Generative artificial intelligence (GenAI) is widely regarded as a revolutionary tool for creativity and innovation, but does it actually lead to more groundbreaking ideas? Recent empirical evidence suggests otherwise. While GenAI improves the overall quality of ideas, it seems to reduce the likelihood of breaking new ground. This counterintuitive finding challenges GenAI's theoretical potential to enhance both the quantity and variety of ideas, including radical breakthroughs. By integrating the body of literature on cognition, creativity, and innovation with the emerging literature on AI, the paper identifies two limitations that hinder human-GenAI dyads from conceiving groundbreaking ideas: epistemic unidimensionality and compounded inertia. Furthermore, it conceptualizes two strategies to address these problems and examines the organizational factors that influence their effectiveness. The resulting framework provides a nuanced understanding of the hindrances that keep humans from breaking new ground with GenAI and the strategies that can be enacted to overcome them