Expression (mathematics)

An expression in mathematics is a finite combination of symbols arranged according to rules of notation to represent a value, relationship, or computation. Expressions form the language through which mathematicians communicate ideas—they're the sentences of the mathematical world.

Expressions can be as simple as a single number like 5, or complex like 3x² + 2x − 1 or ∫₀^∞ e^(−x²) dx. They differ fundamentally from statements or equations: an expression evaluates to something, while an equation asserts equality between two expressions.

The power of expressions lies in their compositionality. Small expressions combine into larger ones through functions, operations, and relationships. Within a given scope or domain, variables take on values, and substitution transforms abstract notation into concrete results.

Expressions appear everywhere: in Algebra, Calculus, Programming, and logic. They can be symbolic (pure form), evaluated (yielding a number), or left abstract (capturing patterns). Understanding how expressions work—their structure, evaluation rules, and transformation laws—is foundational to all mathematical and computational thinking.

Related

Function (mathematics), Algebra, Syntax, Variable (mathematics), Operator (mathematics), Calculus