What does algebra mean?
Algebra is the branch of mathematics that uses symbols—typically letters—to stand for unknown or variable quantities, along with rules for manipulating those symbols to express relationships and solve problems. Where arithmetic works only with specific numbers, algebra allows general statements: instead of asking what 3 plus 4 equals, it can state that x plus y equals y plus x for any values at all. The word entered English from Arabic, deriving from a ninth-century treatise by the mathematician al-Khwarizmi, and its title literally referred to 'the reunion of broken parts.' Today algebra spans everything from schoolroom equation-solving to advanced fields such as linear algebra, abstract algebra, and Boolean algebra, which power modern computing, engineering, and science. It is regarded as a foundational mathematical literacy, essential well beyond the classroom.
nounThe branch of mathematics dealing with symbols and the rules for manipulating them to represent and solve equations and relationships between quantities.
- The general branch of mathematics involving symbols and the manipulation of equations.
- A specific system or structure of mathematical operations, as in linear algebra, abstract algebra, or Boolean algebra.
"She used algebra to work out how many tickets they could afford within their budget."
"Students typically begin learning algebra in middle school, when numbers are first replaced by letters."
"Linear algebra underpins much of modern machine learning and computer graphics."
Rarely used; the plural appears mainly in advanced mathematics when referring collectively to distinct algebraic structures or systems.
"Modern mathematics studies many different algebras, each defined by its own set of axioms."
The word 'algebra' comes from an Arabic title whose literal meaning was 'the reunion of broken parts' — a ninth-century book about restoring what's missing in equations.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of algebra
Algebra derives from the Medieval Latin transliteration of the Arabic word 'al-jabr', meaning 'the reunion of broken parts,' which appeared in the title of Muhammad ibn Musa al-Khwarizmi's influential ninth-century treatise on solving equations. The term entered European usage through Latin translations of that work during the Middle Ages and became established in English by the early modern period. It shares its Arabic heritage with related borrowings such as algorithm, alchemy, and alkali, all of which preserve the Arabic definite article 'al-' in their prefixes.
Related word forms
How algebra is actually used
Algebra is a neutral, academic term with no strong connotations; it appears both in everyday educational contexts and in highly specialized mathematical registers, where qualified forms such as 'linear algebra' or 'abstract algebra' denote particular subfields.
Easily confused with algebra
An algorithm is a step-by-step procedure for solving a problem, while algebra is a branch of mathematics concerned with symbols and equations.