Mark Baum was born in 1903 in Sanok, Poland. He emigrated to the United States with his family in 1919 and settled in New York City. Baum studied at the National Academy of Design in 1924-1925 and at the Cape Cod School of Art in Provincetown, Massachusetts with C. W. Hawthorne in the summer of 1926. He was also trained as a furrier and supported himself and his family as an expert cutter of fur coats.
Early success with his figurative painting gave Mark Baum a reason to hope for a lifelong career as an artist. He had a show of watercolors at the Whitney Studio Galleries in 1929 and work was purchased by Juliana force. Baum followed his success with an exhibit of oil paintings at the Marie Harriman Gallery in 1930. Baum paid a visit to Alfred Stieglitz at his American Place gallery and recorded in his notes that Stieglitz bought a painting for his own collection.
During the Depression, Baum worked for the Works Program Administration in the easel division. He married in 1933 and his sons William and Paul were born in 1936 and 1939. Baum's wife Celia was an elementary school teacher who went on to receive a Ph.D. in education and become a professor of education at Brooklyn College.
In 1941, Mark Baum exhibited his paintings at the Perls Gallery. Other exhibitions at the St. Etienne Gallery in 1947 and the Laurel Gallery in 1948 established mark Baum as painter of sturdy figures, and city architectural views and landscapes. Some time in the late 1940s, Baum stopped painting for a while and, when he resumed, broke completely with his previous style. He adopted a staircase motif for a series of abstract and geometric patterns and elements appearing in endless combinations of vast surfaces of painted space.
In the early 1960s, Mark Baum took up residence in costal Maine, where he converted a spacious barn in Cape Neddick into a studio. He lived there until his death in 1997. The work of Mark Baum is in the permanent collections of the Metropolitan Museum of Art and the Whitney Museum of American Art.