Final answer:
The statement about Theodore Roosevelt that is not true is that he was mayor of New York City. His political career, greatly shaped by his urge for adventure and progressivism, led him to be a significant figure in American politics but never as mayor.
Step-by-step explanation:
Option A: He was mayor of New York City, which is not true of Teddy Roosevelt. Theodore Roosevelt, despite his involvement in New York politics, never served as mayor of New York City.
Roosevelt's political career includes he was a member of the US Civil Service Commission, president of the New York City Board of Police Commissioners, Assistant Secretary of the Navy, and serving as Colonel of the First US Volunteer Cavalry, known as the Rough Riders. His career is marked by a series of progressive and ambitious political positions, fueled by both his family wealth and his drive for adventure and reform. Roosevelt's path of political appointments after surviving a great loss with his North Dakota ranch rigors, his national hero status from the Spanish-American War, and his ascendancy to Governor of New York, Vice President, and finally, President of the United States, showcase his dynamic leadership and immense influence on American politics during the Progressive Era.