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.

Coble was brought up strictly as an Evangelical Lutheran; however, he rejected this Church when he reached adulthood.

[1] Later, Coble recalled how Morley made it "a cardinal point to have on hand a sufficient variety of thesis problems to accommodate particular tastes and capacities.

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.

He wanted to work with Eduard Study, who was well known to mathematicians at Johns Hopkins University because he had taught there in 1893.

He left Johns Hopkins after he was offered a full professorship at the University of Illinois at Urbana-Champaign (UIUC) in 1918.

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

After his retirement, he accepted a one-year post at Haverford College but after teaching for one semester he resigned due to poor health.

He then moved to Lykens, Pennsylvania, and spent his final ten years of his life there.

[1] Early mathematical research papers written by Coble when he was teaching at Johns Hopkins University, include: On the relation between the three-parameter groups of a cubic space curve and a quadric surface (1906); An application of the form-problems associated with certain Cremona groups to the solution of equations of higher degree (1908); An application of Moore's cross-ratio group to the solution of the sextic equation (1911); An application of finite geometry to the characteristic theory of the odd and even theta functions (1913); and Point sets and allied Cremona groups (1915).

[3] In 1946, he published Ternary and quaternary elimination,[3] 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.