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- เผยแพร่เมื่อ 29 ต.ค. 2017
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Math is full of symbols: lines, dots, arrows, English letters, Greek letters, superscripts, subscripts ... it can look like an illegible jumble. Where did all of these symbols come from? John David Walters shares the origins of mathematical symbols, and illuminates why they’re still so important in the field today.
Lesson by John David Walters, directed by Chris Bishop.
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Wow, what my middle school math teacher meant by “Mathematicians are lazy” makes COMPLETE sense now. I never put thought into what he said.
Does all math teacher say that?
@@randomguy263 Mine did.
@@neventomicic330 Yeah, my math teacher also explained what he meant by it.
@@randomguy263 my maths teacher is lazy sorry super lazy
👍🏻 (I'm a math teacher)
This was kinda disappointing... we only actually got the answer to the question "Where do math symbols come from?" for 3 symbols: =, +, and !
Higgins2001
You know how long it took me to realize that ÷ LITERALLY symbolizes a fraction?
I don't think you watched the entire video, they clearly explained × ÷ sigma and ². They also gave more subtle explanations for other symbols, such as pi and not equal to.
Menno - I did indeed watch the whole video. They explained why the symbols exist and what they represent, but not where they come from (and most of us already know what they represent, and why we need symbols overall)
Sorry, I misunderstood. Perhaps the origin of some symbols couldn't be traced to one person, or no one knows who thought of them.
By the way, you responded quite quickly. Were you online since you posted the original comment?
Menno Astfalck notification
It's interesting how there are still different ways of writing some of these, •, * and x are used for multiplication etc.
sometimes, especially when youre dealing with parentheses, you dont even need to write any symbol for multiplication
so (x + y)(x - y) is the same as (x + y) * (x - y)
2 X 2 is primary school
* and • represent the same symbol basically, dot for writing and * for typing. • is used in more advanced grades to not mix up with a possible variable in case you continued using x. In the presence of a variable or parentheses, no symbol is necessery.
2x, 3y, 2(7 + 9). You might even do 2(8)
You are an + Lol!
And in some contexts, they are actually different operations and thus _need_ to have different symbols.
Like with vector math, or pretty much any defined programming language.
Dot and cross are different.
Some elementary students _(trying to be smart)_ saw that there were dots between multiplications for work done or torque...and concluded that it meant the same. It have different meaning in vector physics.
I have seen this personally in my class.
The division sign that we're all wondering about is called obelus and was first used for division by Swiss mathematician Johann Rahn in his 1659 book
th-cam.com/video/-42WaYUTsOg/w-d-xo.html
That is not used in Finland. Instead we use a colon.
@@okaro6595I never really got why we use • and : instead of × and ÷
@@kuutti256 to me it's the other way around, like • is shorter then × and : is shorter then ÷ so why not use • and : instead of × and ÷ to save ever so slightly more time? Especially when the whole point of using symbols is to save time. And before anyone says "oh but they barely save any time/ no time" when your teacher is an Eminem wannabe it actually does save A LOT of time to use • and : instead of × and ÷
''English letters'' that hurts me a bit
Because they're Latin? Just a guess.
He said Latin later, so it’s not as bad
Ça nous fais mal à tous.
pretty much all western European language in the latin derived so calling all of them "latin" alphabet is unhelpful.
"hey man, can you write the Latin letters?"
ok *writes english 26 letters*
"sorry I meant spanish letters!"
American letters*
If math class covered more history like this I probably would have liked it more
How would that be useful for getting and executing a math-related job though?
@@dorol6375 investment makes being motivated towards something easier. Not everyone can just do what they are told in class without asking, why, where did this come from, what is the meaning of this things creation.
@@Tokmurok If you need a reason to be motivated for a subject, that probably wouldn't be your future job though.
@@dorol6375 I was always good at math until I got to Precalc in 10th grade. I simply couldn't understand why we were doing what we were doing and my progress in mathematics came to an abrupt halt. It is only when I looked ahead at Calculus (several years later, out of curiosity) that it all started to click. I re-enrolled in university during the pandemic and now, at 29, am nearly finished with a degree in Applied Mathematics. There were other personal reasons why my academic & life path diverted in the way that it did, but not understanding why we were doing certain things was a huge source of frustration & initial disinterest in STEM - especially since I've always hated traditional systems of education. I hope my future job involves some use of math & problem solving, because it is something I do enjoy, I just can't bear when a task seems utterly pointless.
I would have less, although i find this interesting, i prefer the numbers and applications of the symbols more than the symbols themselves.
I'd like to add a few things: the symbol for the square root √ and the integral ∫ come from the latin letters r for root and s for sum respectively. The minus sign - is what's left of a tilde written over the letter m indicating substraction, π is the greek p for perimeter (of the circle with diameter 1). Most other signs, like * and /, are fairly new and were invented by mathematicians.
The alleged origin of the digits is also very interesting: 0 was the original ten, and is was written a little up, so that 9 and 8 were that circle with one and two little lines coming from its bottom. The 5 was the same circle written low, and with a horizontal line over it for disambiguation. The 6 and 7, again, are that low circle with one and two lines at its top. 1 to 3 are series of straight lines forming just as many angles as their value. 4 was once just a kind of cross, thus forming four angles, but the horizontal line sort of slided to the left a bit and was bent up at its left end. Better google these again. That's all I can tell :D
That's still a lot. Thank you
* may be multiple + laid one on another.
One of the many things I love about Khan Academy is that Sal always reminds us of what the symbols mean, no matter the level of the course. Makes learning so much easier.
th-cam.com/video/-42WaYUTsOg/w-d-xo.html
I didn't know I wanted to know this until now
I didnt know that you didnt know you wanted to know this until now
Yes, is one of those things that you don't wonder abot until some one suggest you to, now that you mention it, yes, where do those come from?
You should also read about how the letters of the alphabet originated from Egyptian unilateral hieroglyphs
Gave u the 300th like
Awesometh videoth. I gave u my liketh and shareth.😂
hahahaha!
Thou shall be thanked (I have no idea if it's correct) 😂
-th was a verb ending. Ironically one of the few words you didn't conjugate was a verb.
Yathu prem 😂😂😂😂thats English from the bible 😂😂
Why do people think this is funny
That was really interesting but I wanted to know more on how the symbols were invented. The divided by symbol was what I was waiting for.
Idk how it was invented but it does simplify a fraction like 5/4 becomes 5÷4. The 2 dots under and over it represent the numbers •/•
It looks like an empty fraction
@@hooman8925 5/4 seems more simplified to me though
I like to think that the line broke a larger dot up (which is the practical definition of division).
I think vertical "equal" signs could get easily mixed up with one & sevens if you're really into a significant number problem.
disappointed that there wasn't a small explanation of ÷
Captaindia it looks like a fraction. Maybe someone made fractions and then decided they needed another way to write it horizontally lol
It actually is a fraction. A blank one tho lol the dots in the top and bottom of the line represent the unknown variable and the line represents the fraction divide.
Ex: '/, is equal to 2/3 or two divided by three lol
Dot over dot is equal to variable over variable to put it simple👌✌
it's an empty fraction, the dots representing where the numerator and denominator would be.
I thought it meant a line cut through a circle to divide it into 2 smaller circles.
@@josephlandry4285 | Sure, but why do we write fraction like this: n/m then?
Actually the symbol of the square-root has a reason why it is that shape :
root in arabic is جذر and its first letter is ج which if rotate it you get the modern symbol
bechir brahem thank you! This video was mostly explaining basic operators, not where they came from like you did
well, from what i know, the square root symbol came from the letter r, because √ kinda looks like r, from earlier texts. At least that's what i know.
리성천 Rhee Sung Chun I have heard that too, because root in Latin is 'radix'.
So I googled it and it turns out both the ج for جذر and the R for radix are noted by historians.
en.wikipedia.org/wiki/Square_root#History
Also @
"Where do math symbols come from?"
Only explains the origin of two symbols.
Three actually. The ! for factorials was basically just a random pick by Christian Kramp.
@@moondust2365 lol
Did you perhaps go to DBS?
Technically, it is the truth. for something to be plural it needs to be at least 2. they explained 2 symbols.
Two symbols are plural
So saying where math symbols come from is not a wrong statement.
Ted-Ed is getting more dank lately.
True Pug Lord that’s not what dank means lol
why are you saying TED-Ed is getting cold and damp?
Where?
The Talking Guest dank means cool nowadays
S,zs
2+2 is 4, minus 1that's 3, quick maths
Ryan Darshen lol
That's right, you are on fire!
Oh, wait, man can never be hot.
MajkaSrajka You ruined it
Scrolled down too low
Skkrraa
They’re called Latin Characters (or letters), not English letters
He says English letters at 0:54
English is based off Latin and other languages. They could have used the 🏴 symbol but they were saying it not writing it!
English is more germanic than latin based. Though nowadays is pretty much the only language that will appropriate a word from any other language and just use it.
Darth so wrong,every language does that
It's not even latin, it's fenician but ok
This was a great TED-ED Talk...
Another would be the exploration into "how" and/or "why" some
languages a more symbol based than others...
Egyptian hieroglyphics and even Chinese Mandarin are more
symbolism and meaning rather than annunciation of a word to
build a more complicated ideas.
That simply boils down to what exactly the symbols represent. Do they represent sounds, syllables, or whole words/names/ideas. The more meaning is crammed into one symbol, the more symbols you'll need in total.
3:52
Those aliens are so adorable like my teeth
hymnson Cheung Or my tounge
Your tetth ain’t adorable
“Kind of like a meme” you mean literally like a meme. That’s the definition of meme.
The Whetstone of Witte
Why doesth it soundeth weirdeth?
Loleth
I hath laugheth out loudeth
I saw you again
Youre everywhere
SpringG1Rl Animations who are you referring to I can't tell.
Love to see TED Ed in its original expertise after long time 😍😘
Alternative origin for + that also explains why we conventionally use base ten.
Scale it up so that you can place a counter in one of the quadrants of this grid, say top left. That symbolises 1. Move it to top right, that's 2. Bottom right 3, bottom left 4. Now leave it there and put a second counter in the top left. What have you got? 1+4=5. Keep moving and adding like this, and when all the quadrants are occupied you have 1+2+3+4=10. An additive place value system of counting.
You can also have a grid with 9 (rather than just 4) spaces to symbolise ten numbers (empty grid represents 0). This is still with us as #.
√ comes from "r" for "radix" (latin for root)
It may also come from the Arabic letter ج.
There is bound to be a new craze, instead of emojis we talk with math symbols QED.
>:( no
!+==-%
8-C=3
_3i-5=x_
QED -> Quite Easily Done? 😇
4:00 - 4:08 just warmed my heart.
Found this while working on a discussion board post. This is so cool!
수학기호를 만드는 과정이 어렵고 잘 갖추어진 시스템인 것이라고 생각 했는데 잘 갖추어진 시스템이 아닌 단지 유행 일뿐이라는 것이 충격적이었습니다. 또 기호의 중요성도 배웠습니다. 유익한 동영상 감사합니다.
Vídeo maravilhoso!!! Parabéns, TED-Ed!!! A Matemática é a mãe de todas as ciências! A Matemática está em todo o universo.
th-cam.com/video/-42WaYUTsOg/w-d-xo.html
Omigosh I would LOVE it if you had books containing this much information. That is a Math book I'll actually enjoy!
2:34
division wasn't mentioned how it repeats something so I guess here:
if you didn't know, since the oppisite of addition is subraction, then the oppisite of repeated addition (multiplication) is repeated subtraction (division)
we will use this equation: x / y = z
to find how it repeats, do as follows:
x - y = a, if a < y, and a not= 0, then there is value after the decimal point, (the remainder is y - a if you don't use decimals) if a >= y, next step.
a - y = b, follow the instructions above replacing a with b. (ex: b > y, y - b)
add new variables respectively.
the amount of times you subtract y is the answer assuming that you start at 0 times.
example: 10 / 5 = ?
10 - 5 = 5, (? + 1 -> ?)
5 >= 5
5 - 5 = 0, (? + 1 -> ?)
0 = 0, stop.
? = 2, which means that 10 / 5 = 2
extra math nonsense below
ever wonder why the division symbol was two dots seperated by a line (or just a slash if you're fancy)
its because fractions (practically the same as division but lazy) are "x over y" or those two dots, filled in with numbers. x is the top dot, and y is the bottom dot.
the slash comes from if a fraction fell over.
percentages also apply, since you can represent every pecantage as x% = x / 100, or "x over 100" which
Two horizontal lines are sometimes used to represent "or" in some programming languages such as C#
It's actually single vertical line if the "or" operation in question is a bitwise or instead of a logical or.
The vertical line is a funny character. Originally it was included for use with APL but as APL decided to use an exclamation point instead they decided to break the vertical line by cutting it by half so that it would not be used. In ASCII 1977 they decided to fix it though the broken line was still common on many systems in the 80s. Then when they extended the character set to add new letters they decided to add the broken bar (¦) back. Why? No programming language uses anything other than pure ASCII in anything besides comments and strings.
Speaking of characters has anyone ever used the international currency symbol (¤). Swedes in their neutrality did not want the dollar sign so they replaced it with that. On modern character sets it is a separate character from the dollar but still it is the shifted function for 4-key. To get $ one needs to use the AltGr instead.
Who else loves the animation?
Of course, Ted Ed = (awesome animation + awesome narration + awesome lesson)^99999
Any riddles coming up soon? I like the riddles/math problems etc that you post to the channel.
Really enjoyed this. Very informative and the cute animations were really fun to watch :)
I though “+” came from the letter _p_ (shortened from “plus”), where the vertical line remained and the bottom part of the loop became the horizontal line, but the loop itself disappeared over time. Same for “−” which came from the letter _m_ (shortened from “minus”) which turned into a squiggly horizontal line, then just into a horizontal line.
Thank you TED ED. for all animate videos .
I am ted ed in real life he stole my name
From reading some comments there is room for a more comprehensive set of symbols to identify, I enjoyed this one too, thanks!
given the thumbnail, you'd think they'd have mentioned the origin of the division sign: it's supposed to look like a fraction, where the two dots represent numerator and denominator.
Wonderful explanation. 😁
Just a crazy idea, but what if the exclamation mark is just PERFECT for factorial, because it looks like an "all until this point" ( ! ) and that's just what factorial IS.
3:18 i literally did that whole thing just to end up seeing a block of text and an equation
2:00I love how the Latin and Greek letters exchange greetings
I wish this was available when I was in school. My math teachers couldn't tell me why we use certain symbols. I had Aspy meltdowns more than once because of it.
3:31 SAT and ACT (standardized tests) style of confusing people's minds and juggling with their emotions.
Sadly, the quote from Russell in the intro, asserting a viewpoint known as logicism, was short lived. This quote was drawn out by the same hopeful zeitgeist as Frege, Hilbert and others dream to axiomatize all of mathematics under one formal system, reducing all of mathematics to pure logic and thus rendering it wholly complete and consistent.
However, the specter of undecidability was soon to unweave the seam binding the whole project together. First, Russell himself pulled on the thread when he responded to Frege's naïve set theory with "Russell's Paradox," finding a liar's-esque paradox at the heart of the system. Next, Turing followed in his footsteps, showing the same must be true of computer systems, but the thread of Logicism came entirely undone when Gödel published his two “incompleteness theorems", which found just the same self-referential paradox arises necessarily in all formal systems capable of arithmetic. This does not include Logic, but is true for all formal mathematical systems. Thus, once and for all, demonstrating Math cannot be reducible to Logic.
👍✔✔✔👍
someone found a thesaurus
th-cam.com/video/-42WaYUTsOg/w-d-xo.html
Could we have more of theses, please.
Ty for uploading vids great animation and important topics
Today I learned that the "equal to" sign caught on like a meme... that's awesome and hilarious at the same time... I never thought I'd be so thankful for memes
3:40 the square root isn't as arbitrary as it might seem. It is supposed to be an r, for root
thank you Anderson for coming back
The possible sign for division / ÷ is a divisive issue, often multiplied • ×.
"Likeths" 0:50
They'd probablg have a symbol for tau, not pi.
PI IS BETTER THAN TAU Y'ALL
No TAU, no PI, give me a TAUPIer
you mean taf
Pi is obviously better than tau, because mostly tau is defined as 2*pi
Notice that mostly, pi haters
Keir McCulloch And people who use tau/taf call π tau/2
To teach, tau actually makes a lot more sense and only the area formula is simpler using π. For the purposes of arithmetic and geometric calculations, tau is usually a much better option. However, though tau does have more mathematical significance, in absolute math, tau or π are just notations for concepts, so it really doesn't matter. However, for notation and SYMBOLS, tau certainly makes things easier.
And if you're going to give the e^πi=-1 argument, just know that e^(taf*i)=1
His voice is so calming
I love this channel!Thank you 💙
Thank you so much for uploading this video. It is helping me get through the pandemic!
Plandemic/Scamdemic
The division symbol is because:
•\• the top dot represent Numerator and botoom represent Denominator
so.. 11 / 2 = 11/2
Well I didn’t know who introduced the = sign. Yet it’s amazing how and 4 minute video titled “where do math symbols come from” was made which explains the origin of just one symbol.
The integral symbol sends shivers to my spine.
0:45 Greetings everyone! Here is a radical idea (😂):For expressing equality instead of using "is equal to" just use this symbol: =
The symbols are like dads they abandon their kid but come back when they win the lottery
Ted ed makes me think of questions I never had before
I like to imaging the division sign was picked because it’s two dots with a line dividing it like a wall.
Leonard Euler is responsible for much of the mathematical notation we use today.
Wherever they come from they're awesome.....
Vieweths, Shareths, Likeths?
The animation team deserves an Emmy at this point
So nicely explained ✨
This video title is wrong. It should've been: "what's the purpose of those symbols"
Anyone could think the huge block of speech, as"Impossible"
Did you even TRY to close a notebook lock?
I would've lived all my life but never would have known this. Thanks!
I always thought the division sign was like the way it was because the line separates the two dots. Which could be reworded, to two dots divided by the line
Love it ! I am a 6 th student girl I like the videos of ted ed I always enjoy it , please make a video of India ' s history on ted ed . 😉🙂
Lol.
@@donnalambs9578 lol for what?
2:09 Oh wow a lemming
= || Parallel lines, equal to each other
+ Shorthand for the letter &
- Shorthand for m, though it could also be shorthand for the tilde in m̃ depending on your source
× Quite literally the symbol + rotated. This is because multiplication is a shortened addition
÷ A symbol where the dividend is placed above a horizontal line, and the divisor below. Left as dots to indicate division
Σ 18th letter in the greek alphabet, though I haven't found anything about its origins, though it probably follows the logic of pi
xʸ Shortened multiplication, apparently didn't need a symbol
π Pi in greek alphabet, the initial of periphery ( περιϕέρεια ), which is nowadays called circumference
√ An elaborate r
The way I see a division sign is that the line broke a larger dot into two, which is the whole idea of division ("breaking" a number into smaller parts).
3:25 167 i chose 7 iluminaty confirmed
You said meme...
*Subscribed*
This made me cry from joy!!!
Well, did you know that the word "meme" was created way before Internet? I think the first person to use it was Richard Dawkins in his book "The Selfish Gene"
Gustavo Miller oh look, a historian!
Pelican I can't believe that word is able to be in a ted ed talk. Wow. The new generation is always evolving...
3:23 Do I add 1 after the decimals???
Addition itself is already a shortcut, at least for integers. m+n is short for "n integers after m"
An interesting fact:
In many of Jewish schools, math teachers use the plus symbol without the bottom part because the similarity to the Christian cross.
Wow. Stupidy mixed in with religion. Nice.
I liketh thy video.
+ plus
- minus
x multiply
÷ divide
= equal to
. decimal
∆ Delta
° degrees
√ square root
π pi
< less than
> more than
%percent
reply if I got some symbols wrong
can explain anamolous expansion in water and
why near ocean beda water doesnt freeze at 0°
i know bescause of pressure but please make a video
The addition sign is the equal sign crossed
The Subtraction is the equal sign with a line subtracted
The multiplication sign is the addition sign tilted
The division sign is 2 multiplication dots on top and bottom of a subtraction sign (repeated subtraction)
Interesting hypothesis.
Division is a fraction (look at the symbol)
All of these are wrong.
0:12 whetstone!? Math requires knife sharpening? JK.
Simply love these videos......But I don't know why ppl give a thumbs down.....Seriously ppl!!!
Love these animations!!!
3:12 He is left handed!
#LeftieSquad
This is why math is so much easier than people actually say
This brings up the square root, or more generally the root symbol as arbitrary but I always thought it meant to visually represent that you're taking a number and like squeezing it underneath the exponent to find the root.
Love the content. Always watch. But I am here to comment on how beautiful the fact is that now you have ads before _and_ after videos. Remember those days when we thought the Internet was for the people?
All those little dots at 1:15 probably mean something in maths
Multiply
I like math
Arta Etemadi nah a lot of ppl in me school like math too
Drage dk
Cool!
Demon
Drage dk says no one
Samuel Crane nah asian
They just explained everything I’ve learned in math since 3rd grade. Besides where they came from
The alien at 4:10 is using their own equals sign in all the expressions
I liketh that posteth!
OH TED ED... You NEVER disappoint in the obscure or mundane things that You exposed the truth of... And so i AM so proud of... Keep up the good work!!!!😉
4:04 that escalated quickly 👽
I've noticed that where I'm from + is very often written without the bottom line(ㅗ kinda like that) and ÷ is always written without the line (:), I write them the computer way cause I was taught them a bit differently and nobody has yet said anything about it to me