Operator grammar is a mathematical theory of human language that explains how language carries information. This theory is the culmination of the life work of Zellig Harris, with major publications toward the end of the last century. Operator grammar proposes that each human language is a self-organizing system in which both the syntactic and semantic properties of a word are established purely in relation to other words. Thus, no external system (metalanguage) is required to define the rules of a language. Instead, these rules are learned through exposure to usage and through participation, as is the case with most social behavior. The theory is consistent with the idea that language evolved gradually, with each successive generation introducing new complexity and variation.