“Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.” ~ Jordan Ellenberg

Mathematics is the study of numbers, shapes and patterns. The word comes from the Greek word “μάθημα” (máthema), meaning “science, knowledge, or learning”, and is sometimes shortened to maths (in England, Australia, Ireland, and New Zealand) or math (in the United States and Canada).1

Mathematics includes the study of:

• Numbers: how things can be counted.
• Structure: how things are organized. This subfield is usually called algebra.
• Place: where things are and their arrangement. This subfield is usually called geometry.
• Change: how things become different. This subfield is usually called analysis.

## Different Branches of Mathematics

### Pure Mathematics

• Number Theory
• Algebra
• Geometry
• Arithmetic
• Combinatorics
• Topology
• Mathematical Analysis

### Applied Mathematics

• Calculus
• Statistics and Probability
• Set Theory
• Trigonometry

## Study of Patterns

As mathematician Keith Devlin states in The Math Gene, math studies patterns that come “from the world around us, from the depths of space and time, and from the workings of the human mind.”2

• Arithmetic — patterns of numbers.
• Geometry — patterns of shapes.
• Algebra — patterns of unknown variables.
• Calculus — patterns of change in equations.
• Set theory — patterns of sets.
• Topology — patterns of surfaces and spaces.
• Combinatorics — patterns of counting.
• Abstract Algebra — patterns of sets and operations (addition, multiplication, etc.) put together.

1 “Mathematics – Simple English Wikipedia, The Free Encyclopedia”. 2018. Wikipedia. https://simple.wikipedia.org/wiki/Mathematics.

2 “Math Is Not The Study Of Numbers”. 2020. Medium. https://mikebeneschan.medium.com/math-is-not-the-study-of-numbers-3c9fd8087772.