Final answer:
The most important characteristic of Oligocene primates is the appearance of fossil monkeys with dental formulas indicative of later monkey species, marking a significant shift in primate evolution.
Step-by-step explanation:
The most important characteristic of Oligocene primates reflects the emergence and diversification of early monkeys as evidenced by the significant fossil discoveries at the Fayum site in Egypt. These primates are characterized by features indicative of both New World and Old World monkeys. Most notably, they possess a dental formula with a third premolar consistent with later monkey species, contributing to our understanding of primate evolution and the lineage leading to modern primates.
Dental features of these Oligocene primates suggest adaptations that could have contributed to their evolutionary success, representing a major shift from the prosimian dominance of the Eocene. With the appearance of early monkeys, the primate family tree became more complex and set the stage for the continued evolution of simians, which includes monkeys, apes, and humans.