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In the 16th century, the mathematician
Robert Recorde

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wrote a book called 
"The Whetstone of Witte"

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to teach English students algebra.

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But he was getting tired of writing
the words "is equal to" over and over.

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His solution?

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He replaced those words with
two parallel horizontal line segments

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because the way he saw it,
no two things can be more equal.

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Could he have used four line segments
instead of two?

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Of course.

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Could he have used vertical line segments?

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In fact, some people did.

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There's no reason why the equals sign
had to look the way it does today.

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At some point, it just caught on,
sort of like a meme.

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More and more mathematicians
began to use it,

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and eventually, 
it became a standard symbol for equality.

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Math is full of symbols.

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Lines,

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dots,

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arrows,

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English letters,

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Greek letters,

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superscripts,

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subscripts.

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It can look like an illegible jumble.

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It's normal to find this wealth
of symbols a little intimidating

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and to wonder where they all came from.

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Sometimes, as Recorde himself
noted about his equals sign,

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there's an apt conformity
between the symbol and what it represents.

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Another example of that 
is the plus sign for addition,

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which originated from a condensing
of the Latin word et meaning and.

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Sometimes, however, the choice of symbol
is more arbitrary,

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such as when a mathematician
named Christian Kramp

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introduced the exclamation mark
for factorials

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just because he needed a shorthand
for expressions like this.

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In fact, all of these symbols 
were invented or adopted

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by mathematicians who wanted
to avoid repeating themselves

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or having to use a lot of words
to write out mathematical ideas.

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Many of the symbols used
in mathematics are letters,

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usually from the Latin alphabet
or Greek.

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Characters are often found
representing quantities that are unknown,

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and the relationships between variables.

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They also stand in for specific numbers
that show up frequently

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but would be cumbersome or impossible
to fully write out in decimal form.

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Sets of numbers and whole equations
can be represented with letters, too.

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Other symbols are used 
to represent operations.

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Some of these are especially valuable
as shorthand

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because they condense repeated operations
into a single expression.

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The repeated addition of the same number
is abbreviated with a multiplication sign

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so it doesn't take up more space
than it has to.

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A number multiplied by itself
is indicated with an exponent

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that tells you how many times
to repeat the operation.

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And a long string of sequential terms
added together

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is collapsed into a capital sigma.

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These symbols shorten
lengthy calculations to smaller terms

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that are much easier to manipulate.

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Symbols can also provide 
succinct instructions

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about how to perform calculations.

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Consider the following set
of operations on a number.

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Take some number that you're thinking of,

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multiply it by two,

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subtract one from the result,

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multiply the result of that by itself,

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divide the result of that by three,

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and then add one to get the final output.

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Without our symbols and conventions,
we'd be faced with this block of text.

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With them, we have a compact,
elegant expression.

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Sometimes, as with equals,

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these symbols communicate meaning
through form.

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Many, however, are arbitrary.

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Understanding them is a matter
of memorizing what they mean

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and applying them in different contexts
until they stick, as with any language.

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If we were to encounter
an alien civilization,

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they'd probably have a totally
different set of symbols.

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But if they think anything like us,
they'd probably have symbols.

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And their symbols may even correspond
directly to ours.

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They'd have their own multiplication sign,

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symbol for pi,

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and, of course, equals.