The origins of the fundamental theorem of surface theory

The Mainardi-Codazzi equations (MCE) and the fundamental theorem of surface theory (FT) are regarded as crucial achievements in the development of surface theory. The paper offers an analysis of three papers by Bour, Codazzi and Bonnet, submitted on the occasion of the Grand Prix des Mathématiques (1859), in which the MCE and the FT were systematically employed to deal with applicability problems. Our analysis provides a new insight into the historical process leading to a recognition of the relevance of the MCE and the FT and helps explaining why previous contributions on the subject could go unnoticed for years.