Math CentralQuandaries & Queries


Question from Barbara, a teacher:

Our current place value system is based on the notion of 10s. Did Aboriginal people use a similar system or did they group numbers differently?

Hi Barbara,

The best reference I have Aboriginal number systems and number words is the chapter Native American Number Systems written by Michael P. Closs from the University of Ottawa in Native American Mathematics, edited by Michael P. Closs, University of Texas Press, 1986.

Many societies have used bases other than ten.  Number systems were based on primary groupings of 20 in the Inuit areas of North America, in most of Mexico, and in Central America.  The Celtic people of northwestern Europe, the Ainu of northeastern Asia, the Yoruba, Igbo, Banda of Africa, and the native Australians of Victoria also used base-20 systems.  The Bushman of Africa used a base-2 system, as digital computers do today.  The Babylonians used a base-60 system, as reflected in our use of seconds, minutes and degrees.

It is clear that number systems are grounded in our surroundings.  Many Native American languages have numeral words that illustrate their origins. Closs describes an incident around an Inuit artist's print titled 'Joyful I see Ten Caribou' which depicts an Inuit with two upraised hands showing all ten digits. An Inuit person, Oshaweetok, was shown this print and commented “We went by hands and then by feet.  Two hands are 10 and one foot is 15. The other foot makes 20.  When you have 20, that’s one person.  One person plus five fingers is 25 and so on.  Five people make 100 and 100 means a bundle.   Often the foxes and sealskins were bundled into 100.” (From Oshaweetok as quoted by Michael P. Closs, Native American Mathematics, pp 5.)

In the Mayan empire, which existed more than 4000 years ago, a number system was developed which used base 20.  Some historians credit the Mayans as being the first to create a symbol for zero and use it as a placeholder. 

Many number words from the Aboriginal languages in North and South America are based on groupings of 10. "This is true, for example, in the regions of North America occupied by the Algonquian, Siouan, Athapascan, Iroquoian and Salish linguistic stocks and in the part of South America dominated by the Quechua." (Michael P. Closs, Native American Mathematics, pp 3.) Quechua is the language if the Inca. The Inca and its predecessor societies in the Andean region used an ingenious method of recording numbers by tying knots on chords in a devise called a quipu.

It appears that our place value, base-10 system originated in India and China, then it spread to the Arab world.  Around 800 years ago, in 1202, Fibonacci, an Italian merchant and scholar, brought Arabic numerals to Europe with his influential book Liber Abbaci.  Much of the notation and methods of arithmetic he introduced are what we still use today.  Of course, it took many centuries for this new number system to replace the well-established Roman Numerals.


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