Aztec Triple Alliance

That is the first thing to grasp about the alliance: it was not a state that ruled territory. It was a cartel that ruled people. Conquered towns kept their own kings, gods, laws and land. What they lost was the right to decide their own foreign policy and a share of their annual produce, paid in cotton cloth, cacao, feathers, maize, salt, dye, jade, gold dust, rubber, paper, incense and, occasionally, in labour and in bodies for sacrifice. The alliance's armies marched out every dry season, and its tribute collectors arrived twice a year. In between, most of the empire ran itself.

The polity matters for three reasons. It was the dominant power in Mesoamerica when Europeans arrived, with perhaps five to six million people inside its tribute network and a capital city whose population is put at 150,000 to 250,000. It left the best documentation of any pre-Columbian American state: not only chronicles written down after the conquest but pictorial tribute rolls that itemise, town by town, what was expected to arrive each year. And it is the clearest historical case of what archaeologists call a hegemonic empire, in which power is exercised through clients and the credible threat of violence rather than through garrisons and governors. Whether that model was a deliberate design or simply the limit of what the Mexica could manage is one of the live arguments in the field.

At a glance

Why did three cities destroy Azcapotzalco in 1428?

In the fourteenth century the Basin of Mexico was a lake full of rivals, and a day's walk north of it stood the empty ruins of Teotihuacan, whose builders nobody could name and whose authority every later dynasty in the valley claimed some share of. Some fifty city-states, called altepetl in Nahuatl, ringed the five lakes, each with its own dynasty, temple pyramid and tract of chinampa farmland. None could dominate the others for long. The Mexica, who founded Tenochtitlan on an island in 1325, arrived last and got the worst land; for a century they survived by hiring out their soldiers.

Their patron was Azcapotzalco, the Tepanec city on the western shore, whose king Tezozomoc built the first real empire in the valley. Tenochtitlan fought for him, and was rewarded with a share of the spoils and with the legitimacy that came from marrying into the old Culhua line. By the 1410s Tezozomoc had broken the Acolhua kingdom to the east and killed its king, Ixtlilxochitl, in 1418. Ixtlilxochitl's son Nezahualcoyotl spent the next decade in exile, hiding in the hills and, according to his own descendants' accounts, in the household of the Mexica king.

Then the machine jammed. Tezozomoc died in 1426, and the succession passed to a son, Maxtla, who murdered or drove out everyone he suspected. The Mexica king Chimalpopoca died in 1427, almost certainly on Maxtla's orders. Tenochtitlan chose a new king, Itzcoatl, an illegitimate son of the old dynasty with a soldier's reputation, and refused the demanded submission. Maxtla put the city under blockade.

The war that followed is the founding story of the alliance, and it is told in some detail by chroniclers writing a century later, with all the tidying that implies. Itzcoatl sent to Nezahualcoyotl, who brought Huexotzincan mercenaries from the Puebla valley. He also found a defector inside the Tepanec system: Tlacopan, a Tepanec town on the western shore with its own dynastic ambitions, whose king Totoquihuatzin agreed to change sides. The three armies attacked Azcapotzalco, stormed it, burned the temple and dispersed the population. Maxtla fled and was caught, probably at Coyoacán, and killed.

The dates have never quite settled. The campaign is put in 1427 or 1428, the fall of the city in 1428, and the formal treaty anywhere from 1428 to 1430. The chronology used here begins in 1429, which is as defensible as any of them and has the merit of marking the alliance rather than the battle. What is not in doubt is the sequence: a subject city, a client town and an exiled dynasty combined to destroy the power that had employed all three, and then divided it.

What did the three cities actually agree?

The treaty of the Triple Alliance was a division of spoils that turned into a constitution. Azcapotzalco's lands were carved up; Tlacopan took the western shore, Texcoco the eastern lake and the Acolhua hinterland, Tenochtitlan the island and the southern chinampas. The three kings swore to campaign together, to hold future conquests in common rather than dividing them into three separate empires, and to split the proceeds.

The split is the most quoted fact about the alliance and the easiest to get wrong. It was not three equal shares. The tribute from jointly conquered provinces was divided into fifths: two to Tenochtitlan, two to Texcoco, one to Tlacopan. Tlacopan's fifth was the price of its defection and the recognition of its smaller size; Texcoco's two-fifths reflected a city that was then the alliance's cultural senior, with the most prestigious dynasty and the largest library of painted histories. Tenochtitlan's two-fifths were, in 1428, no more than parity with Texcoco.

Each king also took the title huey tlatoani, "great speaker", which placed him above the mere tlatoani of an ordinary city-state. In principle the three were equal within the alliance. In practice the title became a marker of seniority, and by the reign of Ahuitzotl the Mexica king was using a doubled form of it to claim precedence over his two partners. Modern accounts often call the Mexica ruler "emperor" and the others kings; that is a translation convenience, not a distinction the sources make cleanly.

The alliance was renewed, in effect, at every succession, because each new huey tlatoani had to be accepted by the other two and had to lead a campaign to prove himself. This is why the deaths of kings are such reliable punctuation in the narrative: 1440, 1469, 1481, 1486, 1502, 1520. Each accession produced a rebellion somewhere, put down in the first year or two of the new reign, and each rebellion was an opportunity for the other partners to renegotiate. The alliance was less a fixed institution than a standing agreement between three dynasties that intermarried constantly and competed for precedence without ever quite going to war with one another.

That internal peace is the alliance's real achievement, and it is easy to underrate. For ninety years the three biggest cities in the valley did not fight each other. Tenochtitlan's eventual dominance was achieved not by conquering its partners but by outgrowing them: by absorbing Tlatelolco in 1473, by taking the largest share of new conquests, and by making its king the arbiter of the whole system. By 1519 Texcoco had been reduced to a junior partner and Tlacopan to a small one, but both still had their own kings, courts and revenues, and both still mattered.

How did Moctezuma I turn a war cartel into an empire?

Itzcoatl died in 1440, and his successor Moctezuma I inherited a valley hegemony and a set of ambitions that went well beyond it. Moctezuma, called Ilhuicamina, "he who shoots at the sky", ruled until 1469 and is the ruler most responsible for the shape the empire took. He worked with two men: Nezahualcoyotl of Texcoco, who was the strategist and lawgiver of the alliance, and his own half-brother Tlacaelel, who held the new office of cihuacoatl, something between chief minister and vizier, and who appears in the chronicles as the ideologue of Mexica destiny.

The first move was ideological. The Mexica had been a subject people with an obscure patron god; they now became the chosen people of Huitzilopochtli, the hummingbird of the left, a solar war god whose cult required captives. The chronicles report that Itzcoatl ordered the old painted histories burned, on the grounds that they gave the wrong account of the Mexica's origins, and had a new one painted. The new history gave the Mexica a line of kings descended from the Toltec lords of Tula and a migration out of a place called Aztlan that ended on the island their god had chosen. Whether that burning happened on the scale later sources claim is uncertain; that the official history was rewritten is not.

The second move was administrative. Moctezuma replaced unreliable dynasts with men of his own choosing, and installed calpixque, tribute stewards, in conquered provinces to collect directly from the towns rather than through their kings. He also began the practice of granting subject lords estates far from their own cities, so that rebellion cost them income they could not defend. Nezahualcoyotl did something similar in Acolhua territory. These are small innovations, but they are the difference between raiding and ruling.

The third move was expansion, and here the natural disasters mattered as much as the politics. In 1449 the lake flooded Tenochtitlan. In 1450 a frost and then a drought destroyed the harvest, and the drought held for four years. The chronicles describe famine so severe that parents sold their children into slavery and the city emptied. Moctezuma's response was to open the state granaries, remit tribute in the worst-hit provinces and, when the cycle turned, to preside over the New Fire ceremony of 1455 that marked the end of a fifty-two-year count. Then he went to war on a larger scale: Cuauhnahuac and Huaxtepec in the warm country south of the valley, Coixtlahuaca and the Mixtec towns of Oaxaca, and the Huastec and Totonac lowlands on the Gulf.

The Gulf campaign mattered for a reason that runs through the whole history of the empire. It gave the alliance access to things the highlands could not produce: cotton, cacao, rubber, tropical bird feathers, marine shell, and the dyes that made both. The Mexica began to call themselves "neighbours of the sea of the sky", a title that was half boast and half economic policy. An empire of the basin would always have been poor. An empire that reached both oceans could dress its nobility in things nobody else in the valley could get.

How was the empire governed without provinces?

The unit of government was the altepetl, the city-state, and it never went away. An altepetl was a town with its own king, its own patron god, its own land and its own commoner population organised into wards. The empire was built by stacking these units, not by replacing them. When a town submitted, its king stayed on his throne, kept his gods in his temple, kept his law courts and his land, and took on three new obligations: tribute at fixed intervals, military service when called, and acceptance of the alliance's foreign policy.

Above the towns sat the tributary province, an administrative fiction that grouped a dominant town and its dependants for the purposes of assessment. The Codex Mendoza lists thirty-eight of them. A province was not a governed territory in the Roman or Chinese sense. It had no governor with a staff, no provincial capital with a garrison, no uniform law. It had a tribute schedule and a steward. The steward, the calpixque, was a Mexica official who might live in the province or visit it, who kept accounts on painted paper, and who had the authority to demand arrears. He did not administer justice, collect taxes for local purposes, or command troops. He collected.

Beyond the provinces lay a range of relationships that the sources distinguish but modern summaries tend to flatten. Some towns were conquered outright and had their kings replaced. Some submitted after a demonstration campaign and kept everything. Some were client states that paid tribute and fought for the alliance but were never formally conquered. Some were buffer states, left independent because their independence was useful. And some, notably Tlaxcala, Huexotzinco and Cholula in the Puebla valley, and the Tarascan state of Michoacán to the west, were enemies the alliance could not take and never stopped probing.

The empire had no standing army. This sounds like a weakness and was in fact a piece of design. The alliance could field enormous forces — the chronicles speak of tens of thousands, and the logistics of feeding them from the lake's granaries were real — but only for a season, because the soldiers were farmers. Campaigns ran from late autumn to early spring. A city that submitted in January might reconsider by July, and often did. The result was a permanent low-level insurgency at the edges, and a permanent cycle of reconquest that the Mexica turned into a ritual of kingship.

What held it together was not force but a mixture of interest, ideology and information. Subject lords were tied to the capitals by marriage, by honours, by invitations to festivals, by the loan of Mexica troops against their own local rivals, and by the simple fact that the alliance's markets were where wealth was. The pochteca, long-distance merchants who travelled in armed caravans, doubled as intelligence officers: they reported on roads, harvests and the mood of distant lords, and they were privileged enough to be consulted by the king before campaigns. Above all, the system was cheap. A garrison in every province would have cost more than the tribute was worth. A steward with a painted account book cost almost nothing.

What do the tribute rolls actually record?

The evidence for all this is unusually concrete, and it comes from two painted manuscripts. The Matrícula de Tributos is a sixteenth-century screenfold on amatl, fig-bark paper, of sixteen surviving folios, each devoted to a single province, with a couple of exceptions. On each page the place-glyph of the province's capital sits at the lower left, the towns that belonged to it run up the margin, and the goods owed are painted across the rest, each item marked with a number. The counting system is pictorial: a white flag for twenty, a feather for four hundred, a pouch for eight thousand. The manuscript is held in Mexico City by the Instituto Nacional de Antropología e Historia.

The Codex Mendoza is the fuller document and the stranger one. It was made in 1541, twenty years after the conquest, on European paper, by Nahua scribes working under Spanish supervision for the viceroy Antonio de Mendoza, who wanted to show the Spanish crown what it had acquired. It has three parts: a history of the Mexica kings and their conquests, a tribute roll, and an ethnographic section on daily life from birth to burial. The tribute section is essentially a copy of the Matrícula, with five provinces added that are missing from the surviving Matrícula. The manuscript was shipped to Spain, captured by French privateers, bought by the cosmographer André Thevet, passed through Richard Hakluyt and Samuel Purchas, and reached the Bodleian Library in 1659, where it lay unread until 1831.

What the rolls record is an assessment, not a receipt. They tell us what a province was expected to deliver, and at what interval — twice a year for many, four times for some — and they tell us the categories of goods in extraordinary detail. Cotton mantles by the thousand, in specified sizes and designs. Maize and beans by the granary-load. Cacao by the sack, from the Soconusco province on the Pacific slope of Chiapas, an exclave of the empire five hundred kilometres from the capital. Feathers: quetzal plumes from the tropical forests, used for the warrior costumes and shields that the rolls also list. Salt from the lakeside towns. Red cochineal dye, which would become one of the great exports of colonial Mexico. Jade, turquoise, gold dust, amber, crystal, rubber balls for the ball game, paper, copal incense, and live eagles for the aviary.

What the rolls do not record is just as revealing. There is no assessment of land, no census, no register of households. Labour service — the building of temples, roads, canals and palaces — is largely invisible, as is military service. The rolls are also silent on whether the goods actually arrived. For that we have to fall back on the chronicles, which record arrears, punitive expeditions and remissions after famine, and which are not disinterested.

The Matrícula's date is genuinely unsettled. Frances Berdan argued in 1980 that it was painted before the conquest, on the grounds that it shows no European influence beyond the glosses; Luz María Mohar argued in 1997 for a colonial date, within twenty years of the conquest; Juan José Batalla Rosado's analysis of six different painting hands supported a pre-conquest compilation; and in 2021 Jorge Gómez Tejada proposed that the leaves are of mixed date, some painted at the very end of the pre-conquest period and some as late as 1560. If any of it is pre-conquest, it is the only surviving Aztec manuscript of its kind, which is a large claim to hang on a stylistic argument.

Both documents have to be read as colonial objects as well as indigenous ones. The Mendoza was made for a viceroy who wanted to know what his new subjects could pay, by scribes who knew what a viceroy wanted to see. The tribute figures may well be conservative, and the picture of a tidy empire of thirty-eight provinces may be tidier than the empire was. But the goods are real, the towns are real, and the numbers are internally consistent across three independent documents — the Matrícula, the Mendoza and a colonial-era tribute list from Tlapa — which is about as good as pre-Columbian economic evidence gets.

Why did the alliance never conquer Tlaxcala?

To the east of the basin, over the volcanoes, lay a pocket of city-states that the alliance never conquered. Tlaxcala was not one city but a confederation of four lordships — Tepeticpac, Ocotelolco, Tizatlán and Quiahuiztlán — sharing a small, poor, hilly territory and a ruling council. Around it lay Huexotzinco and Cholula, both large and both, at different times, allied to one side or the other. This pocket was surrounded on three sides by the empire for most of a century and remained independent until the Spaniards arrived.

The alliance's answer was a kind of war the sources call xochiyaoyotl, flower war. It differed from ordinary campaign warfare in ways the chroniclers describe with some precision: a fixed day and a fixed field agreed in advance, sometimes marked as sacred ground; no ranged weapons, so that fights came to close quarters with the broad-bladed macuahuitl; equal numbers on each side; a smaller proportion of commoners and a larger proportion of noble warriors; and a licence to fight outside the agricultural season, because it did not require the whole levy. Captives were taken rather than killed, and the point of taking them was sacrifice.

Why the alliance should fight in this way rather than simply conquering Tlaxcala is one of the oldest arguments in Aztec studies, and the sources do not settle it. The classic explanation comes from the Texcocan historian Fernando de Alva Ixtlilxochitl, writing in the early seventeenth century: the famine of 1450–54 convinced the priests that the gods were angry, and the rulers of Tenochtitlan, Texcoco, Tlaxcala, Cholula and Huexotzinco agreed to stage wars so that each could supply itself with sacrificial victims. The story is repeated in most modern summaries. It has one serious weakness: Ixtlilxochitl is the only source that tells it, and he does not use the term flower war.

The second explanation is training. Moctezuma II, asked by a Spanish captain why he had never destroyed Tlaxcala when he plainly could, is said to have replied that the wars were a convenient way of exercising his troops and of getting captives for the gods. That answer is reported second-hand, at third hand, decades later, and it is exactly the answer a defeated king might be made to give in a Spanish account. But it is consistent with the way the Mexica trained: young noblemen needed live opponents, and a flower war gave them a bounded, repeatable one.

The third explanation, argued most sharply by Frederic Hicks and developed by Ross Hassig, is that flower wars were ordinary strategy by other means. Muñoz Camargo, a Tlaxcalan mestizo historian who knew the ground, describes Mexica armies besieging Tlaxcalan towns and cutting off their trade — behaviour that makes no sense as a ritual tournament and a great deal of sense as attrition. On this reading the alliance could not conquer Tlaxcala at acceptable cost, because the terrain favoured defence and the Tlaxcalans could put every adult on the wall, so it fought a war of blockade and raid that wore the enemy down while keeping its own army sharp. Hassig's argument is that flower war was a cheap way of sustaining a conflict that could not be settled outright, and of putting on a show of force that might detach the enemy's allies.

All three explanations can be true at once, and probably are. What the flower wars were not is a game. Deaths were real, and over time the conventions eroded: the Chalca wars began with few fatalities and ended with the killing of captured nobles. The tribute rolls also show the economic side of the same policy. Tlaxcala was under a standing boycott — salt, cotton and metal goods were withheld — which forced it into a permanent subsistence economy and kept it poor. When Cortés arrived in 1519, the Tlaxcalans had been encircled, embargoed and bled for two generations, and they were the first people in Mexico with an obvious reason to help him.

What did Axayacatl, Tizoc and Ahuitzotl add?

Moctezuma I died in 1469 and was succeeded by his son Axayacatl, whose twelve years were spent holding what his father had taken. The great event of his reign was domestic: in 1473 he annexed Tlatelolco. The two cities had grown together on adjoining islands and were rivals in trade rather than in war; Tlatelolco had the greater market. A pretext was found in an insult offered by Tlatelolcan nobles, the Mexica army stormed the sister city, and its king Moquihuix was killed, either in the fighting or by his own hand. Tenochtitlan absorbed the market and the merchant community, and from that point the Mexica were the dominant partner in the alliance in fact as well as in title.

Axayacatl also fought the Tarascans. The Tarascan state of Michoacán, west of the valley, was the one power in Mesoamerica that could match the alliance in size, and it had bronze tools and a disciplined army. In 1478 the Mexica invaded and were destroyed on the frontier, at a place the sources call Taximaroa; the figures given are absurd — thirty-two thousand Mexica against fifty thousand Tarascans — but the outcome is not in doubt. Axayacatl was wounded and never campaigned in the west again. It was the first serious defeat the alliance had suffered, and the chroniclers treat it as a wound to the king's reputation that never healed. Some modern accounts date the campaign to 1479 and some to 1476; the year is not secure.

Tizoc followed in 1481 and lasted five years. He put down a revolt in the Toluca valley, began the rebuilding of the Templo Mayor, and commissioned the carved stone that bears his name, on which he is shown grasping a captive by the hair while the gods look on. The stone is propaganda of a defensive kind: it asserts a military prowess the reign did not deliver. The chronicles say he lost several campaigns, that the nobles despised him, and that he died in 1486 of poison, though illness is also given. He is the one Mexica king whose reign the sources treat as a failure.

Ahuitzotl, his brother, succeeded him and was the greatest of the Mexica conquerors. In sixteen years he more than doubled the territory under tribute, taking the Oaxaca valley, the Mixtec and Zapotec towns, the Pacific coast of Guerrero, and the Soconusco cacao country on the Chiapas slope, and pushing the frontier west against the Tarascans with a string of fortified towns. He completed the Templo Mayor in 1487 and dedicated it with a sacrifice whose scale the chronicles report in figures that cannot be true: Durán gives 80,400 victims over four days, a number that would have required a killing every four seconds, day and night, without pause. The ceremony was enormous and it was meant to be seen; the arithmetic is not evidence.

Ahuitzotl's reign is also where the alliance's internal balance tipped for good. He began to style himself huehuetlatoani, "elder speaker", to distinguish himself from the kings of Texcoco and Tlacopan. The title was a claim, and it stuck. He died in 1502, in an accident the chronicles describe with unusual specificity: fleeing a flood in the city, he struck his head on a lintel and died of the injury.

How did Moctezuma II lose what his predecessors had built?

Moctezuma II, called Xocoyotzin, the younger, was elected in 1502 from among the eligible princes, and his reign is the best documented and the worst understood. He was a priest as well as a soldier, had commanded armies in the Oaxaca campaigns, and set out to do what his predecessors had only begun: to make the alliance a single state with Tenochtitlan at its head. He replaced Ahuitzotl's officials with his own men and had some of them executed. He tightened the sumptuary laws that separated nobles from commoners, and he closed the route by which commoners who distinguished themselves in war could be ennobled. He centralised the tribute system further, adding provinces and reassessing others, and he used the famine years at the start of his reign to raise assessments permanently in the valley towns.

He also inherited an unfinished war. Tlaxcala and Huexotzinco were still independent, the Tarascans were still undefeated, and the tributary provinces were still inclined to revolt whenever a king died. In 1515 an army that included the celebrated Tlaxcalan captive Tlahuicole was sent against Michoacán and achieved nothing. In the same period a flower-war campaign against Huexotzinco went badly wrong at Atlixco, and Oaxaca rebelled on the news.

Then, in 1519, reports began to arrive from the Gulf coast of strange men with beards, animals that carried them, and weapons that killed with thunder. Moctezuma's response was not paralysis but diplomacy. He sent gifts — a great disc of gold, a greater one of silver, featherwork, and, according to some accounts, the costume of Quetzalcoatl — and he sent envoys to observe. He also tried magic: his envoys offered the strangers food and drink mixed with the blood of sacrificed children, which the Spaniards refused. He forbade his coastal lords to fight, then allowed them to, and then blamed them for the result.

The idea that Moctezuma believed Cortés to be the god Quetzalcoatl returning from the east is one of the most durable stories in the history of the conquest and one of the least secure. It appears in its full form in later retellings, both Spanish and Nahua, written when it was useful to explain the fall of a great city as fated rather than as politics. The earliest accounts do not say it. What they show is a king trying to place an unknown quantity: offering gifts to see what the strangers valued, inviting them in to see them close, and refusing to commit his army until he understood what he was dealing with.

Cortés entered Tenochtitlan on 8 November 1519 and was housed in the palace of Axayacatl. Within a week Moctezuma was a prisoner in his own city, held hostage for the safety of Spaniards attacked on the coast. He governed through Cortés's captivity for six months, which is itself telling: the machinery of the state kept working. It broke in May 1520, when Pedro de Alvarado massacred the nobility at the festival of Toxcatl, and the city rose. Moctezuma came out on the palace roof to calm the crowd and was struck down — by a slingstone, say the Spanish; by his own people's contempt, say others — and died a few days later. The cause of his death is not established and probably never will be.

What decided the war of 1519–21?

Cortés had about five hundred soldiers, sixteen horses and a handful of cannon. He also had, and this is the part that matters, the ability to turn the empire's enemies into his army. The Tlaxcalans fought him first, hard, and then allied with him in September 1519 on terms that gave them freedom from tribute and a share in the conquest. They provided the bulk of the troops that marched on the capital, at Cholula, at the flight from the city in 1520, and at the siege in 1521. Alongside them came Totonacs, Huexotzincans, Chalcas, Xochimilcas, and eventually Texcoco itself, whose ruler Ixtlilxochitl II displaced his pro-Mexica brother and put the eastern shore, the shipyard and several thousand warriors at Cortés's disposal.

The second decisive factor arrived in the form of a virus. Smallpox reached the Gulf coast in 1520 with the expedition of Pánfilo de Narváez — the infection is usually traced to one sick man among his African slaves — and spread inland with the retreating armies. It reached Tenochtitlan in the autumn, in a city already crowded with refugees and short of food. The Florentine Codex, compiled by Nahua scholars under Bernardino de Sahagún, describes what happened with a precision that no Spanish account matches: sores on the face, the chest, the belly; the sick unable to move or lie down; and, fatally, the collapse of the nursing that kept everyone else alive. "A great many died from this plague," the survivors told Sahagún's informants, "and many others died of hunger." Cuitláhuac, elected after Moctezuma's death, ruled eighty days and died in November or December. The figures are contested. A Dumbarton Oaks exhibition on the epidemic gives five to eight million dead across Mesoamerica in that single outbreak; Robert McCaa's study of the Spanish and Nahuatl sources rejects both the minimalist case, that the outbreak was mild, and the figure of one-half of the population that is often repeated, tracing that number to a text wrongly attributed to Motolinía. What is not in dispute is the political effect: the disease killed the emperor, a large part of the nobility, and the priests and generals who ran the state.

The third factor was the lake. Tenochtitlan was impregnable to an army that could not control the water: three causeways, each broken by removable bridges, and a fleet of thousands of canoes. Cortés had thirteen brigantines built in Tlaxcala, carried in pieces over the mountains, assembled at Texcoco, and launched in the spring of 1521. With them he could cut the causeways, intercept the canoe traffic that supplied the city, and land troops where the defenders had no wall.

The siege began in the last week of May 1521, with the three causeways invested by Alvarado, Olid and Sandoval and the brigantines on the water. It lasted eighty days. The defenders, under Cuauhtémoc, fought street by street for weeks, opening breaches in the causeways, digging stake-pits in the shallows, and capturing men and boats. The attackers took terrible casualties. But the city had no water supply once the aqueduct at Chapultepec was cut, no food once the lake was closed, and no reinforcements once the lakeside towns made their peace. The fighting contracted to Tlatelolco, the old rival city, where women fought on the rooftops. On 13 August 1521 Cuauhtémoc was taken in a canoe while trying to escape, and the surrender was given from a rooftop.

The arithmetic of the conquest is not the arithmetic of the popular account. Perhaps a thousand Spaniards died over the two years; the indigenous allies lost tens of thousands; the Mexica lost more, most of them to disease and hunger rather than to Spanish steel. Cortés's own account puts his indigenous allies at more than 150,000 on the day of the final assault, and admits that he could not restrain their looting. The empire was not conquered by five hundred men. It was conquered by its own subjects, with five hundred Spaniards present.

What did 1521 end, and what survived?

The alliance ended; the tributary system did not. Tenochtitlan was pulled down and rebuilt as Mexico City, its causeways broken to let the lake drain, its temples quarried for churches. But the Spanish crown stepped directly into the Mexica fiscal apparatus: the tribute province became the colonial corregimiento or the encomienda, the calpixque's painted account book became the matrícula de tributos of the viceroyalty, and the same towns paid the same goods to new masters, in the same twice-yearly rhythm, for another three centuries. The word tributo in colonial Mexican documents means what it meant before 1521.

The Nahua nobility survived too, and quickly made itself indispensable. The sons of Moctezuma and of the Texcocan and Tlacopan dynasties were baptised, married into Spanish families, and given lands and titles; the Codex Mendoza was produced by their scribes and painters, in their own pictorial idiom, for a Spanish viceroy. Doña Isabel Moctezuma, Moctezuma II's daughter, held encomiendas and is described in Spanish records as a woman of substance. The Tlaxcalans, who had bet on the winning side, were granted privileges and exemptions that they defended in court for the rest of the colonial period, and Tlaxcalan colonists were settled as far north as the silver frontier.

The demographic catastrophe was the deepest change. Central Mexico's population, whatever its exact pre-contact level — estimates run from fifteen to thirty million for Mexico as a whole, and the higher figures are contested — fell by something like ninety per cent over the sixteenth century, through smallpox, measles, influenza, typhus and the famine and social collapse that followed each. The 1520 outbreak alone is estimated at five to eight million dead across Mesoamerica. The empire that fell in 1521 was already a ruin in demographic terms; the institutions that replaced it governed a fraction of the people they had been designed for.

Memory took longer to settle. The word "Aztec" is not what the Mexica called themselves — they called themselves Mexica, or Culhua-Mexica, and the term "Aztec" was adopted by nineteenth-century scholars from the mythical homeland of Aztlan. The alliance itself was largely forgotten as a political form and remembered as a lost golden age, first by the Nahua nobility of the colonial period, then by Mexican nationalists, and finally by archaeologists, who have spent the last fifty years excavating the Templo Mayor and reconstructing the tribute economy from the rolls. What survives physically is not much: the stone of Tizoc, the sun stone, the Coyolxauhqui disc, a few foundations under the cathedral, and the two painted books in Oxford and Mexico City.

Common myths about the Aztec Triple Alliance

Timeline of Aztec Triple Alliance

What the map shows next

At 1430 on the map the alliance is a strip of territory around the lake, with Texcoco still the senior partner and the Tepanec lands only just divided. Move forward a generation and the tribute provinces have begun to fan out south into Morelos and east towards the Gulf; the shape at 1490 on the map reflects Ahuitzotl's conquests on both coasts rather than Moctezuma II's later consolidation.

The last frame, 1520 on the map, shows the empire at its widest and at its weakest: the provinces reach the Pacific and the Gulf, but Tlaxcala, Huexotzinco, Cholula and Michoacán remain outside, and the lake cities that supplied the siege army sit inside the frontier.