Mathematics Facts for Kids

Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala

A page from al-Khwārizmī's Algebra, a very old math book.

Mathematics is the study of numbers, shapes, and patterns. The word comes from the Greek word "máthema," which means "science, knowledge, or learning." People sometimes shorten it to maths in places like England and Australia. In the United States and Canada, it's often called math. These shorter words are often used for subjects like arithmetic, geometry, or simple algebra that students learn in school.

Mathematics helps us understand:

Numbers: How we count things.
Structure: How things are organized. This part is often called algebra.
Place: Where things are and how they are arranged. This is usually called geometry.
Change: How things become different over time. This is known as analysis.

Mathematics is very useful for solving problems in the real world. Many people, not just mathematicians, use math every day. Jobs in business, science, engineering, and construction all need some math skills.

Solving Problems with Math
Main Areas of Math Study
Famous Math Ideas
How Math is Studied
- History of Math and Mathematicians
Math Awards
Tools for Math
Related Pages
Images for kids
See also

Solving Problems with Math

Mathematics solves problems using logic. One main tool mathematicians use is deduction. Deduction is a special way of thinking. It helps us discover and prove new truths using things we already know are true.

For a mathematician, knowing why something is true (called a proof) is as important as knowing that it is true. This "why" is often found using deduction. This is what makes math thinking different from other sciences. Other sciences might use experiments or interviews to find answers.

Mathematicians use logic and reasoning to create general rules. These rules are a big part of mathematics. They leave out unimportant details so that one rule can work for many situations. By finding general rules, math can solve many problems at once. These rules can be called theorems if they have been proven true. If we don't know if they are true yet, they are called conjectures.

Sometimes, math explores ideas and rules that we don't fully understand yet. Often, ideas in math are chosen because they seem simple or elegant. Interestingly, some of these ideas, first studied in math, are later found to exist in the real world. Learning about math rules and ideas helps us understand the world better. Some basic math problems include addition, subtraction, multiplication, and division. Algebra problems involve finding the value of certain variables. A calculator can help solve many math problems quickly.

Main Areas of Math Study

Understanding Numbers

Mathematics involves studying numbers and how much of something there is. Many math fields, like set theory and mathematical logic, look at numbers. Number theory mainly focuses on how whole numbers work, rather than just what numbers are.

$0, 1, 2, 3, \ldots$	$\ldots, -1, 0, 1, \ldots$	$\frac{1}{2}, \frac{2}{3}, 0.125,\ldots$	$\pi, e, \sqrt{2},\ldots$	$1+i, 2e^{i\pi/3},\ldots$
Natural numbers	Integers	Rational numbers	Real numbers	Complex numbers
$0, 1, \ldots, \omega, \omega + 1, \ldots, 2\omega, \ldots$	$\aleph_0, \aleph_1, \ldots$	$+,-,\times,\div$	$>,\ge, =, \le, <$	$f(x) = \sqrt x$
Ordinal numbers	Cardinal numbers	Math operations	Math relationships	Functions

Studying Structure

Many parts of mathematics look at the structure of objects. Most of these areas are part of algebra.


Number theory	Abstract algebra	Linear algebra	Order theory	Graph theory

Exploring Shapes

Some areas of mathematics study the shapes of things. Most of these are part of geometry.


Topology	Geometry	Trigonometry	Differential geometry	Fractal geometry

Looking at Change

Some parts of mathematics study how things change. Most of these are part of analysis.


Calculus	Vector calculus	Analysis

Differential equations	Dynamical systems	Chaos theory

Applied Mathematics

Applied mathematics uses math to solve problems in other areas. This includes fields like engineering, physics, and computer science.

Some areas of applied mathematics are:

Famous Math Ideas

These are some famous theorems and ideas that have interested many people.

These theorems and conjectures have greatly changed mathematics:

How Math is Studied

Understanding what mathematics is also changes how mathematicians study it.

History of Math and Mathematicians

This section looks at the history of mathematics and the people who study it.

Math Awards

There is no Nobel Prize in mathematics. However, mathematicians can receive the Abel Prize and the Fields Medal for their important work.

The Clay Mathematics Institute has offered one million dollars to anyone who solves one of the Millennium Prize Problems.

Tools for Math

Many tools help us do mathematics or find answers to math problems.

Older tools

Abacus
Napier's bones, slide rule
Ruler and Compass
Mental calculation (doing math in your head)

Newer tools

Images for kids

The ancient Greek mathematician Euclid, as imagined by Raphael.
The Ulam spiral shows how prime numbers are spread out.
The Babylonian math tablet Plimpton 322, from around 1800 BC.
The numbers used in the Bakhshali manuscript, an old Indian math text.
Fibonacci, an Italian mathematician who brought the numbers we use today to the Western world.
Leonhard Euler helped create much of the math notation we use now.
Carl Friedrich Gauss, often called the "prince of mathematicians."
Euler's identity, a famous math formula.
The front side of the Fields Medal, a top award in math.