Ain Jalut is often called the battle that saved Islam — and often called overrated, since Hülegü had already left with the main army. Weigh both claims.

THE SHORT ANSWER

• Why Baghdad, why now. Not plunder-lust but agenda: Möngke’s kurultai of 1251 resolved to finish the two “universal” claims that rivaled the khan’s — the caliphate and the Song (his other brother’s assignment; Ch. 10). The caliph’s spiritual authority made him precisely the kind of power the Tengri mandate could not tolerate as an equal, only as a subject. Read the conquest as constitutional theory enforced by trebuchet.
• A hollow caliphate. Baghdad in 1258 was a memory wearing a crown: the caliphs had been warlords’ puppets for centuries, the treasury feuded with the army, Sunni–Shia riots split the city, and al-Musta‘sim — “a falconer,” his own officials despaired — neither paid for defense nor submitted in time. Hülegü’s Shia astrologer-advisor Nasir al-Din Tusi (saved from Alamut, note the empire recycling talent again) reportedly assured him no cosmic punishment would follow the caliph’s death. None did; the lesson every remaining power absorbed was that sanctity without soldiers is a target.
• The Mamluk anomaly. Egypt’s slave-soldier system accidentally built the one army with the Mongol toolkit and none of the Mongol dependencies: steppe-born horse-archers, centrally barracked, professionally drilled, fighting on interior lines with Egypt’s granary behind them — and with nowhere to retreat to, since Cairo was both their capital and their only home. Where feudal hosts and city militias had shattered, the Mongols finally met a mirror.
• A fatally divided theater. Hülegü’s departure was decisive but so was arithmetic: Syria’s scorched summer pastures could barely water the horses Kitbuqa kept (the ecology thesis again — compare Hungary, Ch. 6), the Crusaders of Acre chose neutrality tilted toward Egypt (safe passage and markets for the Mamluk army — Christendom quietly provisioning Islam’s defense against the power some popes had courted as an ally), and Berke’s Golden Horde, newly Muslim and enraged by the caliph’s death, was already threatening Hülegü’s rear. Ain Jalut was won in Egypt, but it was set up by the empire’s own geometry.

WHAT IT CHANGED

Sunni Islam reorganizes around Cairo. The Mamluks install a refugee Abbasid as shadow-caliph in Cairo and rule as Islam’s sword for 250 years, until the Ottomans. Baghdad, half-ruined and demoted to a provincial town of the Ilkhanate, does not anchor the region again for centuries. When a civilization’s center of gravity moves on this map, it moves because of one week in 1258.

The Ilkhanate is born facing enemies on three sides. Hülegü keeps Persia, Iraq and Anatolia’s overlordship — the Ilkhanate — but Ain Jalut plus Berke’s hostility (next chapter’s war) lock its borders almost immediately. A generation later its khans convert to Islam; the dynasty that killed the caliph ends as patron of Persian miniatures, mosque-builders and the historian Rashid al-Din’s world chronicle. History’s ironies are rarely this legible.

The first check becomes the pattern. Ain Jalut announces the era of limits: from 1260 the tide stops more often than it runs — Syria annually contested, Japan (Ch. 11) and Vietnam ahead. Conquest had been the empire’s solvent for every internal strain; watch what happens, starting next chapter, when the solvent runs out.