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 co

It is often questioned whether items put on display in modern art exhibitions are really art or not. For example, it has been said that the 1996 work by the artist Damien Hirst entitled, “This little piggy went to market, this little piggy stayed at home”, featuring two halves of a pig, one positioned in front of the other, would be more appropriate in the context of a butcher’s shop or a slaughterhouse rather than in a modern art gallery. However, it is rarely questioned whether things are mathematical in nature or not. For example, the photograph below3 shows a crop circle at Litchfield in Hampshire, approximately 7 miles from my house and adjacent to the busy A34 trunk road. Not only was this crop circle mathematical in design but also according to the Crop Circular3, “it emerged that these rings were so placed to reveal a monumental breakthrough in geometry. For here was a crop circle containing the equilateral branch of Gerald's new Fifth Theorem, from which not only all the others were derived, but which to this day over 300,000 scientists and mathematicians have never been able to disprove”.

In conclusion, Mathematics is made up of mathematical methods such as calculation and proof and mathematical concepts such as groups, rings and fields in algebra or random variables and probability distributions in statistics. The mathematical concepts in a particular problem and the axioms connecting them define the method of proof or calculations needed to obtain a solution to the given problem. Therefore no problem can be solved without knowledge of both the underlying concepts involved in it and the method used to solve it. However, according to Reuben Hersh in What is Mathematics, Really?5, “Mathematics is a vast network of interconnected problems and solutions”. Hence, by this definition, Mathematics has to be defined as both the underlying mathematical concepts and the mathematical methods involved in the solution of mathematical problems.

Finally, I would just like to add that this is one of the hardest questions that I have ever had to answer in the course of my study of Mathematics but I have not encountered any unforeseen difficulties as I knew the sort of problems that I might encounter before I started. For example, I knew that none of the sources that I referred to would be able to answer this question either simply or directly as the question is far too complex to be answered in that manner.

I would say that both Computer Science and Statistics are applications of Mathematics because computers are based on and would not work without the binary number system and statistics is basically a study of the variation of scalars, which relies on the concepts of differentiation and integration in order to prove the underlying concepts of the subject. However, I would not say that Mathematics and Statistics are one and the same thing by any means and I will use the following example to support this argument. When asked if the Bachelor of Science course in Mathematics and Applied Statistics at the University of Re

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