Boolean algebra is the algebra of two truth values, usually written as true and false or as 1 and 0, combined by the operations AND, OR, and NOT. It originates with George Boole, whose 1854 work “An Investigation of the Laws of Thought” set out to give Aristotle’s logic a mathematical footing by expressing reasoning as equations.
In Boole’s system, variables stand for propositions or classes, and the operations follow fixed algebraic laws. Statements that are either correct or incorrect can be written symbolically and manipulated, so that conclusions follow from premises by calculation rather than informal argument. The MacTutor archive dates this published system to Boole’s 1854 book on the laws of thought.
What made the idea central to computing was its match to physical switches. A switch is either open or closed, a wire either carries current or does not; these two-state devices map directly onto Boole’s two values. Claude Shannon’s work in the 1930s drew this connection explicitly, showing that networks of relays and switches could implement Boolean expressions.
From that point on, Boolean algebra became the language of digital design. The AND, OR, and NOT operations are realized as logic gates, and every arithmetic and control operation inside a processor is ultimately built from combinations of them. The same algebra also governs the boolean conditions that steer program logic in software.