Development of Algebra
The evolution of algebra from Al-Khwarizmi's rhetorical algebra to symbolic notation.
Who or what
Algebra evolved through three stages: rhetorical (words only), syncopated (abbreviations), and symbolic (modern notation).
Islamic scholars carried algebra from geometric problem-solving to a general theory of equations.
Why it mattered
Al-Khwarizmi's algebra was rhetorical — equations written entirely in words. "A square and ten roots equal thirty-nine."
Omar Khayyam classified and solved cubic equations geometrically; al-Karaji began arithmetizing algebra.
Key works and moments
Thabit ibn Qurra gave a general proof for amicable numbers using algebraic reasoning.
Al-Samawal's work on polynomial division anticipated modern algebra by centuries.
Further detail
The six canonical forms of Al-Khwarizmi were gradually reduced as negative numbers gained acceptance.
The fundamental theorem of algebra (every polynomial has a root) was conjectured but not proven until Gauss.
Legacy
Algebra became the language of all quantitative science.
The abstraction from specific numbers to general symbols enabled modern mathematics and physics.
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