This chapter elaborates on the integral role mathematics plays in shaping sustainable solutions for our evolving world. The mathematical significance and historical development of optimization and sustainability have been discussed. A classification of basic optimization problems has been provided. Emphasizing the symbiotic relationship between optimization and sustainability, it has been discussed how mathematical frameworks, from linear programming to stochastic modeling, provide tools for informed decision-making. Such models not only aim for optimal outcomes but also embed long-term viability. As global challenges amplify, including unpredictable environmental shifts, emerging methodologies, particularly at the intersection of machine learning and optimization, become crucial. Through exploring various mathematical concepts, their applications in sustainability, and future research directions, this article underscores the profound significance of mathematics in charting a sustainable path forward.