A Mathematical Programming Language is an algebraic modeling language designed to describe and solve complex optimization problems for large-scale mathematical computing. Developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories, it is widely used in industrial, academic, and governmental settings. AMPL features a mix of declarative and imperative paradigms, making it effective for formulating optimization models and constructing hybrid algorithms. With open-source and commercial solver support, AMPL allows seamless integration into existing systems across multiple platforms.