This chapter explores how Brouwer’s intuitionistic program was interpreted and transformed by Hermann Weyl and Arend Heyting, each offering distinct versions of intuitionism that prompted varied responses from the mathematical community. Brouwer’s vision, rooted in his philosophical ideals, sought a profound reworking of mathematics’ foundations. Weyl, drawing from idealism and phenomenology, embraced Brouwer’s ideas but modified them to suit his own philosophical framework, while Heyting, taking a more formal approach, restructured intuitionism in a way that made it more approachable to classical mathematicians by removing its more mystical elements. The chapter argues that the community’s differing reactions to these three versions were not merely practical but reflected deeper divergences in how each mathematician viewed the normative boundaries of the discipline. Using Corry’s two-tiered model of mathematical knowledge, which distinguishes between the body of knowledge and its guiding principles, the chapter shows that Heyting’s formalization impacted both layers, engaging mathematicians more broadly than the more philosophically driven approaches of Brouwer and Weyl. Ultimately, the analysis suggests that radical changes to the image of mathematics are more likely to gain acceptance when they are framed in familiar terms.