The content of this lecture has been based on two distinct areas. In the rst part we consider an interesting modern application of mathematics, which is intended to demonstrate that mathematics continues to play an important role in understanding the world around us.
Building on this theme, we make a short excursion to consider an application of the work of Dr F W Lanchester, after whom this Institution was originally named. Having made the case for the value of mathematics in modelling important systems, we turn to the state of mathematics education in the UK, particularly, but by no means exclusively, in Schools.
It will be clear that all is not how it should be, and with the realisation at Ministerial level of the potential danger in the situation, actions have been proposed. The lecture concludes with a summary and discussion of some of these actions.
The two areas can be linked through the use of the word 'fuzzy', because dictionary definitions of 'fuzzy' often include the words 'indistinct' or 'blurred'. When applied to statements we might interpret this to mean that a fuzzy statement is an imprecise statement. We can regard the ability to handle these within mathematics as a positive aspect of fuzzy thinking, the title of this lecture!
On the other hand, if a strategy or course of action seems perverse and we describe it as the result of fuzzy thinking, we mean that it is the result of blurred or muddled thinking. This is the negative aspect and is not a helpful application of fuzzy thinking!