The Language of Mathematics

Math can be an intimidating thing. Unfortunately, many of us go our entire lives without really understanding what it is all about. We may have taken a Spanish or French class in high school, where we learned about a different language, but most of us were never told that mathematics is also a language. It has its own words and grammar. Until we learn to speak mathematics, we cannot understand much of the world around us.

For those who have studied European languages, this connection between mathematics and language may not be obvious. However, the connection between mathematics and language is more obvious when you look at languages like Chinese, Japanese and Korean, which use Chinese characters. This is because the symbols used in mathematics, like Chinese characters, carry meaning separate and apart from the sounds which make up a word. For this reason, a Japanese person can see a sentence written in Chinese and understand much of the meaning in the sentence, even though the Japanese person has no clue about how to pronounce the Chinese sentence.

Thousands of years ago, people in China began to express language in the form of picture. For example to represent the sun, they drew a circle with a dot in the middle. Over the centuries, the circle/dot symbol became stylized. Today this symbol means sun.

When seen by a Chinese, Japanese or Korean person they recognize this symbol as meaning sun, even though they do not know how it is pronounced in the other languages. Likewise, when they see this next symbol, they understand that it means moon.

When combined into a single character, these two symbols together mean bright, because they are both bright objects in the sky.

The language of mathematics is very similar. The symbols used in mathematics, like Chinese characters, carry meaning independent of the way the language is spoken. Thus a person in Russia, India or the United State can look at a mathematical equation and understand it meaning, even though they do not speak the same language.

For those of you who enjoy a good romance novel, watch Dr. Phil or love Oprah, I have great news. The language of mathematics is the language for you. It is the language of relationships. For example, when you see an equal sign, you know that what is on the left side must be that same as what is on the right side. It defines the relationship between the two sides of the equation.

=

Likewise, when you see a not equal sign, you know that what is on the left side is not the same as what is on the right side.

≠

When you see a greater than sign, you know that what is on the left side is bigger than what is one the right side.

>

Fractions often seem to be a challenge, but fractions are simply about proportions. How big is the top compared with what is on the bottom? If the top is bigger than the bottom, then the value of the fraction is greater than one. If the bottom is bigger than the top then the value is less than one. If the bottom and the top are the same, then the value is exactly one. Therefore, when you see this symbol, think about the proportional relationship of what is on top to what is on the bottom.

/

Most of us do okay, when we are simply asked to perform simple mathematical operations. We learn to add, subtract, multiply and divide. But, all of these things we learn to do without really learning to read the language of mathematics. For many, real confusion sinks in when their high school Algebra teacher starts to use letters instead of numbers. What our Algebra teachers do not tell us is that we are now reading a foreign language. They give us sentences, but do not give us a dictionary to translate this new language into English. Instead of the numbers that we were used to seeing in “math” we see x, y, z, a, b and c. We are used to performing operations with numbers, but what are we supposed to do with an “x” or a “c”? What strange grammatical rule is implied by ( )?

The trick is in understanding that you have just made the transition into a new language which is more about the underlying relationships between things than it is about performing operations to come up with a specific number as an answer.

Here is a beginner’s dictionary to some of the symbols you will encounter on your journey into the land of mathematics. Remember, these symbols are not like the letters in the English language. They are like the Chinese characters above. They have meaning independent of any particular language.

= Equal sign (What is on the left is the same as what is on the right)

≠ Not equal sign (What is on the left is not the same as what is on the right)

+ Plus sign. (Combine what is on the left with what is on the right)

- Minus sign. (Take what is on the right away from what is on the left)

/ Fraction (The proportion of what is on the left to what is on the right)

> Greater than sign (What is on the left is larger than what is on the right)

< Less than sign (What is on the left is smaller than what is on the right)

( ) Parenthesis (Do what is inside before you do what is outside)

x, y or z Variables (These letters take the place of numbers that can take different values)

a, b or c Constants (These letters normally represent a number which can have only one value.)

These symbols are probably nothing new. But, now you know that they are a part of a language that can tell us a lot about how our world is interrelated. In mathematics, you can write a sentence about the relationships between the earth, the moon and the sun. You can write a sentence about your chances of winning at a slot machine in Las Vegas, or the relationship between your 401K and increases in oil prices. Mathematics is an incredible language, which can open up entirely new ways of looking at and understanding your world. Now that you understand that it is in fact a new language, I hope that you will enjoy learning about mathematics and all of the hidden relationships around you that it mathematics can reveal.