New Objects, Questions, and Methods in the History of Mathematics

Abstract

This article sums up recent developments in the history of mathematics. The range of mathematics considered has considerably broadened, expanding well beyond the traditional field of original research. As new topics have been brought under consideration, methodologies borrowed from neighboring academic fields have been fruitfully put into use. In the first section, we describe how well-known questions—about the concept of proof and the nature of algebra—have been reconsidered with new questions and analytical concepts. We then sketch up some of the new research topics, among others the history of mathematical education, the inclusion of actors previously neglected, and the prominent role of bureaucracies in the cultural development of mathematics. The last section briefly retraces the development of the Zilsel thesis as a case study illustrating the previous points. Introduced in the mid-20th century, the theory that early modern craftsmen once played a decisive role in the mathematization of nature has recently led to very diverse fruitful studies about the nature and development of mathematical knowledge.