Final answer:
Daniel D. Tompkins was the vice president of the United States under James Monroe, serving from 1817 to 1825.
Step-by-step explanation:
The vice president of the United States under James Monroe was Daniel D. Tompkins. He served as vice president during both of Monroe's terms as president, from 1817 to 1825. Despite the political turmoil and shifts occurring toward the end of Monroe's presidency, particularly during the presidential race of 1824 with the emergence of party politics and regional candidates, Tompkins remained as vice president throughout the Monroe administration's duration. This period was marked by developments such as the Corrupt Bargain and the influential role of figures like Martin Van Buren and John C. Calhoun. However, it's important to note that Tompkins, despite being Monroe's vice president, was not a central figure in the election of 1824 or the succession politics that followed.