Final answer:
Franz Boas is the American anthropologist who argued that cultures evolve uniquely based on their own historical trajectories through interactions, challenging the linear cultural evolutionist views of his time.
Step-by-step explanation:
The American anthropologist who argued that each culture has its own unique patterns of thought, action, and expression, influenced by a certain theme that manifests in social relations, art, and religion, was Franz Boas. Boas challenged the ethnocentric and unilineal evolutionist views of cultural development that were common in the 19th and early 20th centuries.
He emphasized that cultures evolve not in isolation, but through interactions with each other, involving trade, migration, and conquest, thus forgoing a unique historical trajectory rather than following a linear, predetermined path. This view diverged from earlier anthropological theories, such as those of Edward Tylor and Lewis Henry Morgan, who posited that cultures evolve through a set sequence of stages leading towards what they deemed as civilization.
Franz Boas introduced a more dynamic and non-linear approach called historical particularism, recognizing the importance of historical context and the diversity of cultural experiences. Moreover, Boas's work laid the groundwork for 20th-century cultural anthropology, leading to a focus on the contested and dynamic nature of culture, including how it is experienced and expressed differently by various social groups within the same society, rather than as a monolithic entity endorsed unanimously by all members of a geographic area.