Placeholder Image

Subtitles section Play video

  • In the 16th century, the mathematician Robert Recorde

  • wrote a book called "The Whetstone of Witte"

  • to teach English students algebra.

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

  • His solution?

  • He replaced those words with two parallel horizontal line segments

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

  • Could he have used four line segments instead of two?

  • Of course.

  • Could he have used vertical line segments?

  • In fact, some people did.

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

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

  • More and more mathematicians began to use it,

  • and eventually, it became a standard symbol for equality.

  • Math is full of symbols.

  • Lines,

  • dots,

  • arrows,

  • English letters,

  • Greek letters,

  • superscripts,

  • subscripts.

  • It can look like an illegible jumble.

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

  • and to wonder 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 of that is the plus sign for addition,

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

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

  • such as when a mathematician named Christian Kramp

  • introduced the exclamation mark for factorials

  • just because he needed a shorthand for expressions like this.

  • In fact, all of these symbols were invented or adopted

  • by mathematicians who wanted to avoid repeating themselves

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

  • Many of the symbols used in mathematics are letters,

  • usually from the Latin alphabet or Greek.

  • Characters are often found representing quantities that are unknown,

  • and the relationships between variables.

  • They also stand in for specific numbers that show up frequently

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

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

  • Other symbols are used to represent operations.

  • Some of these are especially valuable as shorthand

  • 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 succinct instructions

  • about how to perform calculations.

  • Consider the following set of operations on a number.

  • 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.

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

  • With them, we have a compact, elegant expression.

  • Sometimes, as with equals,

  • these symbols communicate meaning through form.

  • Many, however, are arbitrary.

  • Understanding them is a matter of memorizing what they mean

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

  • If we were to encounter an alien civilization,

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

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

  • And their symbols may even correspond directly to ours.

  • They'd have their own multiplication sign,

  • symbol for pi,

  • and, of course, equals.

In the 16th century, the mathematician Robert Recorde

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

B1 US TED-Ed symbol sign shorthand mathematician multiplication

【TED-Ed】Where do math symbols come from? - John David Walters

  • 5025 623
    osmend posted on 2017/11/04
Video vocabulary