The work of mathematicians has been at the forefront of scientific response to this crisis. The media coverage has raised the awareness of mathematical modelling significantly within our society. At the IMA, we hope that this will mean many more people consider a career in mathematics and its applications and start to see the importance of mathematics to our society. Maybe you have friends and family asking you about mathematical modelling, and yet you work in a completely different area of mathematics, so here are a few thoughts from some IMA members.
Mathematical modelling seeks to represent features from a real-world application using mathematical equations and concepts. It might be used to build understanding of the application area, test a theory or hypothesis, visualize something or predict something. It is used in biology, medicine, physics, engineering, social sciences, in fact almost everywhere within science. Mathematical modellers work with experts from the application domain to ensure that their models contain the most valuable features. A model might range anywhere in complexity from a simple straight line fit of data points to a complex computational simulation.
“All models are wrong but some are useful” – George E. P. Box, Statistician
The above is true; all models are simplifications of reality. They will make assumptions, are often based on limited data, use a smaller set of parameters than exist, and there can be a range of different models that represent the same thing. Models are useful though; they increase our understanding by representing the world in a manner we find easier to grasp, they can help make tentative predictions, help us visualize what is going on, test our hypothesis, and by comparing models we can start to identify what is important.
How does a responsible mathematical modeller behave?
- They understand the limitations of their models and freely share that information, this includes knowing the range of validity, recording their assumptions, understanding the re-producibility and variability in the model, understanding model biases, knowing where it is sensitive and where not.
- They try to make models that are transparent and explainable
- They engage in peer review with other modellers with competing approaches
- They accept that predictions have caveats and might change with more data or more model fidelity and give their advice accordingly.
- They know when to use their model and when it is not applicable or needs to be updated.
- They understand how much risk and reward is associated with their recommendations.
It is reassuring that we see the above traits in the recent modelling of Coronavirus: competing suggestions and changes as more data become available are good signs when modelling an uncertain world.
Featured image by Martin Sanchez on Unsplash