A brief history of numerical systems – Alessandra King

One, two, three, four, five, six,
seven, eight, nine, and zero. With just these ten symbols, we can
write any rational number imaginable. But why these particular symbols? Why ten of them? And why do we arrange them the way we do? Numbers have been a fact of life
throughout recorded history. Early humans likely counted animals
in a flock or members in a tribe using body parts or tally marks. But as the complexity of life increased,
along with the number of things to count, these methods were no longer sufficient. So as they developed, different civilizations came up
with ways of recording higher numbers. Many of these systems, like Greek, Hebrew, and Egyptian numerals, were just extensions of tally marks with new symbols added to represent
larger magnitudes of value. Each symbol was repeated as many times
as necessary and all were added together. Roman numerals added another twist. If a numeral appeared before one
with a higher value, it would be subtracted rather than added. But even with this innovation, it was still a cumbersome method
for writing large numbers. The way to a more useful
and elegant system lay in something called
positional notation. Previous number systems needed to draw
many symbols repeatedly and invent a new symbol
for each larger magnitude. But a positional system could reuse
the same symbols, assigning them different values
based on their position in the sequence. Several civilizations developed positional
notation independently, including the Babylonians, the Ancient Chinese, and the Aztecs. By the 8th century, Indian mathematicians
had perfected such a system and over the next several centuries, Arab merchants, scholars, and conquerors
began to spread it into Europe. This was a decimal, or base ten, system, which could represent any number
using only ten unique glyphs. The positions of these symbols
indicate different powers of ten, starting on the right
and increasing as we move left. For example, the number 316 reads as 6×10^0 plus 1×10^1 plus 3×10^2. A key breakthrough of this system, which was also independently
developed by the Mayans, was the number zero. Older positional notation systems
that lacked this symbol would leave a blank in its place, making it hard to distinguish
between 63 and 603, or 12 and 120. The understanding of zero as both
a value and a placeholder made for reliable and consistent notation. Of course, it’s possible
to use any ten symbols to represent the numerals
zero through nine. For a long time,
the glyphs varied regionally. Most scholars agree
that our current digits evolved from those used in the
North African Maghreb region of the Arab Empire. And by the 15th century, what we now know
as the Hindu-Arabic numeral system had replaced Roman numerals
in everyday life to become the most commonly
used number system in the world. So why did the Hindu-Arabic system,
along with so many others, use base ten? The most likely answer is the simplest. That also explains why the Aztecs used
a base 20, or vigesimal system. But other bases are possible, too. Babylonian numerals were sexigesimal,
or base 60. Any many people think that a base 12,
or duodecimal system, would be a good idea. Like 60, 12 is a highly composite number
that can be divided by two, three, four, and six, making it much better for representing
common fractions. In fact, both systems appear
in our everyday lives, from how we measure degrees and time, to common measurements,
like a dozen or a gross. And, of course, the base two,
or binary system, is used in all of our digital devices, though programmers also use base eight
and base 16 for more compact notation. So the next time you use a large number, think of the massive quantity captured
in just these few symbols, and see if you can come up
with a different way to represent it.

Comments 100

  • still hate math….

  • so after doing home work i watch ted ed and see math in number sytem and you know what happend ?

    i got to just dance 2017 lean on by majør lazer. still i love studying but after math and calculating stuff especialy exam, man i need a break

  • Even before Aryabhatta discovered Zero, Zero was used in worldwide famous THIRUKURAL written by Thiruvalluvar, it dates 31 BC.

    Kural 450:
    பல்லார் பகை கொளலிற் 'பத்தடுத்த' தீமைத்தே
    நல்லார் தொடர்கை விடல்.

    To give up good friends is TEN times worse,
    Than being hated by countless foes.

    Kural 816:
    பேதை பெருங்கெழீஇ நட்பின் அறிவுடையார்
    ஏதின்மை 'கோடி' உறும்.

    CRORE times the wise man's hate
    Is better than a fool intimate.

    Kural 817:
    நகைவகைய ராகிய நட்பின் பகைவரால
    'பத்தடுத்த கோடி' உறும்.

    Ten-fold CRORE you gain from foes
    Than from friends who are vain laughers.

    These Kurals (Couplets) use TEN, CRORE, TEN CRORE (1 CRORE = 10 MILLION) in it. THIRUKURAL has 1330 Kurals (Couplets). Each Kural consists 2 stanzas written using 7 letters. 4 on the up, 3 on the down. Dealing with the everyday virtues of an individual. Considered one of the greatest works ever written on ethics and morality, it is known for its universality and non-denominational nature.

    If these much effort is put in writing THIRUKURAL even before 2047 years back (now it's 2017), then think when the TAMIL language is founded and how much it has grown up for writing this Epic! You couldn't simply write these in any language only using 7 words. A Language must be well grown enough to write something like this and one person should be great to write this.

    So know stuff before you talk. THOLKAPPIAM is even older than THIRUKURAL. Anybody here still not accepting, it's your ignorance.

    Google THIRUKURAL and read it so you can know it's history and the meaning of Life.

    நன்றி (Thanks) 🙏🏻
    தமிழன் (Tamilan) 💪🏻

  • Not aztecs, the mayans.

  • Can someone say what program they use to create the animation?

  • Hey! What about a brief history of Alphabet?

  • 0 was invented in India!

  • Mathematics is a discovery and humans invented a perfect language to understand it.

  • Normal numerics uses base 10, and binary uses base 2. That is such a more simple way of understanding binary than I've ever been told before!

  • 80085

  • zero was invade by the Indian not by mayans.

  • Zero was discovered by Aryabhatt and not invented yet some ignorant people show off saying who counted the 10 heads of The Demon King Ravana if 0 was invented by Aryabhatt.
    (can't even tell the fact in my family group when they send such stuff)

  • I'm taking a Gen. Ed. course in college called Contemporary Mathematics (number theory, stats, set theory, etc.) It's all fairly simple for me but not so much for some of my classmates. We are learning about this right now, and I gotta say…TED Ed, this 5 minute video is easier to understand than 75 mins worth of ramblings from my professor. Definitely gonna share this video with my classmates 👍

  • actually the number zero was invented by Aryabhatta in India. I am not forcing you to agree with me but it's a fact that 0 was invented by Aryabhatta. i regret to say that ted ed has been a little biased in this video

  • el cesar mlp

  • hey 0 was discovered or rather invented by aryabhata rather than e Mayans

  • The narrator makes the common error of suggesting that we encounter Base 12 "in our everyday lives" in our measurements of angular degrees, time, and units such as a dozen. These aren't in Base 12, they are still in Base 10, and her assertion that they are, suggests that she doesn't understand her own topic! The duodecimal system would have two extra digits.

  • my teacher recomendeded we watch this video for are pop quiz on monday

  • its ok

  • Numbers that we use today were invented in ancient India…..

  • A FABULOUS presentation.

  • Some historically inaccurate info.

  • http://www.bbc.com/news/uk-england-oxfordshire-41265057

  • Indians (The Hindu Culture not Religion) used zero extensively. The right form of zero also from them only.

  • I'm disappointed by how ridiculous most of the comments on this channel are. A bunch of nationalist Indians and people not understanding what was said.

  • I hope you can visit another type of insigt, thanks.

  • U should make "y is math important?"

  • 1 2 3 4 5 6 7 8 9 X E and 0 with these 10 symbols we create every number possible

    For duodecimal people

  • Please, learn more about the numbers written with the ideograms of the abacus and numbers origins. Thanks.

  • An interim stage in the move from a tally to a decimal positional system might have occurred with using a stencil or impression of an outspread hand on a horizontal surface.

    Five fingers but just four gaps between them. Place a small pebble between the thumb and index to represent 1. Move it to to the next position and it becomes 2. Then 3, and then 4. What then? Leave the pebble in its last position and put another where you first put the first. That's 5, then move it along to get 6 and then 7. Use a third to get 8 and 9, and a fourth for 10, which is when all gaps are occupied. So an additive positional system based on 1+2+3+4=10.

    Of course other visual devices with four places could be used, and a very convenient one would be a cosshair grid, still with us as the + sign. A nine place grid (as for the tic-tac-toe or noughts and crosses game) could also be used to positionally represent the quantities one to nine. With an empty grid to represent 0, we have an easy transition to replacement with ten numeral symbols. This particular grid is still with us as the # sign for the word "number".

    As for duodecimal systems, I suggest the additive property they exploit is 1+2+3+3+2+1=12, useful for cycles – especially the tides.

  • What is the narrator trying to explain…? .

  • 0 was invented by Aryabhatt !

  • The invention of printing resulted in the standardized symbols we use today. In particular 5 closely resembled an "open" 4 but 5's shape was altered to the "hook" shaped symbol of the present. 7 was also an upside-down V shape but was changed, probably to avoid confusion with a V or capital A.

  • I think the narrator needs to brush up her history lessons.

  • Can people stop saying someone "invented" zero, they introduced a concept of creating a placeholder with no value

  • What about base 10100101010101101010101001010101010101010110010101010101010101010101010010101010010101010010101000101010010101010100

  • Zero (Shunya) was first used by Indians later it was spreaded to other countries by Arabs who were traders of these lands.

  • Nice video it was showed in my school during math lesson today 😃

  • Beautiful animation and great info! Meanwhile in the comments, people are fighting over who invented what.

  • "We Owe A Lot To Indians Who Tauht Us How To Count Without Which No Worthwhile Scientific Discovery Could Have Been Possible"-Albert Einstein…

  • Your wrong I'm a indian, who is seeking yogic science…

  • This video is strangely vaporwave

  • zero was invented in india

  • The abacus was used to developed the decimal system. Please visit the site. Thanks.

  • This was by far the best animation of ted ed.

  • Wow this is amazing💗

  • Why use zero if we can use zero less base system or bijective numeration.

  • First of all zero was invented by indians . Then

  • Commendable

  • Basically Arabs we're copying everything China and India had to offer, translated it and named as their own

  • I think the indians came up with zero,because of their philosophical concept of nothingness in their religions, especially Buddhism and Jainism. Even the concept of infinity one can find in Jainism..


  • Hory sheeto 666 comments. Lemme fix that

  • i thinkk that indians write from left to right if they invented the numbers they should write them from left to right , not from right to left that how we right arabic

  • Sorry to bother, but could it be, there is a mistake at 4:11, in the right column under digit 12, which when divided by 8 is 1.5 not 1.6? or am I missing something ? thanks

  • The first verse in Quran consist of 19 arabic letters. The quran have 114 chapter which is 19×6. The quran consist of 6234 numbered verse, and 112 not numbered verse, 6234+112= 6346 = 19x 334. Also 6+3+4+6= 19.

  • I think that the base 60 is probably the coolest of the ones developed.  Minus the writing system.  But if you could have a Hindi-style numerical system in base 60, I'd be all for that alternative history.

  • Wasn't zero developed by Aryabhatta and not the Mayans?

  • Muslim Arabs not Hindu… get it right.

  • Is there a triangle in the middle to represent the illuminati or is it just for fun

  • What a load of nonsense. The true story of how we got numbers is here:


  • Jai hind!

  • sure this Ted belongs to the Illuminatis !!!

  • 0123456789 symbols has been developed in north africa

  • Current-1 2 3 4 5 6 7 8 9 0
    Hindu -१ २ ३ ४ ५ ६ ७ ८ ९ 0

  • Vedic Mathematics was born long before Hinduism….it was the Vedic times….Not sure it should be called Hindu numerical system as it's called "Vedic Mathematics" in India…Vedic Mathematics also talks about Trigonometry and Astronomical calculations…which was later used to build Panchanga which was adopted by Hinduism.

  • so many indian/Hindus don't accept the fact

  • the numbers 123 are created by arabics or indians ?

  • A symbol for zero, a large dot likely to be the precursor of the still-current hollow symbol, is used throughout the Bakhshali manuscript, a practical manual on arithmetic for merchants.[29] In 2017 three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from 224-383 AD, 680-779 AD, and 885-993 AD, making it the world's oldest recorded use of the zero symbol. It is not known how the birch bark fragments from different centuries that form the manuscript came to be packaged together

  • All the 10 digital are from India..We had these systems well before any other civilisation.

  • Why 6 and 12, is not logical

  • Numbers don't account for and, because and is not a number. its one hundred twenty, not one hundred and twenty. (120, 100 and 20)


  • Arabic numerals, Indians didn't create it.

  • shoutout kaufman like if u in bths comp sci

  • 00:00

  • 0:00

  • 0:01

  • India should include current Pakistan and Bangladesh as well as parts of eastern Afghanistan.

  • Really liked this vid!

    I just posted something similar on my channel! Check it out!

  • India is always first in history

  • So technically number system was invented by indians and not arabians 🧐

  • Life is a simulation

  • I could be wrong but didn't Sumerian culture pre-date Babylon. It was also shown that the Sumerian culture had a base 60, but Babylon is getting the credit here.

  • most americans don't even realise that we are using the Arabic numbering system lol XD time for primary school ?????

  • Bharat Mata Ki Jai 🙌🏾🇮🇳

  • These aggressive Hindu chauvinists hear a noise about "hindu" and they come out barking. The Arabic numerals are nothing were it not for the concept of "zero," sepher or "zephyr." There is nothing Indian in it. The 10 base counting system is from 0 to 9 and there is nothing Indian about it.
    I suggest that those curry-breathers should worry about the 600 millions of their citizens urinating & defecating in the streets and fields rather than impress us about how fine a nation they were.


  • Who invented what? Some here deny the good old things and insist that their ancestors own the sience. No, look think better, to learn that the credit for all, every civilization that has done something, is succeced by another civilization which gives more evolution, and so on until we arrived to this time. From pharaohs era until the digital era

  • Intentional understatement of India?

  • Zero was invented by the Indian Arya Bhatta ! Who is an Indian !

  • Muslim contributed nothing to the numerical system.

  • I made up some weird counting system, and I'm just hoping someone deciphers it
    †‡,I‡H†G this is a number, if you need a hint (aka the number) then i can give it and solve it based on the number

  • Arabs didn't invent anything or even use math. It is called "hindu-arabic" because backward Europeans at the time didn't know much about math nor science. The 0 was invented in India, in Persia which the Arab muslim invaders occupied it spread. It did so because there were numerous Persian scientists, as Persians valued science and art, in contrast to the Muslim Arabs which saw scientists as unmanly. And so this numerical system spread to Europe by Persian writings, who spoke and wrote in Arabic, not Persian (because Persian was forbidden by the Arabs). Then the Europeans called it "arabic numerals". Only recently when Europeans finally found out that it wasn't invented by the Arabs they started calling it "Hindu-Arabic", even though still inaccurate, but maybe they just cannot admit their stupidity.

  • i am in a science class watching this lol

  • im watching this for class lol

  • 700th comment

  • Very interesting, helped me a lot with my revision for my upcoming Math Test. 🙂

  • Is 5th century not 8th century because Aryabhatta was in 5th century.

  • 0 was created by khwarizmi, a muslim scientist.

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