Whereas traditional science maps emphasize citation statistics and static relationships, this paper presents a term‐based method to identify and visualize the evolutionary pathways of scientific topics in a series of time slices. First, we create a data preprocessing model for accurate term cleaning, consolidating, and clustering. Then we construct a simulated data streaming function and introduce a learning process to train a relationship identification function to adapt to changing environments in real time, where relationships of topic evolution, fusion, death, and novelty are identified. The main result of the method is a map of scientific evolutionary pathways. The visual routines provide a way to indicate the interactions among scientific subjects and a version in a series of time slices helps further illustrate such evolutionary pathways in detail. The detailed outline offers sufficient statistical information to delve into scientific topics and routines and then helps address meaningful insights with the assistance of expert knowledge. This empirical study focuses on scientific proposals granted by the United States National Science Foundation, and demonstrates the feasibility and reliability. Our method could be widely applied to a range of science, technology, and innovation policy research, and offer insight into the evolutionary pathways of scientific activities.