Finding meaningful and workable applied mathematics problems in science

TL;DR

This paper shares personal research experiences across mathematical biology, probability, and discrete math, highlighting lessons learned from initial wrong approaches to guide students and junior researchers.

Contribution

It provides a reflective overview of research initiation and mistakes in applied mathematics to aid learning for students and early-career researchers.

Findings

Lessons from wrong approaches in research

Importance of research process details

Guidance for students and junior researchers

Abstract

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.