1403 words - 6 pages

The Nature of Mathematics

Mathematics relies on both logic and creativity, and it is pursued

both for a variety of practical purposes and for its basic interest.

The essence of mathematics lies in its beauty and its intellectual

challenge. This essay is divided into three sections, which are

patterns and relationships, mathematics, science and technology and

mathematical inquiry.

Firstly, Mathematics is the science of patterns and relationships. As

a theoretical order, mathematics explores the possible relationships

among abstractions without concern for whether those abstractions have

counterparts in the real world. The abstractions can be anything from

strings of numbers to geometric figures to sets of equations. In

deriving, for instance, an expression for the change in the surface

area of any regular solid as its volume approaches zero,

mathematicians have no interest in any correspondence between

geometric solids and physical objects in the real world.

A central line of investigation in theoretical mathematics is

identifying in each field of study a small set of basic ideas and

rules from which all other interesting ideas and rules in that field

can be logically deduced. Mathematicians are particularly pleased when

previously unrelated parts of mathematics are found to be derivable

from one another, or from some more general theory. Part of the sense

of beauty that many people have perceived in mathematics lies not in

finding the greatest richness or complexity but on the contrary, in

finding the greatest economy and simplicity of representation and

proof. As mathematics has progressed, more and more relationships have

been found between parts of it that have been developed separately.

These cross-connections enable insights to be developed into the

various parts; together, they strengthen belief in the correctness and

underlying unity of the whole structure.

Mathematics is also an applied science. Many mathematicians focus

their attention on solving problems that originate in the world of

experience. They too search for patterns and relationships, and in the

process they use techniques that are similar to those used in doing

purely theoretical mathematics. The difference is largely one of

intent. In contrast to theoretical mathematicians, applied

mathematicians, in the examples given above, might study the interval

pattern of prime numbers to develop a new system for coding numerical

information, rather than as an abstract problem. Or they might tackle

the area/volume problem as a step in producing a model for the study

of crystal behavior.

The results of theoretical and applied mathematics often influence

each other. Studies on the mathematical properties of random events,

for example, led to knowledge that later made it possible to improve

the design of...

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