Abstract

In this article, I compare the formulation and applications of the “principle of permanence of equivalent forms” due to George Peacock, to whom the principle is first attributed, with the formulation and applications due to Hermann Hankel, the German mathematician to whom the popularity of the principle is owed. Despite Hankel’s explicit references to Peacock and the British algebraic tradition more broadly, I argue that Hankel’s project and applications of the principle show a rather different interpretation of the latter than what is to be found in Peacock, Hankel’s source. The principle has been regarded as key for the emergence of a broadly formalist understanding of mathematics. My claim is that it is only in Hankel’s understanding of the principle, but not in Peacock’s, that such a formalist outlook can be detected.