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Scientific progress is driven by innovation-which serves to produce a diversity of ideas-and imitation through a social network-which serves to diffuse these ideas. In this paper, we develop an agent-based computational model of this process, in which the agents in the population are heterogeneous in their abilities to innovate and imitate. The model incorporates three primary forces: the discovery of new ideas, the observation and adoption of these ideas, and the endogenous development of networks. The objective is to explore the evolving architecture of problem-solving networks and the critical roles that different agents play in the process. A central finding is that the emergent network takes a chain structure with innovators (those most skilled at generating new ideas) being the main source of ideas and those most skilled at imitating acting as connectors between the innovators and the masses. The impact of agent heterogeneity and environmental volatility on the network architecture is also characterized.