In 1924, he joined friends Yosl Cutler and Zuni Maud to be set and costume designers for Maurice Schwartz's production of Abraham Goldfaden's Di Kishefmacherin.

In 1929 America entered into the great depression; following the economic collapse President Franklin D. Roosevelt initiated the Work Projects Administration.

As chairman, Tworkov invited known artists to teach, including Al Held, Knox Martin, George Wardlaw, and Bernard Chaet.

Among the students of that era were Chuck Close, Jennifer Bartlett, Richard Serra, Nancy Graves, Rackstraw Downes, and Brice Marden.

as an important and influential artist, along with Rothko, de Kooning, Philip Guston, Franz Kline, and Pollock, whose gestural paintings of the early 1950s formed the basis for the abstract expressionist movement in America.

After the 1950s one can see from Tworkov's art that he takes a more geometric approach to his work; this is easily identifiable by his artwork specifically Indian Red Series #2 (1979).

What was formerly the UBS Art Gallery in New York exhibited five decades of Tworkov's work in the 2009 show Against Extremes, "a tantalizing historical survey" charting everything from his de Kooning roots to his omnipresent "dream of freedom".