Sometimes it is the little things that are the most important and
you could lump mathematical symbols into this category. It is undeniable
that symbols not only enhance understanding but also provide a universally
perceivable manner in which to show a certain math function or illustrate
a sequence. This is not a new concept. It has been around in math
since ancient times. It was probably even around in one form or another
during the stone age!
The fundamental need in math is to represent the relationship between
a sign and the number or value it refers. Certain ideas and concepts
can be clearly illustrated only by the creation and use of symbols.
Measuring the relationship between numbers and representing the relationship
symbolically not only serves to simplify the process but also gains
a better understanding of the concept than a wordy description of
the same. This is where the issue of languages comes in.
In more simple terms, a plus sign, a minus sign, a multiplication
sign are all symbols. We need them for a very simple reason: we have
to express what we are doing in a clear manner. When we are adding
it would be ridiculous to always write out one plus on equals two
when we could express this symbolically with 1 + 1 = 2. Imagine trying
to perform calculus if you have to write a lengthy equation out in
several paragraphs. Not only would such prose be voluminous, it would
be confusing and prone to error. Plus, what language do you want to
write it in? Remember, math is universal but languages are incredibly
vast. Simply put, without proper symbols math becomes next to impossible.
In fact, you could look at it this way: the symbols of math are reflective
of a mathematical language.
Math is comprised of primarily two things: numbers and symbols.
Symbols are found in simple math, algebra, geometry, calculus, statistics,
etc. Symbols are essentially representative of a value. Decimals and
fractions, for example, are symbols of parts of a whole. These symbols
allow us to "work with" parts in a theoretical manner. Without symbols
you simply could not perform math. Remember, much of math is abstract.
How could you possibly perform simple algebra - much less calculus
-without having the use of the symbol "X"? Could you even imagine
trying to perform geometry without symbolic representations of triangles,
squares and rectangles? It simply can not be done or if it was done
it would be so laborious that it wouldn't be as efficient.
It is important to understand that the key to comprehending math
is in the interpretation of the concept and not really in the nature
or amount of symbols and the role they play. However to understand
concepts one must essentially have a good grasp of the role and meaning
of symbols and also be able to appreciate their usefulness in making
math that much more simpler to understand and duplicate. The logic
of signs and symbols in math is undeniable and is often stressed as
a vital tool in making math a universal science.
Because symbols are so common in math we sometimes take them for
granted. The reason we take them for granted is that they make math
so easy to perform (actually, they make math performable period) we
do not really tip our hat to their true value. That does not seem
like a great way to treat the very thing that makes expressing math
possible. Without various symbols you would be forced to go back to
counting your fingers and toes and you don't want to do that again