Finding meaningful and workable applied mathematics problems in science

In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and what wrong approaches were applied. Such details are important in learning how to do research, but they cannot be read out from research papers. I wish that students and junior researchers in applied mathematics could learn a lesson from this summary.