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River of knowledge

The River of Algebra

When did separate procedures become a language for mathematical structure?

Building on Babylonian, Greek, Indian, and Chinese equation traditions, al-Khwarizmi gave a systematic ninth-century account of *al-jabr*. Arabic, Hebrew, and Latin texts moved through several Mediterranean routes into Renaissance work on equations.

820–16003 city-to-city segments

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What changed between the cities?

  1. 1

    820–850

    translation

    BaghdadCordoba

    Birth of Algebra

    Al-Khwarizmi published al-jabr in Baghdad, establishing algebra as a distinct field.

    Kitab al-jabr wal-muqabala
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  2. 2

    1140–1200

    translation

    ToledoBologna

    Algebra Reaches Latin Europe

    The Toledo translation movement produced two twelfth-century Latin versions of al-jabr—Robert of Chester at Segovia in 1145 and Gerard of Cremona at Toledo around 1175—helping seed algebra in Bologna and across Europe.

    Robert of Chester’s Liber algebrae (1145, Segovia) and Gerard of Cremona’s second translation (c.1175, Toledo)
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  3. 3

    1500–1545

    scholars and schools

    BolognaNuremberg

    Renaissance Cubic Equations

    Mathematicians in Brescia, Bologna, and Milan found methods for cubic equations; Cardano’s Ars Magna was printed in Nuremberg in 1545 and brought imaginary quantities into print.

    Cubic methods of Tartaglia and Cardano, Bombelli’s complex arithmetic, and Ars Magna (1545, Nuremberg)
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How to read the lines

Each line is an editorial route through problems, texts, and practices. It does not imply one book moving in a straight line, a sole invention, or identical adoption everywhere.