The conquest changes networks of patronage

Al-Azhar shows how mathematics was transmitted through teaching communities rather than only through famous books and individuals.

Students from Africa, Asia and the wider Islamic world carried methods and texts across linguistic and political boundaries.

The Abbasid caliph surrendered on 10 February 1258, followed by the sack of a city central to centuries of scientific exchange.

Libraries and institutions suffered catastrophic loss, although the familiar story that all books were thrown into the Tigris cannot be treated as a precise inventory.

Knowledge survived through manuscripts and scholars in Maragha, Damascus, Cairo, Central Asia and other centers, preventing a simple rise-and-collapse narrative.

Pope Gregory XIII issued the bull Inter gravissimas. It reformed leap-year rules to bring the civil calendar closer to the solar year.

The reform used astronomical calculation and a revised leap-year cycle to limit the drift of the equinox through the calendar.

The calendar illustrates how numerical models become social institutions through political and religious authority.

Catholic states adopted the reform first, while other societies accepted, adapted or resisted it at different times; calendar history was not a single global switch.

In several Catholic territories, Thursday 4 October was followed by Friday 15 October 1582. Ten numbered dates were omitted to realign calendar and season.