THE academy AMCA, founded in December 2014 in USA, aims at promoting the progress and upholding the development of combinatorics and Smarandache multispaces with mathematical sciences, i.e., mathematical combinatorics, including algebra, topology, geometry, differential equations, theoretical physics, theoretical chemistry and mathematical theory on recycling economy or environmental sciences, for instance, the industrial ecology, and so as to advance a sustainable developing for global economy. Its major activities include organizing meetings of the membership, discussions on important topics, edit and publish scientific journals, special volumes and members monographs, awards and honours, recognizing mathematical talent, improvement of mathematics education and taking up other issues of concern to the mathematical community.