His research interests shifted from several complex variables and differential geometry to discrete inverse problems in the middle of his career.

Morrow was born in Little Rock, Arkansas and attended high school in Dallas, Texas.

His dissertation "The Topological Type of Non-Singular Deformations of Singular Surfaces" was written under the supervision of Kunihiko Kodaira.

[2] In 2005, Morrow received the Pacific Institute for the Mathematical Sciences (PIMS) Education Prize, which recognizes mathematicians who have "played a major role in encouraging activities which enhance public awareness and appreciation of mathematics, as well as fostering communication amongst the various groups and organizations concerned".

In that same year he was awarded a University of Washington College on Arts and Sciences Alumni Distinguished Professor.