The Fall and Rise of Resemblance Diagrams

Abstract

A recent investigation of the changes in the use of diagrams in published mathematics papers shows that diagrams were frequently used at the end of the 19th century and the beginning of the 20th. They then largely disappeared in the period 1910–1950, whereafter they reappear [1]. Although this story is unsurprising considering the dominance of formalist ideology in the first half of the 20th century, the detailed investigation of the development points out several interesting open questions. Especially, we do not know if the diagrams that disappeared with the advent of formalism are the same as those that are used today.

In this paper, we will focus on so-called “resemblance” diagrams, which are one of three general categories of diagrams covered in the investigation in [1]. We will analyze and compare resemblance diagrams used in the late 19th century with those used in the early 20th century to determine if there have been substantial changes. The comparison shows that even though the diagrams can be said to belong to the same general category and share certain general features, the resemblance diagrams used today are very different from those used before the advent of formalism. The criticism raised by the formalist movement of the diagrams used in the late 19th century can be seen as a possible explanation of this change.