Back at the peak of the Aztec empire, meanwhile, the emperors had things to do. Each one had to enlarge the pyramid-temple that dominated Tenochtitlan. Each one had to aggressively expand the empire. If they did not, their reigns proved suspiciously short, and they were succeeded by more bellicose rulers, of which there was by now (thanks to Acamapichtli's stalwart efforts) an endless supply. At its peak the Empire, which extended right across middle America, was astonishingly prosperous, with a population of many millions and cities numbering hundreds of thousands of inhabitants. It did, however, depend upon the subjugation of people unwilling to be subjugated, but who were unwisely allowed to keep their own militias. Which is why, when Hernan Cortes and his Spanish cohorts rolled up with their weapons of mass destruction and their no less deadly European diseases, they found a surprising number of enthusiastic allies waiting for them.

Montezuma's island capital of Tenochtitlan, at the time the Spanish arrived, was one of the largest cities in the world and a wonder to behold. 250,000 people lived there. With its waterways, bridges and aqueducts, the invading soldiers and priests likened it to Venice. Others, struck by the massive central feature of the great temple-pyramid, described it as an enchanted kingdom from a fairytale. So what? They destroyed it, without compunction. The great buildings were demolished, the golden treasures sent back to Europe to be melted down to finance wars, the religion suppressed. Spanish policy was systematically to eradicate all traces of the Aztec civilization. In this they were remarkably successful, but they had not counted on two things. First, the Aztecs buried or otherwise hid many of their finer trinkets. Second, when the Aztec monuments were reduced to rubble to make other buildings - like the new Renaissance-style cathedrals, churches and monasteries - nobody thought of a future activity known as archaeology, which would reveal them all again.

So plenty escaped. When the foundations of what was to become Mexico City were being laid on the site of Tenochtitlan and its drained lakebed in 1790, Aztec artifacts started to be dug up. Already by this time, archeology was a growth industry. The Aztec remains fitted in with the new idea of Mexican nationhood. Finds were collected. The first federal republic of Mexico was set up in 1825, and a national museum founded. The first London exhibition of Aztec objects took place as early as 1824. The discoveries accelerated, and continued all through the 19th and 20th centuries.

By the time Montezuma (more properly spelled Motecuhzoma) and his son yielded to Cortes and his army of disenchanted former subjects, the leaders of the Aztec empire had become rather too numerous and too accustomed to extravagant luxury. "They had copper, and they had gold, but they did not have steel," as Adrian Locke puts it. He does not need to add that the Spanish had plenty of steel. They had plenty of technology, and a hunger for new lands. In contrast, the Azttecs had too many chiefs, all wanting cosseting. Too many makers of the Aztec equivalent of Louis Vuitton luggage. Not enough jobsworths to keep the empire in order, collect the taxes, act on intelligence. Which suggests that the empire would have disintegrated anyway. Both Locke and Rosenthal share this view.

"Like the great cities of the region before them, which were based on trade networks, were highly influential for a period of time and then suddenly went into decline, there is a sense of inevitability that Tenochtitlan would have gone the same way," says Locke. "The more refined the culture became, the more people you needed to make the artworks, to be the nobility, to be the priesthood. All these people were paying no tax. It was a top-heavy society that had to be supported in some form or other by the state."