This chapter analyzes Lukas M. Verburgt’s historiographical framework for understanding transitions in the history of mathematics and scientific thought, particularly focusing on his concept of a ‘break’ between different intellectual frameworks. It examines how Verburgt’s model reveals the incompatibility between two images of knowledge, even when they are rooted in the same a priori principles, making reconciliation difficult. The chapter then explores the impact of Brouwer’s intuitionism on Soviet mathematicians such as Aleksandr Khinchin and Andrey Kolmogorov, showing how Brouwer’s ideas prompted them to critically reassess their assumptions. The chapter concludes by questioning Verburgt’s model, highlighting its limitations in explaining how framework transformation happen at the personal and communal level, and how individual mathematicians, motivated by social and political factors, either embraced or resisted new frameworks. It calls for a deeper exploration of these social and intellectual dynamics to fully understand such transitions.