Shaw was a well-educated man whose circle of friends included F. Scott Fitzgerald, Cole Porter and Albert E. Gallatin. A graduate of Yale University, Shaw studied architecture at Columbia, served briefly in World War I, and then worked for years as a free-lance writer. As an heir to the Woolworth fortune, his social status and financial security enabled him to travel widely, and exposed him to many of the artistic developments of the European avant-garde. At the age of 36, Shaw enrolled in the Art Students League and studied under Thomas Hart Benton and George Luks. Influenced by his interest in architecture, Shaw created a series of shaped canvases in the 1930’s that evoked the city’s modern skyline. These works were shown by Gallatin in 1935 at The Museum of Living Art, the first museum of modern art in the United States.
Shaw later became a founding member of the American Abstract Artists and served on the advisory board of the Museum of Modern Art in 1936 and 1941.