## Section 3.7 Profile: John Robert Kline (1891-1955)

J. R. Kline was the most influential mathematician in the Philadelphia area during the 1920s, and he became one of the most significant figures in the Philadelphia Section. Indeed, his career is important in the history of mathematics in the United States for two reasons – his relationship with the famed topologist R. L. Moore and his support for African-American students at a time when such encouragement was unusual.

Kline spent almost his entire life within the section’s boundaries. It seems only fitting that his place of birth, Quakertown, lies midway between the section’s institutional parents, Penn and Lehigh. The child of Henry K. and Emma (Osman) Kline, he was born on December 7, 1891.

Kline obtained an A.B. in 1912 from Muhlenberg College, which granted him an honorary doctorate in 1934. A photo of the college on the front page of the May 30, 1934, edition of the Allentown Chronicle includes him as one of the inset faces. Back in 1912 Kline went directly from Muhlenberg to the graduate program at the University of Pennsylvania. The preceding year two new instructors on the Penn faculty were EPADEL founder H. H. Mitchell and R. L. Moore. Apparently Kline took two courses with Moore – Foundations of Mathematics, and a sequel called Theory of Point Sets. Beyond these, individual study was the fashion, with Moore encouraging his better students to work with him. Kline was the best. He obtained a masters degree in 1914 and a Ph.D. two years later. His dissertation, “Double elliptic geometry in terms of point and order”, was published in the Annals of Mathematics in September 1916. This makes Kline the first in a long, distinguished list of doctoral students of the legendary Texan.

Although Moore strongly disapproved of students getting married before completing their studies, Kline married Anna B. Shafer in June 1915 when he was midway through his thesis. In fact, following the ceremony Moore tendered a luncheon to the newly married couple. Anna and John Kline had one son, John Shafer Kline.

While completing his dissertation during 1915-1916, Kline was an instructor at his alma mater, Muhlenberg. After receiving his doctorate he returned to Penn, winning a Harrison Fellowship for the year 1916-1917 and accepting an instructorship for the next year. This enabled him to continue his studies with Moore. Kline left Penn in 1918, but after one year at Yale and one at the University of Illinois, he returned in 1920 to replace Moore, who had accepted a professorship at Texas. Although Moore remained at Texas and Kline at Penn for the rest of their careers, the archives at the University of Texas contain a steady stream of letters between the two, and each sent students to study under the other, either during their graduate studies or as post-doctorates.

The correspondence between Kline and Moore does not seem to address the origin of the famous Moore Method of teaching. More than likely, Moore’s techniques evolved over time, as evidenced by course descriptions in the course catalogs at Penn and his influence on fellow faculty members (particularly EPADEL founder H. H. Mitchell). Besides, the dissertation topics of Moore’s Ph.D. students at Texas in the 1920s were similar to Kline’s and to Moore’s other two Penn students, George H. Hallett, Jr. (1918) and Anna Mullikin (1922). Knowing how Moore directed his students from basic axiomatic systems to doctoral dissertations, it seems clear that the first person to benefit from the Moore Method was J. R. Kline.

At Penn Kline served as chairman of the department from 1928 until the year before his death in 1955. He also held the University’s prestigious Thomas A. Scott Professorship from 1940. Kline took several leaves of absence during his tenure. The first was during the year 1925-1926 as a Guggenheim Fellow at Göttingen University, which had arguably the very best mathematics department in the world at the time. Later he was a visiting professor at four different institutions: Bryn Mawr College (1935-1936), Swarthmore College (1938-1939), the University of Colorado (summer of 1949), and the University of Tübingen (first semester of the 1952-1953 academic year). His trip to Göttingen occurred while J. B. Reynolds was advancing the idea of forming an MAA

^{ 1 }section, which explains why Kline was not one of the founding members of the Philadelphia Section. However, he played an active role thereafter, being elected secretary- treasurer for 1927-1928 and chairman for 1932-1933. In addition, he attended numerous annual meetings.Kline contributed to the national MAA

^{ 2 }in one decisive way. During World War II the MAA^{ 3 }formed a Subcommittee on Available Teachers in College Mathematics, with Kline one of its three members. (Another was Arnold Dresden. The two friends resided in Swarthmore.) This subcommittee compiled and maintained a register of vacancies and availability of mathematicians for service throughout the war. Kline was also an important AMS^{ 4 }officer, serving as associate secretary 1933-1936 and as secretary 1941-1950. When he took ill in 1943, his place was taken by Arnold Dresden. (With Everett Pitcher of Lehigh serving as secretary of the AMS^{ 5 }1967-1988, an EPADEL member held that position for 31 of the 47 years from 1941 to 1988.) Kline also served as an associate editor of the Transactions of the AMS^{ 6 }, the Bulletin of the AMS^{ 7 }, and the American Journal.During his tenure at Penn, Kline directed 19 doctoral dissertations. His first graduate, in 1925, was longtime MAA

^{ 8 }secretary-treasurer Harry Gehman. Kline was a particularly fair and unbiased man who, unlike his academic father, R. L. Moore, permitted any qualified candidate to study under him. Two cases are particularly noteworthy. In 1928 he supervised the doctoral dissertation of Dudley W. Woodward, who became the second African-American student to receive a Ph.D. in mathematics in the United States. William Claytor became the third when he completed his dissertation under Kline in 1933. Recently Claytor’s widow Mae recalled that Kline continued to support her husband even after he received his degree, encouraging him to participate in both the AMS^{ 9 }and the MAA^{ 10 }.J. R. Kline became a respected member of the international mathematical community, publishing four papers in the Polish journal Fundamenta Mathematicae and three in the Proceedings of the National Academy of Science. Moreover, Kline wrote a joint paper with his advisor, the only publication Moore ever coauthored. Most of Kline’s publications appeared from the time of his dissertation in 1916 to a long paper on separation axioms in topology in 1928. Administrative duties demanded most of his time and attention after that. Nonetheless, he was elected secretary of the International Congress of Mathematicians for the meeting held in 1950 in Cambridge, MA.

Unfortunately, Kline’s life was difficult after the 1950 congress. First, his wife Anna died that year at age 59. However, he married Eunice Story Eaton the following year and the two of them went to Germany with much hope for a renewed life. Kline expected to write a book on the Jordan curve theorem, its extensions, and its applications to topology and analysis, but it never materialized. He was beset with administrative problems upon his return to Penn. Combined with personal tragedy and physical ailments, the torture was too much for him to handle, and Kline committee suicide. He was buried in Quakertown after his death on May 2, 1955.

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