Christian Wolff’s Elementa Matheseos Universae, Methodology, and Mathematical Education

Christian Wolff (1679–1754), well known as a leading philosophical figure in the Enlightenment, has received relatively little attention from historians of mathematics despite his having had a vast mathematical production. The main reason for this neglect is that Wolff was not an original mathematician, his mathematical activity being predominantly devoted to the writing of textbooks and compendia. In this contribution, I shall survey his most successful textbook: Elementa matheseos universae. Originally published in two volumes in 1713–1715, it went through several editions and extensions throughout the eighteenth century, becoming a reference text for the teaching and learning of mathematics in continental Europe until about halfway through the eighteenth century. In my survey, I shall pay particular attention to Wolff’s methodological considerations, advancing the thesis that they should be understood in connection with his pedagogical concerns about teaching mathematics in the most proficient way.