Alexander Jacob Schem was born on March 16, 1826 in Wiedenbruck in Westphalia to a vinegar manufacturer named Freidrich Schem and his wife Adolphine von Felgenhauer. He was educated first at the Paderborn Gymnasium and then went on to the Universities at Bonn and Tubingen, studying Catholic theology. He was ordained as a Catholic priest in April 1849 and served a parish in Bielefeld for two years. He became disaffected from the Church of Rome, however, and emigrated to the United States in 1851.
He held tutoring positions for a time before taking up a post in 1853 at the Collegiate Institute in Mount Holly, New Jersey. From there he was appointed in 1854 as professor of ancient and modern languages at Dickinson College in Carlisle, Pennsylvania, where he remained for six years. A remarkable linguist who could read in fourteen languages, he taught French and German to the junior and senior class. All his life, Schem was an advocate for the standards and structures of scholarship then emerging in Germany, and his influences were no doubt felt among the faculty of his time. While at the College he also authored, with the Reverend George R. Crooks, a Latin-English dictionary, titled A New Latin-English School-Lexicon on the Basis of the Latin-German Lexicon of Dr. C.F. Ingerslev, which was published in Philadelphia in 1857. Always a serious and studious man of tolerant views, Schem gave up his position at Dickinson in 1860 to devote himself fully to a career in scholarly and journalistic writing.
He worked at the Tribune in New York City for a decade until 1869 when he took on the post of editor-in-chief of Deutsch-amerikanisches Conversations-Lexicon which appeared in eleven volumes between 1869 and 1874. All the while, he was a prolific writer for encyclopedia collections, and he published in 1877, with Henry Kiddle, Cyclopedia of Education. He also wrote a very well received book on the Russo-Turkish War called The War in the East and published in 1878. By this time, he had been appointed as the assistant superintendent of schools of New York City, a post he served in until his death. Schem had over the years become a devout Methodist and wrote pieces for both The Methodist and the Methodist Quarterly Review, together with his own American Ecclesiastical Almanac in 1860.
Alexander Schem had married the daughter of his first employer on his arrival in the United States in 1853. He had become diabetic in his later years and died of a stroke at his home in Hoboken, New York on May 21, 1881. He was fifty-five years old.