Oliver Kellogg. David Westfall graduated from Yale in 1901 and then remained on campus for the next two years. He then went to Göttingen and completed his doctorate under David Hilbert in 1905 for a dissertation on integral equations. When Westfall accepted a position at Missouri upon receiving his degree, he joined the chair Earl Hedrick and Oliver Kellogg in forming the Hilbert outpost in the U.S. Westfall remained at Missouri until retiring in 1949. We expand on his exploits in Chapter 4. Charles Albert Noble (1867-1962) was the son of California settlers who moved from Salem, MA, to Soquel, CA, around 1850 because his father had purchased a land grant and became a farmer and orchardist with his brother. Consequently, our mathematician was born and raised in northern California, attended high school in San Francisco, and graduated from Berkeley in 1889. While there he studied under Irving Stringham, who had obtained a Ph.D. at Johns Hopkins (under J. J. Sylvester) and studied at Leipzig (with Felix Klein), thus receiving a sound education not only in the courses he took but in the primacy of research. Noble taught high school mathematics and English for the next four years and then headed to Germany to study with Felix Klein and David Hilbert at Göttingen for another four years, 1893-1896. A memorial article written upon his death some 66 years later records that, “Like other American mathematicians of the period, he acquired an idiomatic knowledge of German, and a happy, intimate knowledge of German student life.”22 His fellow students in Hilbert’s English-speaking colony selected him as “patriarch,”23 following in the footprints of the first and second heads, Earle Hedrick and Max Mason. Although Charles Noble returned to California in 1896 without a degree, he published his first paper that year (in German!) on a boundary value problem, and then spent the next year continuing his studies on a fellowship at Berkeley. By that time the Berkeley faculty included another active researcher, the former Klein student Mellen Haskell. The following year, 1897, Noble was hired by department chair Irving Stringham as an instructor, and he remained there until his retirement in 1937.24 During that 40- year tenure Noble viewed close at hand the evolution of Berkeley from a small institution to one of national prominence. Fiscal problems had plagued the university up to 1899, when Benjamin I. Wheeler assumed the presidency. Over the next 20 years the classical scholar stabilized finances and attracted library and scholarship funds, research grants, and a distinguished faculty to the University, so the campus

grew in size and distinction as its reputation improved rapidly. The largesse of benefactor Phoebe A. Hearst helped construct such elegant and stately structures as Hearst Memorial Mining Building (1902-1907), Hearst Greek Theatre (1903), Doe Library (1911-1917), the Campanile (1914), and Gilman Hall25 (1917). Charles Noble became one of Berkeley’s distinguished faculty members, returning to Gottingen in 1901 only to submit his dissertation on the calculus of variations, “Eine neus Methode in der Variationsrechnung.” He rose through the ranks to full professor in 1919. During that time, he served a two-year term as secretary of the fledgling San Francisco Section of the AMS 1909-1910. Although he published one paper on partial differential equations in the Annals and one on the concentration of a mixture when strong alcohol is added to weak alcohol, his enduring fame rests with his translation (with Earle Hedrick) of Felix Klein’s popular book Elementarmathematik vom hoheren Standpunkte aus, which was based on lectures that Klein gave at Gottingen in 1908-1909. John Wesley Young wrote a detailed review in the Bulletin the next year,26 but the real leap forward in the U.S. occurred when the Hedrick/Noble translation appeared as two volumes in 1932 and 1939 under the title Elementary Mathematics from an Advanced Standpoint. The first volume covered Klein’s lectures on arithmetic, algebra, and analysis, while the second concerned geometry. The first garnered generally positive reviews, with former Klein student of Cornell stating, “The translation, the printing and the proofreading have been excellently well done.”27 However, the review of the second volume by David Curtiss, whom we meet shortly, niggled about material not included by the translators and wondered if a third volume was in the planning.”28 (If it was, it never appeared.) Perhaps the most balanced view was expressed by Raymond Archibald, who wrote that the two volumes “rendered real service to students and college teachers of mathematics in this country.”29 Charles Noble was 70 years old when he retired in 1937, yet he returned to the Berkeley campus during World War II to donate his services to the university in place of the many mathematicians who were involved with war work. By then severe arthritis began to limit his favorite pastime of back packing expeditions with the Sierra Club, so he reverted to entertaining others inside the lodge of the Sierra Ski Club. He was 94 years old when he died in 1962, having been a charter member of the MAA since its founding in 1915. Unlike Hilbert’s other male colonists, William DeWeese Cairns (1871-1955) spent his teaching career at a small college, so he made his mark on the mathematical community more for service to the MAA than to original contributions, although he did publish a dozen papers in

various journals, including the Annals. Born and raised in Ohio, Will Cairns graduated from Ohio Wesleyan College in 1892, after which he taught physics in high school until 1896, whereupon he enrolled at , earning second bachelor’s degree and a master’s degree, each in one year. Cairns then taught in high school for another year before accepting a position as instructor and surveyor at Oberlin College back in his native Ohio. He remained in this position 1899-1904 before being promoted to assistant professor of mathematics. In 1905 he took a two-year leave for study at Göttingen, earning his doctorate in 1907 under Hilbert for a dissertation on integral equations and the calculus of variations: “Die Anwendung der Integralgleichungen auf die zweite Variation bei isoperimetrischen Problemen.” Like Noble, Cairns was a charter member of the MAA and became the Association’s first secretary-treasurer in 1916. When he resigned from the position in 1942, Earle Hedrick summarized his vital role within the MAA as follows: 30 To these two men [H. E. Slaught and Cairns] far more than to any others the Association owes its success and its present strong position … For many decades to come [Cairns’] high achievement, his constructive leadership, and his great devotion will be remembered, and will serve as an inspiration to younger men who desire to advance the cause of mathematics in America. Will Cairns’s devotion to mathematics inspired mathematicians young and old, for he was elected president of the MAA for a two-year term in 1943 at age 72. Another MAA activist, Lester Ford, added to Hedrick’s note, “It is a fortunate circumstance for us that he will guide the destinies of our organization during the difficult days that lie ahead,” a clear reference to the battles taking place across the Atlantic and Pacific Oceans at the time.31 At the end of his term in 1944 the MAA bestowed upon him the unprecedented title of Honorary President for Life. Cairns had served as professor and chair of the Oberlin department 1920-1939, yet, as his example with the MAA shows, retirement did not equal cessation of activity. First, he taught a course in meteorology at the University of New Mexico during World War II, and later he taught at Cal Tech for a year at age 77. He died in Pasadena seven years later. David Clinton Gillespie (1877-1935) came from a long stock of Virginians, being born and raised in the state. He received his AB at Thomas Jefferson’s University of Virginia in 1900, spent a year at Johns Hopkins, and then went abroad. He received his doctorate in 1906 for the dissertation on the calculus of variations “Anwendungen des Unabhängigkeitssatzes auf die Lösung der Differentialgleichungen der Variationsrechnung.” Upon his return to the U.S., Gillespie accepted an instructorship at Cornell University, where he joined Virgil Snyder, the

former student of Felix Klein. Gillespie remained at Cornell for the rest of his life; he was promoted to full professor in 1924 and served as chair of the mathematics department 1932- 1935. He published several papers in the Transactions and Annals, most in analysis but some in applied mathematics, and served as associate editor of the Annals 1927-1929. He also directed one Ph.D. dissertation, in 1935. His attitude toward students bears repeating: “The careless or inattentive student frequently feared his scorn; but the earnest student found him a kindly and sympathetic friend. He was amazingly tolerant of ignorance, even of stupidity; but impatient with laziness or pretence.”32 The two remaining figures are related to women mathematicians, a sure sign of the surge in the ranks of women who pursued graduate degrees in mathematics despite having been prevented from traversing this path just a decade earlier. We have labeled Arthur Robert Crathorne (1873-1946) an American even though he was born in Scarborough, , because he came to the U.S. as a young boy. Arthur Crathorne was associated with the University of Illinois for almost his entire career, including undergraduate instruction leading to his 1898 B.S. degree. Upon graduation, he taught at the University of Maine for two years before accepting an instructorship at Wisconsin 1900-1904. During this time, he earned another bachelor’s degree, this one from the University of Chicago in 1902. After leaving Wisconsin, Crathorne traveled to Göttingen to work under Hilbert, completing his dissertation on the calculus of variations in 1907. Titled “Das räumliche isoperimetrische Problem,” the 59-page work was published in Germany the same year. Upon his return to the U.S., Crathorne accepted a position at the University of Illinois, where he moved through the ranks to become full professor in 1935. He formed half of a very successful authoring team of elementary textbooks with Henry Lewis Rietz (1875-1943), producing College Algebra in 1909 (the 5th edition appeared posthumously in 1951 and a 6th was revised by another author in 1959), Mathematics of Finance in 1921 (revised edition 1932), Introductory College Algebra 1923 (revised edition 1933), Trigonometry in 1930 (also with E. B. Lytle; revised edition 1938), and Intermediate Algebra in 1942 (posthumous revised edition 1947). In addition to these texts, Crathorne also directed eight doctoral dissertations at Illinois, the last two of which were completed when he reached age 68. Of related interest is Crathorne’s wife, Charlotte Elvira Pengra-Crathorne (1875-1916). Born and raised in Wisconsin, where her father was a well-to-do farmer (and later mayor and bank manager), Charlotte Pengra received her AB degree in mathematics at the University of

Wisconsin in 1897. Her four younger siblings also graduated from Wisconsin as well. Upon graduation Pengra, like most highly educated women at that time, taught in high school (two years) before entering a graduate program. She was awarded a fellowship at the Madison campus in 1899 and received her Ph.D. two years later for the dissertation on the conformal representation of plane curves titled “On functions connected with special Riemann surfaces, in particular those for which P equals 3, 4, and 5.” The dissertation was directed by Linnaeus Dowling, the Clark 1895 Ph.D. graduate mentioned in Chapter 3. It appears that Pengra’s dissertation was never published. It is noteworthy, however, that she became only the third woman to obtain a doctorate at Wisconsin, and the first in mathematics. She probably met Arthur Crathorne when their paths intersected at Wisconsin during the year 1900-1901. With Ph.D. in hand, Pengra followed the traditional woman’s trajectory of high-school teaching; she was head of the department at an Illinois school 1901-1904. The two married in June 1904 and then traveled together to Göttingen. The young wife also attended classes but her pursuit of a higher degree ended with the birth of the first of the couple’s three children in that quaint, German, university town in November 1906. (The other two were born in the U.S.) But tragedy struck in 1916 when she came down with breast cancer and died at her parents’ home in Wisconsin at age 40. Charles Haseman (1880-1931) is another Hilbert student with a link to a woman mathematician. Haseman graduated from the University of Indiana with an AB in 1903, joined the faculty two years later, and earned an A.M. the next year. He spent 1906-1907 on leave in Göttingen, where he wrote a 46-page dissertation on integral equations under Hilbert, “Anwendung der Theorie der Integralgleichungen auf einige Randwertaufgaben in der Funktionentheorie.” Haseman returned to Indiana after that, but remained only two years before accepting a position in 1909 at the University of Nevada at Reno, where he stayed until 1930. He died the next year after a year’s illness. I know only two tidbits about him. First, he was honored on campus foremost as the organizer of the university’s glee club in 1911 and its director from 1930. Second, he published one textbook, Differential and Integral Calculus and Analytic Mechanics (1929); we suspect the text had a small adoption because even the Library of Congress lacks a copy. What seems of more interest to us are the accomplishments of his amazing family. All nine children from this farm family located in the central Indiana town of Linton were college educated, and five earned doctorates. Imagine, five Ph.D.s in the same family at such an early

time in the country’s history! In addition to Charles, William Peter (b. 1878) received a Ph.D. in physics from Pennsylvania in 1907, Leonard earned a Ph.D. in entomology from Cornell in 1910, and John Diedrich, Jr. (b. 1887), was awarded a Ph.D. from Columbia in zoology in 1911. While the men in the family received their doctorates from Göttingen, Pennsylvania, Columbia, and Cornell, it is the seventh of the nine children who accomplished the most in mathematics. Mary Gertrude Haseman (1889-1979) received an AB degree cum laude from the University of Indiana in 1910, and then taught for a year at a two-year college in southwestern Indiana. Next she won a fellowship to Bryn Mawr College, where she studied under department head Charlotte Angas Scott and her colleague James R. Conner from 1911 until 1915. The next year she left Bryn Mawr without a degree and traveled to Baltimore to attend lectures by , who had been recruited to succeed as head of the department at Johns Hopkins in 1900. For the previous 13 years, Morley had taught at Haverford College, the all- male school located near the all-female Bryn Mawr; during that time Morley worked closely with . Gertrude Haseman taught at a private school in Baltimore 1915-1917 while writing her dissertation. She completed that work and passed her final exam in May 1916, and the Bulletin states that she received her degree that year, yet Bryn Mawr awarded it in 1917. In any event, the dissertation written under Scott and Conner, “On knots, with a census of the amphericheirals with twelve crossings,” has garnered acclaim as late as 1999.33 Amphericheiral knots are of particular interest because of the special kind of symmetry they exhibit. After expressing her indebtedness to the pair of Bryn Mawr professors for their helpful criticisms, Haseman wrote, 34 I am especially glad to have this opportunity of expressing to Professor Scott my sincere gratitude for her valuable help and unfailing encouragement during the writing of this dissertation as well as throughout my graduate course. She presented her work at a meeting of the Royal Society of Edinburgh in June 1917 and an extension of it in November 1918. Both presentations were published in the Transactions of that Society.35 Haseman taught at a women’s junior college called Harcum School in 1917-1918 and then high school for another year back home in Linton, Indiana. She accepted an instructorship at the University of Illinois in 1920 but only remained as a colleague of Hilbert’s colonists Edgar Townsend and Arthur Crathorne until late October 1927, when she resigned suddenly to become the first mathematics professor at a junior college that is now the University of Bridgeport in

Connecticut. Yet she remained there only until the fall of 1928, when she accepted a professorship (and advisor to women) at Hartwick College in Oneonta, New York. Haseman must have been possessed of a fiery temperament, however, because she left that position after only one year, reputedly over a dispute with college administrators. After that she moved to Columbia, MO, where her brother Leonard was head of the department of entomology at the University of Missouri. She returned to Linton in 1936 and lived there for the rest of her life, apparently without employment. She died at age 90 in a nursing home after having lived with nephews. Gertrude Haseman is remembered today as one of the early contributors to knot theory and she is listed prominently on a web site devoted to the history of the subject.36 Although her brother Charles did not attain such acclaim, the two of them formed the first brother-sister team to earn Ph.D.s in mathematics in the U.S. In fact, they are the only such team we are aware of. Table 2 summarizes the 13 members of the Hilbert colony according to their undergraduate institution and year the bachelor’s degree was awarded (columns 2 and 3), the institution attended immediately before departing for Göttingen (column 4), and the university generally associated with the person (column 5). This listing highlights the attraction of Hilbert for students from the U.S. Midwest, with only Noble coming from the west coast and Kellogg and Westfall from the east. Kellogg is the only person on the list from a Big 3 university (Chicago, Harvard, and Princeton).

Name Bachelor’s Year Before Göttingen University Bosworth Wellesley 1868 Rhode Island Rhode Island Cairns Ohio Wesleyan 1892 Harvard Oberlin Crathorne Illinois 1898 Wisconsin Illinois Gillespie Virginia 1900 Johns Hopkins Cornell Haseman Indiana 1903 Indiana Nevada Hedrick Michigan 1898 Harvard Missouri, UCLA Hurwitz Missouri 1906 Harvard Cornell Kellogg Princeton 1899 Princeton Missouri, Harvard Mason Wisconsin 1898 Wisconsin Noble Berkeley 1889 Berkeley Reid Virginia Military 1899 Haverford Townsend Albion 1890 Illinois Illinois Westfall Yale 1901 Yale Missouri

Table 2. Thirteen members of the Hilbert American colony.

Endnotes:

1 On pp. 93-94 of Constance Reid, Hilbert, New York/Berlin/Heidelberg: Springer-Verlag, 1970. Oliver Kellogg is the only othe members of the Hilbert American colony mentioned in this well-received biography. 2 Minutes from faculty meeting held June 5, 1961, at Haverford College. The author of the memorial article is unknown; I suspect it was Cletus Oakley, who succeeded Legh Reid at Haverford in 1934, and taught there until his retirement in 1964. 3 On p. 143 of Rufus M. Jones, Haverford College: A History and an Interpretation, New York: MacMillan, 1933. 4 On p. 228 of George Bruce Halsted, Supplementary report on non-Euclidean geometry, Amer. Math. Monthly 8 (1901), 216-230. 5 John H. Washburn, Annual Report of the Corporation, Board of Managers, Rhode Island College of Agriculture and Mechanic Arts, 1902. Washburn resigned as president in August 1902, right after Bosworth’s resignation. 6 On p. 410 of W.B. Ford, Obituary: Earle Raymond Hedrick, Amer. Math. Monthly 50 (1943), 409-411. 7 Idem. 8 On p. 504 of Joseph D. Zund, Oliver Dimon Kellogg, American National Biography, Vol. 12 (1999), 503-504. 9 On p. 658 of Patti Wilger Hunter, Max Mason, American National Biography Vol. 14 (1999). 10 As quoted on p. 208 of Warren Weaver, “Max Mason 1877-1961,” Biographical Memoirs, National Academy of Sciences, Vol. 37 (1963), 205-236. 11 On p. 69 of Raymond C. Archibald, A Semicentennial History of the American Mathematical Society, 1888-1938, New York: Amer. Math. Soc., 1938. 12 On p. 659 of Hunter, Max Mason. [Endnote 9.] 13 As quoted on p. 217 of Weaver, Max Mason. [Endnote 10.] 14 On p. 274 of George Bruce Halsted, Book review, Amer. Math. Monthly 9 (1902), 274-275. 15 On p. 308 of George Bruce Halsted, Book review, Science 16 (1902), 307-308. 16 B. F. Finkel, Book review, Amer. Math. Monthly 16 (1909), 78. 17 On p. 228 of Hans H. Dalaker, Book review, Amer. Math. Monthly 24 (1917), 228-229. 18 On p. 330 of Albert W. Raab, Book review, Amer. Math. Monthly 36 (1929), 330-332. 19 On p. 201 of Archibald, Semicentennial History. [Endnote 11.] 20 Ibid., pp. 22 and 24. 21 On p. 100 of Mark Kac, Enigmas of Chance: An Autobiography, New York: Harper & Row, 1985. 22 Griffith C. Evans, Thomas Buck, and Hans Lewy, In memoriam: Charles Albert Noble (1867-1962), University of California at Berkeley, 1963. 23 On p. 209 of Weaver, Max Mason. [Endnote 10.] 24 Formally, Stringham was not the chair of the department, as that term did not come into use at Berkeley until 1920, when it was applied to Mellen Haskell, who assumed the position upon Stringham’s death in 1907. Both Stringham and Haskell had studied under Felix Klein, the former at Leipzig and the latter in Göttingen. 25 The last-mentioned building is named for Daniel Coit Gilman, the initial president of the University of California at Berkeley who, a few years later, brought J.J. Sylvester to Johns Hopkins University. 26 J.W. Young, Book review, Bulletin Amer. Math. Soc. 16 (1909-1910), 254-265. 27 On p. 171 of Virgil Snyder, Book review, Amer. Math. Monthly 40 (1933), 170-171. 28 D.R. Curtiss, Book review, National Math. Magazine 15 (1940), 158. 29 On p. 224 of Raymond C. Archibald, A Semicentennial History. [Endnote 11.] 30 Earl [sic] Raymond Hedrick, Our retiring secretary-treasurer, Amer. Math. Monthly 50 (1943), 1. 31 Lester R. Ford, Our retiring secretary-treasurer, Amer. Math. Monthly 50 (1943), 1. 32 On p. 299 of W.A. Hurwitz, David Clinton Gillespie—In Memoriam, Bulletin Amer. Math. Soc. 42 (1936), 298- 299. 33 Jósef H. Przytyki, Little and Haseman—early American tabulators of knots, lecture at the AMS Special Session on “The Development of topology in the Americas,” Austin (TX), October 8-10, 1999. 34 Mary Gertrude Haseman, On knots, with a census of the amphericheirals with twelve crossings, Transactions Royal Soc. Edinburgh 52 (Part I) (1917-1918), 235-255. 35 Besides the one cited in the Endnote 34, there is Mary Gertrude Haseman, Amphericheiral knots, Transactions of the Royal Society of Edinburgh 52 (Part III) (1919-1920), 597-602. 36 The website http://www.maths.ed.ac.uk/~aar/knots/ is maintained by Jozef Przytycki and Andrew Ranicki.