The Four Things They Don’t Tell You About Mathematical Modelling

By Tim Kay, The University of Melbourne

Mathematical modelling is an exciting prospect when one first comes across it. One can take near every imaginable system, be it physical, financial, epidemiological etc., describe it with maths and thereby deduce much about the system – very neat. You can imagine, then, how I might have been drawn into spending 6 weeks of my summer break modelling a tiny rod-and-ball fluid system. But here are 4 things they don’t tell you about mathematical modelling:

1. We only really like spheres in vacuums.

Or rather in my case, the ball is a point particle, the rod is a point particle and the fluid is unbounded. Unfortunately, fluid dynamics is so mathematically complicated that geometry of any kind was utterly banned in my project. This kind of simplification is justifiable really, but everyone laughs when you explain it.

1. It takes both persistence and luck to find a solution.

First, you’ll work away for a couple of weeks contentedly. Then you’ll realise you’ve gone wrong but can’t work out where. Along the road to solution you’ll write grievous bugs into your code and subsequently debug them. You’ll feel like you’ve consulted the entire internet. If you’re really stuck, you might even start having dreams (read: nightmares) about your project. So, when things are going poorly, it takes a lot of motivation to come in everyday and tackle your problem. But answers come in the most unlikely forms. 5 weeks into my project, interesting results were scarce. Lo, a chance encounter in the tea room (all my best ideas were born here) with an old lecturer saved the day.

1. The majority of your work is of no interest to anyone.

All those weeks of failing may well have left you with permanent mental scars but, sadly for you, only your mother cares. When you present your work, there can be no cathartic discussions of the complex details which so bogged you, rather, you must present only good results, as if it were all smooth sailing.

‘So why the hell do you do applied maths if you find it so irksome?’

1. After all this, the joy when your model finally comes together is unparalleled.

Additionally, I learnt oodles along the way – fluid theory, practical skills, but most importantly, the confidence and determination required to undertake a difficult problem.

So should you go down the mathematical modelling path? The cost-benefit analysis is left as an exercise for the reader.

Tim Kay was a recipient of a 2018/19 AMSI Vacation Research Scholarship.