He was notable as an African-American attorney and leader in the civil rights movement.
Born on a farm near Sulphur Springs, Texas, Durham attended Emporia State University in Kansas.
After serving in the United States Army in France during World War I, he moved to Sherman where he studied law in the office of a white attorney, Benjamin F.
Durham spent the rest of his life fighting for equal rights for blacks in Texas, despite a race riot in Sherman in May 1930, where the black business district, including Durham's office, was burned.
His most famous case was Sweatt v. Painter (1950) which resulted in the integration of the University of Texas School of Law.