Mathematics is the study of numbers, shapes, and patterns.
The word comes from the Greek μάθημα (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to math or maths.
It is the study of:
Applied math is useful for solving problems in the real world. People working in business, science, engineering, and construction use mathematics.
Mathematics solves problems by using logic. One of the main tools of logic used by mathematicians is deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true (called a proof) is just as important as the fact that it is true, and this reason is often found using deduction. Using deduction is what makes mathematical thinking different from other kinds of scientific thinking, which might rely on experiments or on interviews.
Logic and reasoning are used by mathematicians to create general rules, which are an important part of mathematics. These rules leave out information that is not important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time as these rules can be used on other problems. These rules can be called theorems (if they have been proven) or conjectures (if it is not known if they are true yet). Most mathematicians use non-logical and creative reasoning in order to find a logical proof.
Sometimes, mathematics finds and studies rules or ideas that we don't understand yet. Often in mathematics, ideas and rules are chosen because they are considered simple or neat. On the other hand, sometimes these ideas and rules are found in the real world after they are studied in mathematics; this has happened many times in the past. In general, studying the rules and ideas of mathematics can help us understand the world better. Some examples of math problems are addition, subtraction, multiplication, division, calculus, fractions and decimals. Algebra problems are solved by evaluating certain variables. A calculator answers every math problem in the four basic arithmetic operations.
Natural numbers | Integers | Rational numbers | Real numbers | Complex numbers |
Ordinal numbers | Cardinal numbers | Arithmetic operations | Arithmetic relations | Functions, see also special functions |
These theorems and conjectures have interested mathematicians and amateurs alike:
These theorems and hypotheses have greatly changed mathematics:
These are a few conjectures that have been called "revolutionary":
There is no Nobel Prize in mathematics. Mathematicians can receive the Abel Prize and the Fields Medal for important works.
The Clay Mathematics Institute has said it will give one million dollars to anyone who solves one of the Millennium Prize Problems.
There are many tools used to do math or find answers to math problems.
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