The transition from formula-centered to concept-centered analysis Bolzano's purely analytic proof

as a case study

Iris Loeb

Stefan Roski

pp. 113-129

in: Gerhard Heinzmann (ed), Standards of rigor in mathematical practice, Philosophia Scientiae 18 (1), 2014.

Abstract

In the 18th and 19th centuries two transitions took place in the development of mathematical analysis: a shift from the geometric approach to the formula-centered approach, followed by a shift from the formula-centered approach to the concept-centered approach. We identify, on the basis of Bolzano's Purely Analytic Proof [Bolzano 1817], the ways in which Bolzano's approach can be said to be concept-centered. Moreover, we conclude that Bolzano's attitude towards the geometric approach on the one hand and the formula-centered approach on the other were of a different nature; the for­mer being one of rejection, the latter of non-participation. Bolzano supports his concept-centered methodology by philosophical views, which were partially shared by mathematicians with a formula-centered approach to analysis.

Cited authors

Bolzano Bernard