2400 W Chew St, Allentown, PA 18104, United states
Miller went to Allentown, Pennsylvania, where he studied at Muhlenberg College for his baccalaureate which he received in 1887. Continuing his studies he was awarded a degree of Master of Arts by Muhlenberg College in 1890.
Gallery of George Miller
1 Cumberland Square, Lebanon, TN 37087, United States
Miller graduated with a doctorate from Cumberland University in 1892.
Gallery of George Miller
Baltimore, MD 21218, United States
Miller went to Johns Hopkins University to spend the summer of 1889.
Gallery of George Miller
500 S State St, Ann Arbor, MI 48109, United States
Miller went to the University of Michigan to spend the summer of 1890.
Career
Gallery of George Miller
1940
Urbana, Illinois, United States
George Abram Miller in his senior years.
Achievements
Membership
National Academy of Sciences
Miller was a member of the National Academy of Sciences.
American Academy of Arts and Sciences
Miller was a member of the American Academy of Arts and Sciences.
London Mathematical Society
Miller was a member of the London Mathematical Society.
Société Mathématique de France
Miller was a member of the Société Mathématique de France.
Deutsche Mathematiker-Vereinigung
Miller was a member of the Deutsche Mathematiker-Vereinigung.
American Mathematical Society
Miller was a member of the American Mathematical Society.
Indian Mathematical Society
Miller was a member of the Indian Mathematical Society.
Real Sociedad Matemática Española
Miller was a member of the Real Sociedad Matemática Española.
Mathematical Association of America
Miller was a member of the Mathematical Association of America.
2400 W Chew St, Allentown, PA 18104, United states
Miller went to Allentown, Pennsylvania, where he studied at Muhlenberg College for his baccalaureate which he received in 1887. Continuing his studies he was awarded a degree of Master of Arts by Muhlenberg College in 1890.
George Abram Miller was an American mathematician. He was an early group theorist.
Background
George Abram Miller was born on 31 July 1863, on a farm near Lynnville, Pennsylvania. He was the son of Nathan Miller and Mary Sittler. He was descended from Christian Miller who emigrated to the United States from Switzerland around 1720.
Education
During 1882-1883 Miller attended Franklin Academy which was a part of the College of Lancaster. From there he went to Allentown, Pennsylvania, where he studied at Muhlenberg College for his baccalaureate which he received in 1887. Continuing his studies he was awarded a degree of Master of Arts by Muhlenberg College in 1890. By now Miller was 27 years of age, much older than one might expect, but this was just a consequence of having to support himself financially through his education. In fact, he had been the principal of schools in Greeley, Kansas, in 1887-1888 and professor of mathematics at Eureka College in Illinois from 1888 while he worked for his Master's Degree. When teaching was finished at Eureka College, Miller went to Johns Hopkins University and the University of Michigan to spend the summers of 1889 and 1890.
Cumberland University in Lebanon, Tennessee, offered a doctorate as a correspondence course. This did not require an original thesis, in fact, it was not examined by the thesis at all but was awarded on the basis of examinations taken on advanced courses. These courses could be studied as correspondence courses and this is exactly what Miller did. What is perhaps more surprising, he offered himself the same courses for a doctorate to students at Eureka College where he was a professor of mathematics. He graduated with a doctorate from Cumberland University in 1892 and in the following year he left Eureka College to take up the position of instructor at the University of Michigan.
Miller served as principal of the schools in Greeley, Kansas, during the year 1887-1888 and as professor of mathematics at Eureka College (Illinois) from 1888 to 1893. Miller was offering some courses toward a doctorate to his students at Eureka. In 1893 he became an instructor at Michigan for three years and lived in Cole’s home during the first two years of that period. It was Cole who inspired him to pursue the research in group theory that was to engage his talents for the rest of his life. Cole, incidentally, had been a pupil of Felix Klein, who had made groups basic in his “Erlanger Programm.”
Miller spent the years 1895-1897 in Europe, attending the lectures of Sophus Lie at Leipzig and Camille Jordan in Paris. He soon was publishing papers independent of their specializations, although Lie had become instrumental in Miller’s study of commutators and commutator subgroups and Jordan’s interest in questions of primitivity and primitivity was reflected in Miller’s investigations of those problems throughout his career.
Upon Miller’s return to the United States, his European experience and mathematical productivity gained him an assistant professorship at Cornell (1897-1901). This was followed by an associate professorship at Stanford University (1901-1906), and in 1906 an appointment at the University of Illinois, an affiliation that lasted for the rest of his life - first as an associate professor, then as a professor, and finally as professor emeritus. His retirement in 1931 was from classroom responsibilities only, for he continued his research and writing in his office at the university. The university undertook, as “a fitting memorial of his contributions to mathematical scholarship and to the renown of the University,” the collection and reprinting of Miller’s studies in the theory of finite groups as well as other studies. It is said that of the more than 800 titles that appeared in some twenty periodicals over forty years approximately 400 made direct scientific contributions to that theory. Other papers were written in the hope that teachers of elementary and secondary mathematics might be inspired to study advanced mathematics. Miller himself aided in the preparation of these memorial volumes.
Most of Miller's publications dealt with the theory of finite groups, substitution groups, and, later, with abstract groups. He was also interested in the history of mathematics, which he taught at Eureka, Cornell, Stanford, and Illinois. His Historical Introduction to Mathematical Literature (1916) was developed in connection with his teaching at Illinois. His Collected Works lists 820 journal articles, excluding reviews and short articles collected elsewhere. The publication in five volumes of his collected works was undertaken in 1934 by the University of Illinois. A committee of his colleagues supervised the project, but Miller himself did much of the work on the first volume and wrote additional papers on the history of group theory for the periods covered by the first three volumes. The last volume was published in 1959. Miller's history of group theory was based on his own deep involvement with the subject during a period of rapid growth. His other historical work, however, was based on secondary sources and tended to emphasize what he perceived as errors, exaggerations, or inconsistencies in the writings of other historians. This inclination led him into occasional errors and petty interchanges. His expository writing, in addition to attempting to explain group theory and its possible uses to the secondary schoolteachers and general readers, also included essays on the nature of mathematical research and the uses of the history of mathematics.
Miller’s interest in the history of mathematics was second only to that in the theory of finite groups. His articles on the history of his own subject were of particular significance and value. He became a severe critic of historical methodology in mathematics and was zealous in rooting out an error in conjecture or assumed fact. His letters in the David Eugene Smith collection at Columbia University offer ample evidence of this missionary fervor. His “History of Elementary Mathematics” remained unpublished, although there was originally the intention to include it in a volume of the Collected Papers.
Membership
Miller was elected to the National Academy of Sciences in 1921 and was a fellow of the American Academy of Arts and Sciences. He was a member of the London Mathematical Society, the Société Mathématique de France, and the Deutsche Mathematiker-Vereinigung, an honorary life member of the Indian Mathematical Society, and a corresponding member of the Real Sociedad Matemática Española. He was an active member and served in various high offices of the American Mathematical Society and the Mathematical Association of America, serving also as an editor of the latter’s American Mathematical Monthly (1909-1915).
National Academy of Sciences
,
United States
American Academy of Arts and Sciences
,
United States
London Mathematical Society
,
United Kingdom
Société Mathématique de France
,
France
Deutsche Mathematiker-Vereinigung
,
Germany
American Mathematical Society
,
United States
Indian Mathematical Society
,
India
Real Sociedad Matemática Española
,
Spain
Mathematical Association of America
,
United States
Personality
Miller has been described as easy and responsive in conversation but devoted to his work routine and to the goals of scholarship and research. He never thought it important to tell his friends and colleagues that by judicious investments he had accumulated a fortune of nearly $1 million, and there was much surprise when it was revealed that upon his death he had left essentially his entire estate to the University of Illinois.
Quotes from others about the person
"If he had thought a million dollars was important it would have appeared in the journals." - H. R. Brahana, Miller's biographer
Interests
Philosophers & Thinkers
Frank Nelson Cole
Connections
On December 23, 1909, Miller married Cassandra Boggs of Urbana, Illinois. They had no children.