# History of mathematics

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How did mathematics begin ?
Human beings, form our earliest begining, have searched for solutions to basic problems.
Building homes, mesuring space, keeping track of season and counting objects.
Because 30 000 years ago, early paleolitic people kept track of the passing seasons and the change of weather for planting.
To represent the passing of time, they carved tally marks on cave walls, or slash tallies on bones, wood or stone.
Each tally stood for ''one''.
But this is the most akward when it came to large amounts, so symbols were eventually created that stood for groups of objects.
Sumarian clay stones have been found the date of the fourth millenium B.C.
A small clay cone was used for one, a clay ball was used for ten and a large cone stood for sixty.
Written records from around 3300 B.C. show that Babylonians inscribed amounts on a clay tablet with a reed.
They used a nail shape for ones and a "V" on its side for tens,
combining these symbols to create other numbers, for exemple, Babylonians wrote the number 19 as
The ancient Egyptians used objects of their everyday life as symbols.
A rod stood for one, a cattle huble was ten, a coiled rope was a hundred, a lotus flower was a thousand and so on.
The number 19 was a cattle hubble and nine rods.
The early Romans created a number system that we still see today.
Along with other symbols, they used an "X" for ten and a "I" for one.
By the middle ages, Romans were putting the "I" to the right of the "X" for eleven and to the left for nine,
so they wrote 19 as "XIX".
All of these creative number systems showed groups of objects, as well as individual object.
Some of the oldest human counting system rely on finger and toes, so they were based on ones, fives, tens and twenties.
The Zulu word for six means to take the thumb of the right hand,
meaning that all the fingers on the left hand had been added up and the other thumb was needed.
Other systems evolved from commerce, the Uruba in Algeria used collar shells as curency,
and developped an amazingly complex number system.
It was based on twenties and on the operations of multiplication, substraction and addition.
For exemple, they tought of 45 as 3 times 20, minus 10, minus 5.
Knots tying cords and strings were used for recording amounts by many cultures, like the Persians.
The Incans used a more refined version called the Khipu, a thick cord held horizontally from wich hunged knotted strings.
The kind of knots the Incans used along with the lenght and color of the cord represented ones, tens and hundreds.
In today's world, almost every industrial culture uses the numerals 0 through 9,
but these symbols weren't invented until the 3rd century B.C. in India.
And it took another 800 years for the idea of ''0'' with placed value to be constructed.
This big idea dramatically changed the face of mathematics
We humans have always shared with one another.
When early cultures shared their food and water or wanted to divide their land in ways that were fair and equal,
fractions gradually emerged these symbols for these fair share situations.
The ancient Egyptians used unit fractions. Fractions where the numerator is 1 like one half, one third and one fifth,
and would add and halve these fractions.
If they wanted to divide 3 loafs of bread equally among five family members,
they'd first divide the first and second loafs into thirds.
Then they'd divide the third loaf into fifths
Finally, they'd take the remaining one third from the second loaf, and divide that into five pieces.
They wrote this as 1/3, 1/5, 1/15.
Today, we would represent this sharing with a fraction 3/5.
3/5 of a loaf for each person, or 3 loafs divided by 5 people.
The Sumarians and early Babylonians invented a number system of fractions based on 60 that we still use 4000 years later.
Our days have 60 minutes hours and 60 seconds minutes.
And our circles encompassed 360 degrees.
Chinese societies used in abacus with a system based on tens, altough it had no zero.
An early form of decimal fractions came from the abacus, for exemple, 3/5 would be 6 out of 10 on an abacus.
The chinese lovingly named the numerator the son, and the denominator, the mother.
It wasn't until the 12th century that common fraction with the bar notation that we use today were invented.
Even then those fractions weren't widely used until the renaissance period, only 500 years ago.
Throughout history, every culture around the globe has created inventive ways to calculate.
To solve a problem, say 12 x 15, the early Russians peasants used a system of doubling and halving.
When an odd number, halved, resulted in a fraction,
they rounded it down,
then they added the factors associated with the odd multipliers.
Ancient Egyptians relied on a doubling procedure, until they produced enough groups.
Then they added these groups to find the answer.
Across Europe and Asia, during the middle ages, the abacus was the hand-held calculator of his day.
But only few people knew how to use it, usually wealthy merchants and money lenders.
By simply moving beads each had placed value, an abacus was a highly efficient way to compute.
Then, the great Arab mathematician Al-Khwarizmi,
introduced the Hindu Arabic numerals 0 through 9 into North America and Europe,
and created new procedures for computation.
These algorithm could be written unto paper.
Over the centuries, learning the algorithms became the hallmark of an education,
as student were taught to compute long columns of figures,
borrow and carry, and do long division efficiently and reliably.
They can now keep record of these procedures and check results.
Today, complex calculations are done with a hand-help calculator.
This means students need the ability to check the reasonableness of the answer,
and to have a rich repertoire of mental math strategies to do that.
Most simpler computation like 12 x 15 can be solved mentally using a variety of strategies.
As we journey through the rich and vibrant history of mathematics,
we can see how ideas and creations grew out of our very human need to solve the problems in our everyday lives.
Through time, the mathematical explorations of men and women from around the globe,
had given us fascinating lenses to help us to mathematicaly view and make sense of our world.