# Mathematical modelling

December 8, 2016 2 Comments

I had the good fortune to attend a public talk on mathematical modelling, organised by the University of Birmingham (UK). The speaker, Dr Nira Chamberlain CMath FIMA CSci, is a council member of the appropriate institution, and so may reasonably be thought to be speaking for mathematicians generally.

He observed that there were many professional areas that used mathematics as a tool, and that they generally failed to see the need for professional mathematicians as such. He thought that mathematical modelling was one area where – at least for the more important problems – mathematicians ought to be involved. He gave examples of modelling, including one of the financial crisis.

The main conclusion seemed very reasonable, and in line with the beliefs of most ‘right thinking’ mathematicians. But on reflection, I wonder if my non-mathematician professional colleagues would accept it. In 19th century professional mathematicians were proclaiming it a mathematical fact that the physical world conformed to classical geometry. On this basis, mathematicians do not seem to have any special ability to produce valid models. Indeed, in the run up to the financial crash there were too many professional mathematicians who were advocating some mainstream mathematical models of finance and economies in which the crash was impossible.

In Dr Chamberlain’s own model of the crash, it seems that deregulation and competition led to excessive risk taking, which risks eventually materialised. A colleague who is a professional scientist but not a professional mathematician has advised me that this general model was recognised by the UK at the time of our deregulation, but that it was assumed (as Greenspan did) that somehow some institution would step in to foreclose this excessive risk taking. To me, the key thing to note is that the risks being taken were systemic and not necessarily recognised by those taking them. To me, the virtue of a model does not just depend on it being correct in some abstract sense, but also that ‘has traction’ with relevant policy and decision makers and takers. Thus, reflecting on the talk, I am left accepting the view of many of my colleagues that some mathematical models are too important to be left to mathematicians.

If we have a thesis and antithesis, then the synthesis that I and my colleagues have long come to is that important mathematical model needs to be a collaborative endeavour, including mathematicians as having a special role in challenging, interpret and (potentially) developing the model, including developing (as Dr C said) new mathematics where necessary. A modelling team will often need mathematicians ‘on tap’ to apply various methods and theories, and this is common. But what is also needed is a mathematical insight into the appropriateness of these tools and the meaning of the results. This requires people who are more concerned with their mathematical integrity than in satisfying their non-mathematical pay-masters. It seems to me that these are a sub-set of those that are generally regarded as ‘professional’. How do we identify such people?

Dear Dave,

Thank you for your views on your talk. Your response I mostly agree with. In future, I will state that mathematical modelling isn’t a field exclusive for mathematics, but it is a good field for them. In my professional experience, my job is to come in when mathematical models have gone wrong or the maths has been to complex for the model to be built. However, I must acknowledge the help of the SME who I questioned and interview, before I turn their ideas into mathematics. As for who is the right candidate to be a mathematical modeller? Well, this is a person who embraced a wide field of mathematics. In modelling – it a free for all, any method along as it is robust, logical and efficient works. A Mathematical modeller must have the confidence to challenge models that do not reflect reality and the ability to produce a model beyond a theoretical abstract world.

Best regards

Nira

Thanks for replying to my critique. I think we need to distinguish between areas where there are genuine experts, and those such as economics and cyber where the state-of-the-art leaves a lot to be desired. In the first case modelling formalises what is already a good understanding, and makes it more precise. In the second case the modelling can be part of a collaborative process for critiquing and developing understanding. In my experience the actual mathematical product may be much less important than helping SMEs and policy makers to develop some loosely expressed ‘expertise’. Here everyone should have the insight and confidence to challenge everything.

Regards and seasons greetings, Dave