J. Howard Redfield

John Howard Redfield (born June 8, 1879 in Philadelphia , † April 17, 1944 ) was an American civil engineer who was versatile and also made significant achievements as a mathematician, but this was only known after his death. He discovered in the combinatorics before George Pólya 1927 his counting theory (counting theorem of Pólya ).

Life

Redfield was the grandson of William Charles Redfield , his great-grandfather, William Charles Redfield , known as the pioneer of steamship passenger transport on the Hudson and a geologist. He graduated from Haverford College with a bachelor's degree in 1899. One of his teachers was mathematician Frank Morley . He was then briefly apprenticed to an engineering firm in Philadelphia, but then studied civil engineering for two years at the Massachusetts Institute of Technology with a degree (SB) in 1902. He worked for a construction company in Wayne for two years and when business subsided he left in 1904 to New York City, where he was a draftsman in a steel construction company. The activity as an engineer did not satisfy him. He studied languages again and, thanks to a small inheritance, accompanied his sister to France in 1906. He then tried his hand at teaching, but could not find a permanent position. Redfield was shy and a little unworldly, which made him not a good class teacher or a good academic teacher. In 1907/08 he studied mainly French language and literature in Paris with a degree from the Sorbonne. Back in the USA, he studied Romance studies at Harvard University , where he received his master's degree in 1910 and his doctorate in the Basque language in 1914 . One of his professors was the English scholar George L. Kittredge . During his studies at Harvard, he was an instructor in mathematics at Worcester Polytechnic Institute in 1908-09, taught French at Swarthmore College in 1910-11 and was an instructor in Romance studies at Princeton University from 1912 to 1915 . From 1916 until his death he was a civil engineer in Wayne, Pennsylvania (where his family had lived since 1892). First he was with a construction company and from the early 1920s to 1931 with the United Gas Improvement Company in Philadelphia. In 1931 he accepted an offer to serve a year at Haverford College as a substitute professor, and gave up his position despite concerns. After the year was up he couldn't go back to his old job because of the Great Depression. He got by mainly with patent translations, taught in 1938 in the Navy Yard of Philadelphia to engineers and soon afterwards became an engineer at the chemical company DuPont in Wilmington. That left him with less time for math, which he had increasingly turned to. He attended frequently the Math Club at Haverford College and gave lectures there in 1940 on electronic computers. In 1942/43 he fell ill with cancer.

His brother Alfred Clarence Redfield was an oceanographer.

While studying in Paris, he met Elli Proschwitz, the daughter of the mayor of Kolberg . They wrote to each other during their separation of several years and married in Kolberg in 1913. Due to the anti-German atmosphere, his wife left the USA in 1915 and taught in Kolberg as a teacher before returning to the USA in 1919. They had a daughter together.

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In the 1920s he also turned to mathematics (alongside studying languages). He studied the textbook of group theory by Camille Jordan ( Traité des Substitutions ), the Combinatorial Analysis by Percy Alexander MacMahon and the Principia Mathematica by Alfred North Whitehead and Bertrand Russell .

His only mathematical work published during his lifetime, published in 1927, anticipated Polyas counting theory and applied group theory to combinatorics, but remained largely unnoticed, although Redfield was in correspondence with Percy MacMahon, who also drew Thomas Muir's attention to him. His old teacher Frank Morley, with whom he kept in contact, had encouraged him to publish. His work also solved a problem by McMahon and was a follow-up to another work that he submitted to the American Journal of Mathematics in 1940, but which was rejected (it did not appear until 1984). In 1950, John Edensor Littlewood drew attention to Redfield's 1927 work, and Frank Harary in 1960 .

He was also interested in logic, game theory, applications of combinatorics in linguistics and knot theory and developed complex puzzles (preserved in his estate). He attended mathematical seminars and colloquiums in Haverford and Pennsylvania. In 1932 he was elected to the Phi Beta Kappa section of Haverford.

Redfield had a variety of interests. Among other things, he was a very good linguist who spoke many languages. Even as a teenager he was interested in it and also learned the artificial language Volapük. He later translated patents from and into most European languages. As a student, he played in the mandolin orchestra and composed a comic opera that was performed at Haverford College.

Fonts

The Theory of Group-Reduced Distributions, American Journal of Mathematics, Volume 49, 1927, pp. 433-455
Enumeration by frame group and range groups, Journal of Graph Theory, Volume 8, 1984, pp. 205-223
Group theory applied to combinatory analysis, Communications in Mathematical and in Computer Chemistry, Volume 41, 2000, pp. 7-27 (lecture by Redfield)

literature

J. Sheehan: Redfield discovered again , 9th British Combinatorial Conference 1983, pp 135-165, abstract
E. Keith Lloyd: J. Howard Redfield 1879-1944, Journal of Graph Theory, Volume 8, 1984, pp. 195-203
Frank Harary, Robert W. Robinson: The rediscovery of Redfield's papers , Journal of Graph Theory, Volume 8, 1984, pp. 191-193
JI Hall, EM Palmer, RW Robinson: Redfield's lost paper in a modern context , Journal of Graph Theory, Volume, 8, 1984, pp. 225-240
E. Keith Lloyd: Redfield's proofs of MacMahon's conjecture , Historia Mathematica, Vol. 17, 1990, pp. 36-47
E. Keith Lloyd: Redfield's 1937 lecture , Communications in Mathematical and in Computer Chemistry, Volume 41, 2000, pp. 29-41
E. Keith Lloyd: Redfield's contributions to enumeration , Communications in Mathematical and in Computer Chemistry, Volume 46, 2002, pp. 215-233.

Individual evidence

↑ One listener described his teaching in his final years at Haverford College in a letter to Frank Harary in 1963: he never looked at the students, spoke gently and usually with his eyes on the floor, mostly turned his back on the class, but his blackboard was of exemplary clarity.
↑ Also reprinted in the Collected Papers by Percy McMahon (Ed. George E. Andrews, MIT Press, from 1978)

personal data
SURNAME	Redfield, J. Howard
ALTERNATIVE NAMES	Redfield, John Howard
BRIEF DESCRIPTION	American mathematician, civil engineer, and linguist
DATE OF BIRTH	June 8, 1879
PLACE OF BIRTH	Philadelphia
DATE OF DEATH	April 17, 1944

[1] One listener described his teaching in his final years at Haverford College in a letter to Frank Harary in 1963: he never looked at the students, spoke gently and usually with his eyes on the floor, mostly turned his back on the class, but his blackboard was of exemplary clarity.

[2] Also reprinted in the Collected Papers by Percy McMahon (Ed. George E. Andrews, MIT Press, from 1978)