Final answer:
The role referred to as 'the most insignificant office that was the invention of man' is the vice president.
Step-by-step explanation:
The role that has been referred to as 'the most insignificant office that was the invention of man' is the vice president. This quote is often attributed to former U.S. Vice President John Nance Garner, who held the position from 1933 to 1941. Garner reportedly made this statement to emphasize the lack of influence and power traditionally associated with the vice presidency.
Learn more about Role of the vice president in the U.S. government