Updated date:

The Language of Mathematics

People used language to express themselves and communicate. It is usually spoken, signed or written in symbols. Language is like the internet that connects people in the world and there is no doubt that language is an indispensable thing. Math is also not a different matter. Mathematics has its own language which makes it easy to express its thought. Math is part of our everyday life. We use math in the grocery, in our work, school and even at home. In fact, we use decimal digit right after we woke up to determine the time. And even the number of years of our existence is an example of mathematical language.

Mathematical Language

Mathematical language is a system used to express, communicate and convey mathematical information. It is distinct and unique from the usual language that people are used to, and is used to communicate abstract and logical ideas. Mathematical language is characterized by abstraction symbols and rules, non-linearity and complexity of language, arrangement, coding and decoding information.

The following are the three (3) characteristics of mathematical language.

1. Precise. Precision of mathematical language means that mathematical language is able to make very fine distinction of things. Mathematical language as being precise means “accurate or exact”. This is one of the reasons why math is considered as exact science.

2. Concise. Mathematical language as being concise means mathematical language is able to say or write things briefly. For instance, instead of writing “the sum of two and a number” we can write the expression 2+x.

3. Powerful. Mathematical language is a powerful tool because it can express thoughts with relative ease.

Mathematical Symbols

Mathematical symbol is used to refer certain quantities, concepts, ideas and others. The commonly used symbols in math are:


The combination of variables, operations, notations and symbols form a mathematical expression or mathematical sentence. What is the difference between the two?

Mathematical Expression

A mathematical expression is a mathematical analogue of an English noun. It DOES NOT state a complete thought. The most common expressions are numbers, variables, sets and functions.




y - 3

Mathematical Sentence

A mathematical sentence is a mathematical analogue of an English sentence. It state a complete thought.


1 + 6 = 7

8x = 16

x - 3 > 2

It always used symbols such as equality and inequality symbols.
Mathematical sentences have verbs.

In 1+6=7, the verb is the equal sign. A mathematical sentence can be

1. Always TRUE
2. Always FALSE
3. Sometimes True / Sometimes False

Translating English Statement or Phrases into Mathematical Expression

The success of solving mathematical problem correctly lies on how the students will going to translate English language (phrases or statement) into mathematical expression and sentence. An appropriate use of variables, symbols, operations and notations in translating language will give correct equation and representation to solve a given mathematical problem.

Examples of Translating English Language (Phrases / Statement) to Mathematical Expressions (using symbol, notations, operations and variables).


Translating English Sentences to Mathematical Sentences

Examples of Translating English Sentences to Mathematical Sentences (using symbol, notations, operations and variables).


Kinds of Mathematical Statement

1. A Universal Statement expresses an idea that is true for all the elements in a set describe. It commonly used the word, all, For all, For every, For each symbol.

All negative numbers are less than zero.

2. A Conditional Statement expresses a conditional idea that if one thing is true then some other thing also has to be true. It commonly uses the word: “If then”, “if and only if” or the symbol: “iff”.

If a number is even then it is a multiple of 2.

3. An Existential Statement expresses an idea that may or may not be true or at least one thing for which the property is true. It commonly used word: There exist, in symbol: “ⱻ”.

There exist a prime number that is even.

Classification of Mathematical Statement

Mathematical Statement can also be classified as: TRUE mathematical statement or FALSE mathematical statement.


The Science of Self


Aikz Adonis (author) from CITY OF TABACO on October 18, 2020:

Thank you sir for the suggestion. :)

I'll work for it. Thank you.

George Dimitriadis from Templestowe on October 17, 2020:


Your article is informative and structured, with examples provided of each type of mathematical term/symbol/concept covered.

However, there might be too much information for the length of the article.

Perhaps you can expand on each definition with more examples or split the article into two or more articles.