There have been a lot of marvelous results revealed by string theory, which deeply relate different aspects of mathematics. All these mysterious relations are connected by a core idea in string theory called "duality". In this talk, I will focus on a duality between Chern-Simons gauge theory and topological string theory. Some integrality structure in the Calabi-Yau geometry will be discussed. I will also discuss some related problems in low dimensional topology.