How many years old is the city of Rome?

How to get close to this number

Subtract from the traditional founding date of 753 BCE. Adding the years since gives something under three thousand, and the arithmetic is straightforward once you have the date — which is one of the most widely taught in European history.

The word "traditionally" is doing real work. The founding date comes from Roman legend rather than from evidence, and archaeology shows settlement on the site earlier and more gradually than a single founding year implies. Ancient founding dates are almost always national myths given a calendar entry.

The population history in the explanation is the more remarkable fact: over a million in the second century, collapsing to around twenty thousand in the Middle Ages, and only recovering in the 1930s. A city losing ninety-eight percent of its population and taking seventeen centuries to recover is a scale of decline and revival with almost no parallel.