Born in 1841 in the Leeward Islands, Crogman spent his early years as an able-bodied seaman. After years of self-study, he took his degree at Atlanta University in 1873. He then became Professor of Greek at Clark University, and served for more than 40 years. From 1903-1910 he was Clarks president. He was a member of the American Philological Association from 1898 until his death in 1931.