Math is full of symbols: lines, dots, arrows, English letters, Greek letters, superscripts, subscripts … it can look like a great big mess. Who decided these were the symbols we would use? John David Walters describes the origins of mathematical symbols and shows us why they’re still so important today.

In the 16th century, the mathematician Robert Recorde wrote a book called “The Whetstone of Witte” to teach English students algebra. He was over writing the words “is equal to” repeatedly. So, he replaced that phrase with two parallel horizontal lines, because to him, “no two things can be more equal.” There’s no real reason the equals sign looks the way it does today. It just caught on, sort of like a meme. More and more mathematicians began using it as shorthand, and eventually, it became the standard symbol.

It’s understandable to think this overwhelming system of symbols is a little intimidating and to ask where they all came from. Sometimes, as Recorde himself noted about his equals sign, “there’s an apt conformity between the symbol and what it represents.” Another example is the plus sign for addition, which came from a condensing of the Latin word “et” which means “and”.

Sometimes, however, a symbol is more random. Like Christian Kramp, the mathematician who used the exclamation mark for factorials all because he got tired of writing expressions like 4x3x2x1. In fact, all of our math symbols were created by people who wanted to avoid repeating themselves or having to use a lot of words to write out equations.

Many of the symbols we use in math are letters, usually from the Latin or Greek alphabet. Letters are used to represent quantities that are unknown and the relationships between variables. They also stand in for specific numbers that show up frequently but would be annoying or impossible to write out. Sets of numbers and whole equations can be represented with letters, too.

Other symbols are used to represent operations. Some of these are especially convenient because they condense repeated operations into a single expression. The repeated addition of the same number is abbreviated with a multiplication sign so it doesn’t take up more space than it has to. A number multiplied by itself is indicated with an exponent that tells you how many times to repeat the operation. And a long string of sequential terms added together is collapsed into a capital sigma. These symbols shorten lengthy calculations to smaller terms that are much easier to manipulate.

Symbols can also provide clarity about how to perform calculations. For example, imagine saying or writing: “Take some number that you’re thinking of, multiply it by two, subtract one from the result, multiply the result of that by itself, divide the result of that by three, and then add one to get the final output.” Rather than the quick equation [(2n-1)^{2}/3]+1. Without these symbols, we’d be faced with a block of text. With them, we have a compact, easy-to-read expression.

Sometimes, as with equals, symbols communicate meaning through form. Many, however, are random. Understanding them is all about memorizing what they mean and using them in different ways until they just make sense, like learning a new language.

TED, TED-Ed, TED Education, TED Ed, John David Walters, Chris Bishop, math, math symbols, pi, equals, factorial, integral, multiplication, division, addition, plus sign, Robert Recorde