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Part of Chapter 3

The Science of Maths

Mathematics is a science of quantity which is philosophically artistic and is nothing like the

other sciences. This gives numbers a new meaning, it is an unfettered creation of the mind

and is only controlled by the limitations of the mind. Mathematics is an abstract artistic formof thinking and exists within a world of numbers. This concept is useful in its reference and

quite meaningful and relevant in context.

Today mathematics is one of the bases of the modern world. Almost everything along the

line has been exposed to either an equation or theory. Computers have become a realistic

part of everyday life and have changed the face of the 21stcentury, the digital era. These

computers that have taken over the world run on computer programs, the interesting fact is

that these programs are made up of mathematical equations and we can thus say that this is

applied mathematics.

To some individuals mathematics is limited to monthly home budgets, mortgage repayment,

income tax returns and school fees. To the accountant it is the equation that calculatesprofits and losses, theories of value. It is the key with which scientists unlock the secrets of

natural phenomena.

Mathematics is applied to concrete information that determines value and is in fact a fancy

name for counting. It has its origins with advanced urban civilizations where size and

quantity determining was required, like Babylonia, Egypt, Greece and Rome, as early as

1700 BC. The Babylonians was responsible for inventing the zero number without which the

place value system would lose its simplicity. Egyptians mathematical value system was far

more complicated than that we use today. Greek Mathematics is characterised by deep

reasoning that had no equal in the ancient world, as Greek philosophers strived to explain

natural phenomena, with the use of theories.

Have you ever witnessed the energy of a mathematician? The amount of energy that is usedin their enthusiasm is so electric it is incredible, even particles close enough get charged

and their energy fuel students imaginations with so much confusion. They are overwhelmed

as excitement mounts, the closer they get to the solving the problem. Unfortunately they lost

all attention somewhere among the different calculation techniques and theories.

Now we know, blame the Greeks ancestors.

This is the humble beginnings of mathematics. The order of things, captivated within theories

had its origin with the Greeks.

Although we use the terms algebra, geometry and trigonometry mathematics are in fact not

in different parts but one science. Eventually as mathematics advances it becomes

completely abstract within lateral thinking. It tends to become theoretical philosophical,seemingly distant but still relevant, fuelled by the always searching imagination and alive

within the artistic confines of the mind. This is when magical theories are conjured within its

practicality becoming in the end a necessity within the modern world and the future there of.

Sir Karl Popper - a scientific philosopher pointed out that, In order to deduce prediction one

needs laws and initial conditions, if no suitable laws are available or if the initial conditions

cannot be ascertained, the scientific way of predicting breaks down. This statement holds

fast in all areas where theory is applied.

Within mathematics, addition, subtraction and division are the simplest operation involved in

arithmetic. All numbers once referred to physical objects like a flock of sheep, fingers and

apples to primitive man, and are positive whole numbers. Children are taught to carry out

and use calculation, with whole numbers.

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Addition has interesting properties. In adding two numbers a + b we get a result c

irrespective if we add b to a, the result remains the same, even if this addition should be a +

b + c, there is no change in the answer no matter what we add to which. Addition is said to

be communicative and associative. This does not extend to subtraction, because if you

subtract a from b you will get an answerc, but should you subtract b from a, this will not be

so. The human mind is incredible, it has the ability to think and work in an abstract way, withnumbers that does not really exist. Thus a negative number will be required and is seen as

an extension of absolute whole numbers.

This abstract thinking is best seen in Geometry, were we almost always had to calculate in

another dimension. Geometry originated from Egyptians and was later named by the

Greeks who took up the study thereof and made outstanding theoretical contributions.

Geometry translated means measuring of the earth a possibly was the first science which

enabled a person to determine a shape size and apply it comparatively to another shape,

that could be shaped entirely different, to determine the size of each.

The reason could have been that in ascertaining a fields size the amount of crop that this

field would produce could have been established.

Whatever the reason Geometry made great progress through the centuries. This was

probably after the realization that geometry deals with abstractions of real images and not

with the real image themselves. A precise definition exists in geometry for each concept,

which might seem at times abstruse but have a close similarity to the real objects. To make

geometry less abstract comparisons can be used but this could weaken the argument and

lead to gross errors, to stop reasoning with precise definitions usually leads to

contradictions.

The argument is based on logical propositions and rules, the deduction of these facts are

only true for the entities defined for the starting point of the argument. Although this might

seem to be a limitation, this is a specific characteristic that gives geometry its argumentative

power.