**George Miller** was an American mathematician who worked mostly on group theory but he was also interested in the history of mathematics.

- Since his parents did not have the financial means to support him through his studies, George began teaching at the age of seventeen to support himself through College.
- During 1882-83 Miller attended Franklin Academy which was a part of the College of Lancaster.
- 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.
- 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.
- These courses could be studied as correspondence courses and this is exactly what Miller did.
- When he arrived at the University of Michigan, Miller was offered accommodation in Cole's home.
- He lived there for two years and this was perhaps the most significant event for his mathematical development for Cole was interested in the theory of groups and he soon had Miller totally fascinated by this topic.
- Miller spent the years from 1895 to 1897 in Europe attending lectures on group theory by Lie in Leipzig and Jordan in Paris.
- On his return to the United States Miller was appointed assistant professor at Cornell University.
- Miller worked mostly on group theory but he was also interested in the history of mathematics.
- His collected works appear in five volumes: the first contains 62 papers which Miller published before 1900; the second contains 107 of the 147 papers he published during the years from 1900 to 1907; the third includes 89 of the 180 papers he published during the years 1908 to 1915; the fourth contains 98 of the 232 papers he published during the period 1916 to 1929.
- Many of Miller's group theory papers enumerate the possible finite groups which satisfy given conditions such as: the prime factors which divide the order, the orders of two generating permutations and their product; the types of subgroups; or the degree of a representation as a permutation group.
- Miller did not introduce new techniques to attack these group theory questions and one is tempted to say that he should have applied his undoubted skills to produce fewer yet more significant results.
- In addition Miller wrote a number of books: Determinants (1892); Historical introduction to mathematical literature (1916) and he co-authored Theory and application of finite groups (1916) with Blichfeldt and Dickson.
- Miller became a member of the New York Mathematical Society in 1891, three years after it was founded.
- In 1894 the Society became the American Mathematical Society and Miller helped to organise the San Francisco West Coast section which was set up in May 1902.
- It is difficult to assess Miller's contributions to mathematics.

Born 31 July 1863, Lynnville, Pennsylvania, USA. Died 10 February 1951, Urbana, Illinois, USA.

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Group Theory, Origin Usa, Number Theory, Special Numbers And Numerals

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive