Recently, mathematics has a wide influence on architectural design and performance. It can effectively help in solving design problems and promoting geometrical shapes efficiency. Consequently, the environmental performance has also widely developed with the involving of advanced mathematical branches and computational software. The main aim of the paper is to study the importance of using mathematics in raising the   building's environmental performance. Therefore, the research methodology starts by clarifying the mathematics   ' branches and their application in architecture, then carries out an analysis for different case studies that used mathematics effectively in developing environmental performance. And lastly, apply one of the mathematical optimization techniques on a virtual prototype to illustrate how mathematics can effectively promote the   building's environmental efficiency.