Shulman was born in Russia in 1903. He emigrated to the United States in 1912. He earned his B.A. from Brown University in 1923. He earned an LL.B., and S.J.D. from Harvard Law School, in 1926 and 1927 respectively. He practiced law briefly in New York City before clerking for Justice Louis Dembitz Brandeis from 1929 to 1930.

In 1930, became an instructor at Yale Law School. By 1931, he was an Assistant Professor of Law. He became an Associate Professor in 1933, and a Professor in 1937. He became a Lines Professor in 1939, and a Sterling Professor in 1940. He was a superb teacher.

His scholarly work concerned torts, administrative law scholarship, and labor contracts. His lecture, “Reason, Contract, and Law in Labor Relations,” has been cited hundreds of times.

In July 1954, he became Dean of Yale Law School. He died in 1955 from cancer. A scholarship fund was established in his honor in 1955, a research fund in 1957, and a library fund in 1963.

Shulman was “one of the most influential people in the history of American Labor arbitration.” He was known as an arbitrator of even temperament, common sense, good humor, and exceptional judgment. He was an associate member of the National War Labor Board. He also served on the Connecticut Labor Relations Board and the Alien Enemy Hearing Board of Connecticut.He led a panel on steel workers wages during the 1952 steel strike. He also helped arbitrate an aircraft industry workers' collective bargaining case in 1952, which resulted in a 14 cent an hour wage increase. He was a member of of the Wage Stabilization Board during the Korean War. Many of the cases that Shulman handled involved violence.