Arthur Byron Coble

Arthur Byron Coble (November 3, 1878 – December 8, 1966) was an American mathematician. He did research on finite geometries and the group theory related to them, Cremona transformations associated with the Galois theory of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society from 1933 to 1934.

Biography

Early life Arthur Coble was born on November 3, 1878, in Williamstown, Pennsylvania. His mother Emma was a schoolteacher. When Coble was born, his father Ruben was the manager of a store. Later, he became president of a bank. Coble's parents belonged to Evangelical Lutheran Church. Coble was brought up strictly as an Evangelical Lutheran; however, he rejected this Church when he reached adulthood.

Coble entered Gettysburg College in 1893, and completed his A.B. in 1897. He spent a year as a public school teacher. He entered Johns Hopkins University in 1898 to pursue his graduate studies. He completed his Ph.D. from the university in 1902. His Ph.D. thesis was The Relation of the Quartic Curve to Conics. His thesis supervisor was English-born mathematician Frank Morley.

Academic career In 1902, Coble became an instructor in mathematics at the University of Missouri. One year later, in 1903, he was appointed to Johns Hopkins University as Morley's research assistant. In 1903, he published his doctoral dissertation as The quartic curve as related to conics in the Transactions of the American Mathematical Society and took up the research assistant position in Baltimore, Maryland. In 1902, American businessman Andrew Carnegie founded the Carnegie Institution of Washington. The research of Coble and Morley were one of the first pieces of research the Institution supported. The funding of the institute was generous enough to allow Coble to use the grant to travel abroad. He traveled to Germany where he studied at Greifswald University and the University of Bonn. He wanted to work with Eduard Study, who was well known to mathematicians at Johns Hopkins University because he had taught there in 1893.

Coble was elected to the United States National Academy of Sciences in 1924 and the American Philosophical Society in 1939.

American Mathematical Society Coble was active with the American Mathematical Society (AMS) from 1912 to 1940. At that time, the AMS was in some financial difficulties. Coble dealt with the problem effectively. and it was republished by the American Mathematical Society in 1961 and 1982.

Coble published Configurations defined by theta functions, which reviewed the invariant theory of Cremona transformations as developed by Coble in his earlier papers, in the Duke Mathematical Journal in 1939. A linear homogeneous transformation with integral coefficients is associated with a Cremona transformation. These transformations form a group, which Coble studied.

In 1940, Coble published Trilinear forms in the Duke Mathematical Journal. In 1946, he published Ternary and quaternary elimination, which extends work by mathematicians Francis Sowerby Macaulay and Bartel Leendert van der Waerden, and also extends work done by Frank Morley and Coble some 20 years earlier.