George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist. At age 17 Miller began school-teaching to raise funds for higher education. In 1882 he entered Franklin and Marshall Academy, and progressed to

Muhlenberg College Muhlenberg College is a private liberal arts college in Allentown, Pennsylvania. Founded in 1848, Muhlenberg College is affiliated with the Evangelical Lutheran Church in America and is named for Henry Muhlenberg, the German patriarch of Luthe ...

in 1884. He received his B.A. in 1887 and M.A. in 1890. While a graduate student, Miller was Principal of schools in

Greeley, Kansas Greeley is a city in Anderson County, Kansas, United States. As of the 2020 census, the population of the city was 273. History Early History Nomadic Native Americans, perhaps the Wichita as early as the 1400s and the Osage by the 1700s, ...

and then professor of mathematics as Eureka College in Eureka, Illinois. He corresponded with

Cumberland University Cumberland University is a private university in Lebanon, Tennessee. It was founded in 1842. The campus's current historic buildings were constructed between 1892 and 1896. History 1842-1861 The university was founded by the Cumberlan ...

in Lebanon, Tennessee for his Ph.D. in 1892. He then joined Frank Nelson Cole at

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

and began to study

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

s. In 1895 he went to Europe where he heard

Sophus Lie Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. Life and career Marius Soph ...

lecture at Leipzig and

Camille Jordan Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in group theory and for his influential ''Cours d'analyse''. Biography Jordan was born in Lyon and educated at ...

at Paris. In 1897 he went to

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

as an assistant professor, and in 1901 to Stanford University as associate professor. In 1906 he went to

University of Illinois The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...

where he taught until retirement in 1931. Henry Roy Brahana (1957) Miller helped in the enumeration of finite groups of degree 8, 9, and 10. Arthur Cayley had listed 198 groups of degree 8 in 1891, and Miller found two more making the total 200 in 1893. Camille Jordan had given a list for degree 9 in 1872, re-examined by Cole, and brought up to 258 groups by Miller. In 1894 Miller produced a list of 294 intransitive groups of degree 10. In consequence, the Academy of Science of Cracow awarded a prize and "Miller came to prominence in the mathematical world abruptly." Miller was president of the Mathematical Association of America 1921–1922 and gave a plenary address at the International Congress of Mathematicians in 1924 in Toronto. Miller's ''Collected Works'' were edited by Henry Roy Brahana and published by

University of Illinois Press The University of Illinois Press (UIP) is an American university press and is part of the University of Illinois system. Founded in 1918, the press publishes some 120 new books each year, plus 33 scholarly journals, and several electronic proje ...

, the first two volumes appearing in 1935 and 1939. The final three volumes were published in 1946, 1955, and 1959. His doctoral students include H. L. Rietz.

Publications

* 1892
An introduction to the study of Determinants, with examples and applications
* 1905: ''Groups of subtraction and division''. * 1908: "On the multiple holomorphs of a group", Mathematische Annalen 66(1): 133-142 * 1911: "Abstract definitions of all the substitution groups whose degrees do not exceed seven",

American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United S ...

* 1911: ''The Algebraic Equation'' * 1916: (with H. F. Blichfeldt, &

L. E. Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...

''Theory and Application of Finite Groups''
from

Historical Math Collection, original publisher:

John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, ...

. * 1916
Historical Introduction to Mathematical Literature
from

Historical Math Monographs, original publisher

Macmillan Publishers Macmillan Publishers (occasionally known as the Macmillan Group; formally Macmillan Publishers Ltd and Macmillan Publishing Group, LLC) is a British publishing company traditionally considered to be one of the 'Big Five' English language publ ...

. G. B. Mathews (1917
Review: ''A Historical Introduction to the Mathematical Literature''
from

Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

98:387 (#2464) * 1947: "An Eleventh Lesson in the History of Mathematics",

Mathematics Magazine ''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a j ...

21(1): 48-55.

References

External links

George A. Miller Papers 1895–1947, 1951
from University of Illinois Archives. * * {{DEFAULTSORT:Miller, George Abram 1863 births 1951 deaths Cumberland University alumni Educators from Pennsylvania Group theorists American historians of mathematics Muhlenberg College alumni People from Lehigh County, Pennsylvania Presidents of the Mathematical Association of America The American Mathematical Monthly editors