Creatively Undecided offers a new way to look at how scientific understandings change. Thomas Kuhn has shown us how scientific practice and thinking depends on the normative framework in which it is conducted, but he and his followers have failed to show how such frameworks can be deemed the possible outcomes of the kind of critical assessment that Popper viewed as central to all rational deliberation. How can a scientist subject her standards to rational appraisal if that very act requires the use of those standards? The novel way out argued for in the book is to realize that exposure to external normative criticism is capable of destabializing normative commitment to a far greater extent than mere self-critique. Therefore, while science can only be transformed from within, by people who have standing in the field, criticism from the outside is essential. We may not be able to be sufficiently self-critical on our own, but trusted criticism from outside, even if resisted, can begin to change our perspective—at which point transformative self-criticism becomes a real option. The book’s novel thesis, argued for philosophically in the first four chapters comprising Parts I and II, is put to the test of a detailed case study in the history of British mathematics in Part III.