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Shaw was born in New York City in 1892. His parents died when he was young, and an uncle raised him and his twin brother. He graduated from Yale, studied architecture at Columbia University, went to the Arts Students League to study under Thomas Hart Benton, and finally took private lessons with George Luks.

A wealthy man-about-town, poet and minor novelist, Shaw was in his thirties before he began to paint seriously, and then went on to become a significant figure in the world of abstract art in America. His nonrepresentational work was highly personal in character.

He served in World War I, lived in Europe during much of the 1920s, and wrote articles for Smart Set and The New Yorker before he became focused on painting. Once committed, however, he soon was in the very thick of the abstract movement, exhibiting in important avant-garde shows.

Many of Shaw’s early paintings were notable for their clarity of form and almost architectural construction. Much of his work, in fact, heavily influenced by Jean Arp, was constructed of separate planes of wood and masonite, meticulously joined at the seams, which seem to pass over and under one another.

In the 1930s he did a lively and highly original series of paintings collectively entitled Plastic Polygon, which is now considered the most significant of all his work. Some are painted wood reliefs in which he cut planes out of his surfaces and then replaced them as tightly fitting pieces of an abstract composition. He was especially fond of circles and used them often in different connotations.

In the latter part of his life Shaw turned to abstract expressionism.  His style grew bolder and showed a strong graphic sense. He died in 1974.

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