His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right".
Dilworth was born in 1914 in Hemet, California, at that time a remote desert ranching town.
He went to college at the California Institute of Technology, receiving his baccalaureate in 1936 and continuing there for his graduate studies.
Dilworth's graduate advisor was Morgan Ward, a student of Eric Temple Bell, who was also on the Caltech faculty at the time.
Other notable mathematicians advised by Dilworth include Curtis Greene and Alfred W. Hales.