Insights into the long “genesis” of Dedekind’s lattice theory

In two papers published in 1897 and 1900, Richard Dedekind presents and studies a new notion, the Dualgruppe, which corresponds to what is today called a “lattice”. This concept was the result of a long and, as Dedekind tells us, strenuous research process that lasted around twenty years.

Not only is it possible to identify, in Dedekind’s published works, the major steps of his work towards the notion of Dualgruppe, we also can follow the research process in his – rich and well-preserved – Nachlass. 

Indeed, in Dedekind’s Nachlass, one can find several hundred pages of research, notes and computations leading to the slow, progressive elaboration of the notion of Dualgruppe. These computations and the stepwise generalization of the concept largely disappear from the published exposition of the theory, which appears to be very general and abstract. The drafts highlight the working process and Dedekind’s exploration, through computations, tables, half-written papers…

Using Dedekind’s Nachlass, I will show how Dedekind gradually built his Dualgruppe theory through many layers of computations, often repeated in slight variations and attempted generalization. Insofar as these drafts were working tools for Dedekind, by studying the concealed strata of mathematics they contain, I wish to reveal and clarify the preliminary and intermediary states and steps of the mathematical research during the elaboration of the concept of Dualgruppe. 

While focused on Dedekind’s work, here, I also hope to stress the fruitfulness, for the history of mathematics, of taking into account the various notes and drafts left by mathematicians.