History of algebra

The history of algebra traces how people developed symbolic methods for solving equations and describing mathematical structures across different cultures and eras.

Babylonian mathematics: A Mesopotamian mathematical tradition that used numerical procedures to solve problems involving quantities, measurement, and equations. Old Babylonian scribes solved quadratic problems centuries before algebraic symbolism existed.
Rhetorical algebra: Algebra expressed entirely in ordinary words, without specialized symbols for operations or unknowns. Early equation-solving texts stated procedures in prose rather than compact notation.
François Viète: A sixteenth-century French mathematician who promoted systematic use of letters in algebra. His notation distinguished known from unknown quantities and encouraged general methods.
Fundamental theorem of algebra: The theorem that every nonconstant polynomial with complex coefficients has a complex root. Its proof history exposed changing standards for what counted as a rigorous algebraic argument.
Geometric algebra: A mathematical approach that expresses algebraic relationships through geometric figures and constructions. Greek geometric treatments differed from Babylonian numerical procedures for equations.
Rhind Mathematical Papyrus: An ancient Egyptian mathematical document copied by the scribe Ahmes around 1650 BCE. Its problems show Egyptian methods for finding unknown quantities through arithmetic.
Syncopated algebra: Algebra that abbreviates recurring words or quantities while retaining some verbal explanation. Diophantus and later writers used shorthand before a full symbolic language emerged.
René Descartes: A seventeenth-century French philosopher and mathematician who connected algebraic equations with geometry. His methods helped establish analytic geometry and modern equation notation.
Ruffini–Abel theorem: The theorem that general polynomial equations of degree five or higher cannot be solved by radicals. It ended the search for a universal radical formula and redirected equation theory.
Algebraic geometry: The study of geometric objects defined by polynomial equations. It reverses the historical traffic between algebra and geometry by using equations to study shapes.

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