There have been at least two surprising events to geometers in 80-90s that they had to admit physics really helps to solve classical problems in geometry. Donaldson proved the existence of exotic 4-dimensional Euclidean space using gauge theory and Givental counts rational curves in quintic threefolds using Feynman diagram in string theory. These events hugely popularised new mathematical topics such as mirror symmetry and enumerative geometry via moduli spaces. In this talk, we present what happened in this field in a past few decades and something happening right now.
