The son of Alfred Goldsborough Mayor and Harriet Hyatt Mayor, Alpheus was born in Gloucester, Massachusetts, in the home that later became the Woods Hole Oceanographic Institute. Mayor graduated from Princeton in 1922 and subsequently taught art history at Vassar for one year. He received a Rhodes scholarship and attended Christ Church College at Oxford University, earning a second degree in 1926. Mayor spent the following academic year at the American School of Classical Studies in Athens. After returning home, he met Lincoln Kirstein in 1928 while working at the School of the American Laboratory Theater in New York and assisted with Kirstein’s literary magazine, Hound and Horn. In 1932, Mayor married Virginia Sluder and joined the Department of Prints at the Metropolitan Museum of Art under William Ivins, Jr. In 1946, he succeeded Ivins as curator of the department.
As curator of prints, Mayor expanded the museum’s collection to include works that were often less sought after, but of high quality and importance. Ivins had purchased a number of masterpieces for the print collection, but the result was a collection filled with gaps. By “filling in the valleys between Ivins’ mountain-top masterworks,” Mayor used his excellent connoisseur-ship and critical eye to round out the collection. He acquired works from the Prince of Liechtenstein’s print collection in the late 1940s, focusing on pieces by lesser-known artists and largely ignoring the Rembrandts and Dürers. He included all types of prints in his collection, acquiring wine bottle labels, catalogs, and cigarette insert-cards. An innovative thinker, Mayor also viewed prints as a popular form of communication and wrote a book on the subject in 1952 entitled Prints and People: A Social History of Printed Pictures. He retired from the museum in 1966 but continued to work. In 1969, he translated and published a German print catalog of art historian Max Lehr reissued as Late Gothic Engravings of Germany and the Netherlands. Mayor also edited the new edition of Le Peintre Graveur by Adam Ritter von Bartsch. He was president of the Hispanic Society of America, New York City – founded by his uncle, Archer M. Huntington – from 1955 until his death in 1980.