Distilling the Science from the Art

Geoff Evatt (U o Manchester, UK) gave a ‘Mathematics in the Workplace’ talk at the recent Manchester Festival of Mathematics and its Applications, printed in the Oct 2014 Mathematics Today.

He showed how the Mathematical modeller could turn their hand to diverse subjects of financial regulation and … .

He is critical of the view that ‘Mathematical Modelling is like an Art’ and advocates the prescriptive teaching of best-practice. His main motivation seems to be to attract more students and the up-take by industry (etc).

This … will be achieved by academics from a variety of universities agreeing in what is ‘best practice’ in teaching modelling is … .

Comments

Taking the title, I accept that the term ‘art’ may be misleading, but I am not convinced that there is much science in, for example, finance, or that those funding the mathematics really care, so the term ‘science’ could be equally misleading and more dangerous. I would say that mathematical modelling is often a craft. Where it is part of a proper scientific endeavour, I would think that this would be because of the domain experts and ought to be certified from a scientific rather than mathematical point of view. To me ‘best practice’ is to work closely with domain experts, to give them what they need, and to make sure that they understand what they do – and don’t have. It is good to seek to be scientific and objective, but not to misrepresent what has actually been achieved.

In the run-up to the financial crash best practice included characterising mathematical modelling in this area as an ‘art’ and not a science, to prevent financiers and politicians from thinking that the ‘mathematical’ nature of the models somehow lent them the same credibility normally accorded to mathematics. A key part of the financial problem was that this was not well-enough understood.

A key part of economics is the concept of ‘uncertainty’. The classical mathematical models did not model uncertainty beyond mere probability, possibly because was not covered by contemporary mainstream courses.

Best practice would include ensuring that the mathematics used was appropriate to the domain, or at least in explaining any short-falls. I think that this requires more development than Evatt supposes. I also think that one would need to go beyond academics, to include people who understand the issues involved.

Dave Marsay