Who was the vice president under both President McKinley and President Roosevelt?

The correct answer to the question is Theodore Roosevelt. He served as vice president under President William McKinley and subsequently became president himself after McKinley's assassination in 1901. Roosevelt's tenure as vice president lasted from March 4, 1901, until September 14, 1901, when he ascended to the presidency.

This specific historical context highlights Roosevelt's significant role in American politics at the turn of the 20th century, including his progressive policies and leadership style. Understanding Roosevelt’s influence in both capacities is vital, as it laid the foundation for his subsequent achievements during his presidency, including trust-busting and conservation initiatives.