ABSTRACT
This presentation explores Christian Wolff’s (1679–1754) contributions to mathematical education, revealing a facet that historians often overlook despite his significant philosophical influence during the Enlightenment. Wolff, known for his extensive philosophical work, also made important contributions to mathematics, mainly through the composition of textbooks and compendia.
The focus of this talk is Wolff’s encyclopedic work on the elements of mathematics: Anfangsgründe der Mathematischen Wissenschaften (1713–1715). More precisely, I shall focus on Wolff’s essay on “the method”, which opens the first book of the Elements together with the long commentary in the fifth tome of the second Latin edition (1732–1742). Both texts underscore Wolff’s broader aim to guide the teaching of mathematical sciences, emphasizing the right way of learning in all parts of pure and mixed mathematics.
According to a tradition in the 18th-century German education context, Wolff’s textbook employs an approach that systematically presents mathematics from basic principles to advanced topics for a structured learning.
Wolff’s pedagogical views are rooted in his empirical psychology, which provides the basis for a hierarchical model of mathematical understanding articulated in three stages. The first stage focuses on understanding mathematical propositions through precise definitions. The second degree emphasizes conviction and logical arguments, progressing from mechanical proofs to more rigorous forms. The third degree highlights the highest level of discovery and creation, involving personal effort and creative thinking in unveiling new mathematical truths. This process is seen as foundational for advanced studies, particularly in algebra and calculus, representing a method of discovery in mathematical analysis. Wolff’s framework offers a structured approach to teaching and acquiring mathematical knowledge, progressing from understanding basic concepts to being convinced of mathematical truths and engaging in the creative process of discovering new insights.
Given the wide circulation of Wolff’s Latin edition of the Elementa in continental Europe throughout the 18th century, it is plausible that his guidelines significantly influenced teaching and learning practices in the region during that epoch. If time permits, I will survey the circulation of this influential text in Italy and the Habsburg Empire.
SELECTED BIBLIOGRAPHY
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