Alexander Hamilton (definitely not a President), left, and Millard Fillmore (definitely was a President), right.

If serving as President of the United States doesn’t earn a person an unforgettable place in history, what does? Ask Alexander Hamilton and Millard Fillmore, two notable examples of American statesmen who defy the conventional wisdom of what it takes to be remembered.

A recent study published in the journal Psychological Science showed that 71 percent of those questioned identified Alexander Hamilton as one of the men who served as President of the United States. While that may be flattering to Hamilton, it is also untrue. Hamilton served as the nation’s first Secretary of the Treasury, but he died before ever getting the chance to take the top job.

Remarkably, Hamilton’s recognition rate as a President — even though he wasn’t one — was higher than the recognition rate for several men who actually held the office. Among those who legitimately served as Chief Executive, but who failed to gain as much recognition as Hamilton, were Presidents Chester Arthur, Franklin Pierce, Millard Fillmore, Benjamin Harrison, John Tyler, Warren Harding, Zachary Taylor, Rutherford Hayes, and Martin Van Buren.