Abstract

This paper traces August Comte’s attempts to get clear about the concept of mathematical analysis at various stages in his intellectual development. Comte was especially concerned with distinguishing a method of analysis for the resolution of complex prolems from analysis in the sense of a method of drawing inferences. Geometrical analysis serves as his model for the former. In his attempt to get clear about this notion, he discovers an historical succession of different methods all of which may be labeled “analytic.” In modern terms, Comte reveals how each of these methods of analysis characterizes a research program in mathematics, even showing us how more powerful methods came to supplant less powerful methods of analysis.