Algebra

Mathematical discipline founded by Al-Khwarizmi for solving equations through systematic transformation.

Ask the Islamic Golden Age assistant1 min read · Updated September 9, 2026

Who or what

The word "algebra" comes from "al-jabr" in Al-Khwarizmi's 9th-century treatise on equation solving.

Originally the art of restoring balance in equations by moving terms from one side to another.

Before algebra, mathematics was largely geometric. Algebra introduced symbolic manipulation as a tool for solving unknowns.

It transformed mathematics from a collection of specific solutions into a general method applicable to entire classes of problems.

Al-Khwarizmi solved "a square and ten roots equal thirty-nine" ( $x^2 + 10x = 39$ ) by completing the square to get $x = 3$ .

Omar Khayyam later extended algebra to cubic equations using geometric constructions of conic sections.

Al-Khwarizmi's six canonical forms: $ax^2=bx$ , $ax^2=c$ , $bx=c$ , $ax^2+bx=c$ , $ax^2+c=bx$ , $bx+c=ax^2$ .

Solutions were expressed rhetorically (in words), not symbolically — symbolic algebra came much later with Viète and Descartes.

Algebra underlies all of modern science, engineering, economics, and computer science.

The abstraction of "unknown quantities" enabled everything from physics equations to cryptographic algorithms.

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.