A mathematical formalization of Chomsky’s theory of Merge in generative linguistics. The Minimalist Program advanced by Noam Chomsky thirty years ago, focusing on the biological nature of human language, has played a central role in our modern understanding of syntax. One key to this program is the notion that the hierarchical structure of human language syntax consists of a single operation Merge. For the first time, Mathematical Structure of Syntactic Merge presents a complete and precise mathematical formalization of Chomsky’s most recent theory of Merge. It both furnishes a new way to explore Merge’s important linguistic implications clearly while also laying to rest any fears that the Minimalist framework based on Merge might itself prove to be formally incoherent. In this book, Matilde Marcolli, Noam Chomsky, and Robert C. Berwick prove that Merge can be described as a very particular kind of highly structured algebra. Additionally, the book shows how Merge can be placed within a consistent framework that includes both a syntactic-semantic interface that realizes Chomsky’s notion of a conceptual-intentional interface, and an externalization system that realizes language-specific constraints. The syntax-semantics interface encompasses many current semantical theories and offers deep insights into the ways that modern “large language models” work, proving that these do not undermine in any way the scientific theories of language based on generative grammar.