Digitising Euler: 21st-century methods for the study of 18th-century mathematics

Cretney, Rosanna Elizabeth (2016). Digitising Euler: 21st-century methods for the study of 18th-century mathematics. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f6c8

Abstract

This thesis aims to introduce ideas and methods from the emerging field of digital humanities into the study of history of mathematics, through case studies relating to the role of correspondence, communication, and collaboration in Leonhard Euler's mathematical practice. Euler's known correspondence numbers almost three thousand letters, exchanged with hundreds of correspondents from across Europe. The correspondence is a vital source for understanding Euler's mathematics, but it has not yet been examined in great detail; this thesis is a contribution towards such a study.
The thesis is motivated by a case study which highlights the central role of correspondence and personal contact in Euler's work on continued fractions. A desire for better understanding of the correspondence leads to the use of methods from the digital humanities, a relatively young field which has been evolving rapidly since the beginning of the 21st century. The thesis considers the particular challenges encountered when using such methods in the study of eighteenth- century mathematical texts. A database is used to facilitate the exploration and comprehension of Euler's correspondence. This enables the identification of a corpus of letters, all connected with the same mathematical topic, which would be suitable for further study. A prototype digital edition of one of these letters is presented, featuring a transcription, editorial annotations, and digital facsimiles of the original manuscript. Finally, it is shown how existing digital tools that were designed for use in other fields, such as mathematics and cartography, may be appropriated to aid understanding of primary sources in the history of mathematics.