 Geller studied drawing with his father, and the attended art classes at the Brooklyn Museum.A 1938 painted self-portrait won him a scholarship to the New York High School of Art and Music (1939), and he subsequently studied architecture at Cooper Union, where he took drawing class with Robert Gwathmey, father of architect Charles Gwathmey.Geller later worked as a naval architect for the United States Maritime Commission designing tanker hulls and interiors (1939–42).