The Shaping of Dedekind’s Rigorous Mathematics: What Do Dedekind’s Drafts Tell Us about His Ideal of Rigor?

Abstract

In this paper, I propose to examine Dedekind’s ideal of rigor in the context of some of his mathematical drafts. After a presentation of his ideal of rigor based on statements in his published works, I use drafts from his Nachlass to study his invention of the new concept of Dualgruppe (equivalent to our modern lattice). I question the extent to which these preliminary researches hold up to the same standards of rigor. Focusing on a specific law of Dualgruppe theory, I show that the elaboration of a rigorous work can be the outcome of a process that is not necessarily so. I put forward the trial-and-error and inductive aspects of Dedekind’s research practices. I consider whether the Dedekindian ideal of rigor guided mathematical research in its various phases, and what the consequences were of such an ideal of rigor, if any, on mathematical research.