**Arthur Coble** was an American mathematician who worked on finite geometries and group theory.

- Ruben and Emma Coble were Lutherans and they were part of the large Lutheran community of Pennsylvania.
- The Lutheran community was, however, split into many different factions and the Evangelical Lutheran Church in America, to which the Cobles belonged, had a long history of growth, mergers, and amalgamations and was going through a difficult period when Arthur was young.
- Although Arthur was brought up strictly as an Evangelical Lutheran, he rejected this Church when he reached adulthood.
- Coble entered the Pennsylvania College of Gettysburg, the oldest existing Lutheran college in the United States founded in 1832, in 1893.
- Coble graduated with an A.B. in 1897 and, after spending a year as a public school teacher, he began his doctoral studies at Johns Hopkins University in 1898.
- Coble was appointed an instructor in mathematics at the University of Missouri in 1902 and then was appointed to Johns Hopkins University in 1903 where he became Morley's research assistant.
- The Carnegie Institution of Washington had been founded in 1902 by Andrew Carnegie to contribute to various areas of scientific research and one of the first pieces of research the Institution supported was that of Coble and Morley.
- The funding was generous enough that Coble was able to use the grant to travel abroad and, as was the custom for American mathematicians at that time, he travelled to Germany where he studied at Greifswald University and Bonn University.
- Returning to the United States for the start of the 1904-05 session, Coble was appointed as an instructor in mathematics at Johns Hopkins University.
- Except for being a visiting professor at Chicago in 1919 and the year 1927-28 which he spent back at Johns Hopkins University, Coble remained at the University of Illinois for the rest of his career.
- In 1929 Coble published the monograph Algebraic geometry and theta functions in the American Mathematical Society Colloquium Publications, being the tenth such volume.
- This paper reviews the invariant theory of Cremona transformations as developed by Coble in his earlier papers.
- A linear homogeneous transformation, with integral coefficients, is associated with a Cremona transformations and these transformations form a group which Coble studied.
- In the year before he retired he published Ternary and quaternary elimination (1946) which extends work by Macaulay and van der Waerden, and also extends work done by Morley and Coble some 20 years earlier.
- In 1934 Coble became Head of the Department of Mathematics at the University of Illinois and continued in this role until he retired in 1947.
- Coble worked hard and effectively for the American Mathematical Society over many years.
- The Society at that time was in some financial difficulties and it was to Coble's great credit that he dealt so effectively with the problem.

Born 3 November 1878, Williamstown, Pennsylvania, USA. Died 8 December 1966, Harrisburg, Pennsylvania, USA.

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Group Theory, Origin Usa

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