Open Problems in Mathematical Biology

TL;DR

This paper discusses key open problems in mathematical biology, emphasizing the importance of mathematical models in understanding complex biological data and systems, and highlighting the mutual benefits for biology and mathematics.

Contribution

It presents a selection of open problems in mathematical biology that are of both biological and mathematical interest, illustrating current challenges and opportunities.

Findings

Mathematical models help test biological hypotheses.

Complex data and hypotheses pose challenges for systematic analysis.

Open problems highlight areas for future research in mathematical biology.

Abstract

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.