A native of Virginia, A.P. Montague graduated from the University of Virginia in 1875. He was a Latin instructor at Columbian (now George Washington University, in Washington, D.C.) beginning in 1879 and obtained his Ph.D. from Columbian in 1888. Montague was dean of the faculty in 1895. He received an LL.D. degree from Richmond College in 1896.

The National Cyclopedia notes:

'As a Latin scholar and classicist Montague had few equals in the South and he was editor of Selected Letters of Cicero (1890) and Selected Letters of Pliny (1893).'

Montague was chosen as Furman University president in 1897. Unlike his predecessors who were pastors, Montague was a layman. He was also the first member of the faculty who held a Ph.D.

Montague became president of Howard College, Birmingham, Ala., in 1902; president of Columbia College, Lake City, Fla, 1912; Professor of Latin and public speaking at Mercer University, Ga., in 1919; dean in 1923; VP in 1924; acting president in 1927-1928.

Montague died on 3 December 1928 (aged 74) Panama City, Bay County, Florida.