Karl M. Peterson: The earliest derivation of the Mainardi-Codazzi equations and the fundamental theorem of surface theory

In 1853 Karl M. Peterson, a young Latvian student at the University of Dorpat Tartu], submitted a candidates' dissertation a requirement for obtaining a degree] containing a derivation of the Gauss-Mainardi-Codazzi equations and a proof of the Fundamental Theorem of Surface Theory. This predates the publications of equivalent equations derived by G. Mainardi 1856] and D. Codazzi 1860 and 1868–1869], as well as O. Bonnet's proof of the Fundamental Theorem. Although Peterson later 1865–1881] played a major role in the formation of a school of differential geometry at Moscow University, this early work remained virtually unknown until its translation into Russian] and its publication in 1952. The contents of the dissertation and the probable sources of Peterson's ideas and techniques are discussed.