What is Math?


What is Math?
Throughout centuries, many people have had many controversies over the true definition of mathematics.  Some people believe mathematics is the study of patterns. However, that is a broad definition and is a common misconception.  Math is not the study of a pattern, it is a language.  Most people around the world understand the basic concepts of math and have used them during jobs.  Such a study, Cryptology, is a way of hiding information through mathematical concepts such as substitution. Besides Cryptology, mathematics is used in the curriculum of science, computer science, etc.

“Mathematics may be defined as the economy of counting.  There is no problem in the whole of mathematics which cannot be solved by direct counting.  ~Ernst Mach2

The best way of summarizing “what is math” is saying it is “a science that studies quantity, change, shape, structure, and arrangement.”
People who excel in the areas of math are called mathematicians.  Such people formulate conjectures, find relationships between objects (such as PHI, the golden ratio), and deduct logic as well as use problem-solving skills to find solutions to everyday problems.  Famous mathematicians include Leonardo Pisano and Isaac Newton.
A famous conjectures formed by mathematicians is Fermat’s Last Theorem.
Leonardo Pisano forever changed the world of mathematics by discovering a sequence in the field of quantities.  Today, this famous sequence is also known as the Fibonacci sequence, named after Pisano’s nickname.  An example is 0,1,1,2,3,5,8, 13… Starting with zero, each number is the sum of the two numbers before it. 
Isaac Newton, a physicist and scientist, contributed to a main branch in math today also known as calculus.  Calculus focuses on limits, series, etc.  Isaac also discovered three important laws of motion.

“Black holes result from God dividing the universe by zero. 
 ~Author Unknown2

Quantities in math are the study of numbers and the size of such numbers.  This is widely known as number theory.  Examples of quantity topics include infinite concepts and modular arithmetic.  Number theory plays an important role in communication. There are a few unproven conjectures in this field of mathematics; such as the Twin Prime Conjecture, which states that there are infinitely primes that have a difference of 2.  (41 and 43 is an example).  Some types of numbers are rational, irrational, real, integers, counting numbers, complex numbers, natural numbers, etc.  An everyday example of using quantities in math is saying there are 100 cookies in the refrigerator.
The study of change in nature is studying “natural sciences”.  Calculus was developed to analyze such change.  Calculus manipulates small figures and graphs and analyzes the change. The slope formula, change of y over change of x demonstrates calculus.  Sometimes calculus can be explained as change over time.

“One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.  ~Philip J. Davis2

The study of shape involves two and three dimensional objects; such as geometry and trigonometry.  There are many types of geometry; Euclidean, Algebraic, Differential, etc.  In general, this geometry covers many different concepts.  For example, Euclidean geometry covers 2-D planes.
The study of structure examines functions and shapes and asks a menacing question; why are they in this structure”.  This includes sets, rings, and groups.
The study of arrangement leads into a combinations, permutations and counting.  This type of math is widely known as combinartorics. 
Math is an abstract concept.  Abstract is a topic that is vague and away from concrete realities. Problem-solving skills used in mathematics turns something incomprehensible into something easier to understand.  This leads, of course, to the rhetorical question again; what is mathematics?
To me, math is an art.  It is the way you think about something.  You math skill depends on your creativity.  This art does not depend on memorizing strategies and theorems. That is math.




References
1. Contrast, By. "Abstraction." Wikipedia, the Free Encyclopedia. <http://en.wikipedia.org/wiki/Abstraction>.
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3. "Mathematics." Wikipedia, the Free Encyclopedia. Web.. <http://en.wikipedia.org/wiki/Math>.
4. "What Is Math." Bakersfield College. Web.. <http://www2.bakersfieldcollege.edu/math/what_is_math.htm>.
5. "What Is Math? : Good Math, Bad Math." ScienceBlogs. Web.. <http://scienceblogs.com/goodmath/2009/12/what_is_math.php>.
6. "1.2 What Is Calculus and Why Do We Study It?" MIT Mathematics. Web.
7. "Problem Solving." Free Management Library (SM). <http://managementhelp.org/prsn_prd/prob_slv.htm>.