Direct interaction of mathematics with science and technology is a global new trend. Along that, Mathematics Program "Alliance for Breakthrough between Mathematics and Sciences" at JST started under the leadership of Yasumasa Nishiura in 2007. As a research team, "a mathematical challenge to a new materials science based on discrete geometry" has been carried out by the author. She, a mathematician, is now Director of Advanced Institute for materials research, Tohoku University. In the present article, she explains what is discrete geometric analysis and what is the mathematical challenge in the Mathematics Program, or at AIMR Tohoku University.