Final answer:
The two significant 19th-century anthropologists were Franz Boas, who emphasized cultural diversity and the importance of field research, and Edward Tylor, known for his unilineal evolution theory.
Step-by-step explanation:
The two big anthropologists of the 19th century were Franz Boas and Edward Tylor. Boas, a German scientist initially trained as a physicist, became renowned for his role in the field of anthropology, particularly at Columbia University. He advocated for the meticulous gathering of ethnographic information directly from indigenous peoples and established the standards of field research, which are foundational in modern anthropological practices. His influential work also struck a blow against the ethnocentric and racist theories of the day, showing that cultural development is not linear but diverse, based on each culture's unique history and interactions.
On the other hand, Edward Tylor, a British anthropologist, proposed the now-obsolete theory of unilineal evolution, which suggested that cultures naturally progress through stages of 'savagery', 'barbarism', and ultimately 'civilization'. His theories reflect the ethnocentric perspective of the 19th century, which placed European civilization as the pinnacle of cultural evolution. However, Tylor's work on culture and religion also laid important groundwork for the anthropological study of comparative religions and the development of the field.