Born in Greenfield, Massachusetts, Stoddard studied art history at Williams College under the direction of Karl Weston, the charismatic chair of Williams's art department and museum.
Upon graduation in 1935, Stoddard decided to pursue his interests in art history by entering a doctoral program at Harvard University, where he worked with Chandler Post and Wilhelm Koehler on the sculpture of Chartres Cathedral.
Alongside colleagues S. Lane Faison and William Pierson, Jr., he trained a new generation of art history students at Williams for careers as art historians and museum curators.
Under his leadership, the Williams art history program developed into one of the finest undergraduate curricula in the country.
Stoddard, Whitney S. Sculptors of the West Portals of Chartres Cathedral: Their Origins in Romanesque and Their Role in Chartrain Sculpture: Including The West Portals of Saint-Denis and Chartres.