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What is math?

The word math stands for mathematics. It is a field of study. The word mathematics originates from the Greek word máthema. The meaning of máthema word is science, knowledge or learning. Both math and maths are short forms of mathematics. So, the word mathematics is the same as math. These short words often used by students and their schools for arithmetic, geometry, and algebra.


Definitions of Math

Commonly, there is no accepted definition of math. Aristotle defined mathematics as, the science of quantity. The definition given by Aristotle prevailed until the 18th century.

The study of numbers, shapes, and patterns is called math. In other words, we can define the term math as, the field of study that uses numbers and symbols for measurement, properties, relationships of quantities, and sets.

According to the German philosophers Carl Friedrich Gauss, mathematics is the Queen of the Sciences.

Modern philosophers do not consider mathematics as a science because science is based on empirical observations and seek to understand some aspect of phenomena. While math defines the relationship between quantities and objects and seeks to use logic to understand. The mathematics do not relate to any phenomena.

The study of math includes the following:

  • Numbers: The study of numbers involves how can we count the things.
  • Structure: The study of structures involves how things can be organized. The subfield of structure is called algebra.
  • Place: The study of place involves the arrangements for the things. The subfield of place is called geometry.
  • Change: The study of change involves how things become different. The subfield of change is called analysis.

Why math is important?

Math is very important in our daily lives. In reality, it is implemented everywhere. It is useful for solving problems that occur in the real world. This is the reason that so many people besides mathematicians study and use mathematics. There are too many fields such as natural science, engineering, medicine, finance, etc. that uses mathematics.

There are the following reasons that makes the mathematics as a powerful tool.

  • Math is involved around us. So, it is an essential and powerful discipline in today's world. Our perspective of the important issues facing us as individuals, families, businesses, and nations.
  • It provides an effective way of building mental discipline.
  • It improves mental rigor for developing logical, analytical, and problem-solving skills.
  • The knowledge of mathematics plays a crucial role in understanding other subjects such as physics, art, music, etc.

Fields of Mathematics

In mathematics there are two main branches:

  • Pure Mathematics
  • Applied Mathematics

Pure Mathematics

In pure mathematics, we study the mathematical concept independently of any application outside mathematics. It includes proof theory and mathematical logic or symbolic logic which is further divided into several distinct subfields such as arithmetic, algebra, geometry, calculus, topology, analysis, etc.

  • Proof Theory: It includes set theory and model theory.
  • Number Theory: It includes arithmetic, elementary number theory, analytic number theory, algebraic number theory, and other number theories such as computational number theory, geometric number theory, etc.
  • Algebra: It includes order theory, general algebraic system, field theory and polynomials, commutative rings and algebras.
  • Combinatorics: It includes graph theory.
  • Geometry: It includes convex geometry, discrete geometry, differential geometry, and algebraic geometry. The algebraic geometry further includes arithmetic geometry, Diophantine geometry, and real algebraic geometry.
  • Topology: It includes general, algebraic, and differential topology.
  • Analysis: It is a branch of mathematics that is rapidly expanding. It includes other subdivision of the mathematics. It finds both, direct and indirect applications in subjects as diverse as number theory, cryptography, and abstract algebra.

Applied Mathematics

The combination of mathematics and specialized knowledge is known as applied mathematics. It is used in different fields such as science, engineering, computer science, and business. It includes probability, statistics, computational sciences, and physical sciences.

  • Probability: It includes the random theory of random-phenomena.
  • Statistics: It includes the study of surveys and experiments.
  • Computational Sciences: It includes numerical analysis and computer algebra.
  • Physical Sciences: It includes mechanics, mechanics of structure, mechanics of deformable solids, fluid mechanics, particle mechanics.

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