I shall try to answer the above question by firstly giving a formal definition of the concept under study. In continuing to answer this question I will then submit my own thoughts on the matter, illustrated with appropriate diagrams and photographs, as well as quoting the opinions of other individuals on this topic before finally giving a conclusion that will hopefully provide a definitive answer to this demanding question. .
I shall begin, as promised, by providing a current formal definition of Mathematics. Thus, according to the Oxford English Dictionary1 the definition of Mathematics is:.
1. Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations. Colloq. abbreviated maths, (N. Amer.) math.
As one can see from this the definition of Mathematics has changed significantly through time and will continue to change as new branches are added to the discipline. As an analogy, numerical modelling of the weather by the Met. Office is a recent development but this has now become the standard forecasting technique used. Mathematics as used by the Egyptians, for example, was always used to solve distinct practical problems rather than practised for its own sake. So in essence, pure mathematics as we know it was not in existence at that time, only applied mathematics, as mathematics was considered to be more of a tool for solving problems rather than as an intellectual stimulant.
However, I feel that Mathematics is much more than this straightforward definition. For me, Mathematics is the creation of order from chaos, the application of rules to the anarchic world in which we live in order to achieve a definitive solution, which is both simple and elegant but also guaranteed to be correct assuming that the procedure being used has been followed without error.
