HISTORY OF NUMBERS

Today we use very confidently the numbers in our daily lives without having an idea of ​​their history. Is there a need to know at least a little bit their history? It is hardly necessary, but this knowledge will give us a cultural understanding in depth about what a long way people have come in order to know better the world around them. We will not go into a big detail, but we will mention about some milestones in the development of the numbers.

The need to have signs of the numbers comes from the need to count and measure. Initially people have used stones or traits/tallies to count the killed animals during the hunt.

It took centuries to move from the marks and tallies that have meant something very specific, to the symbol of the number that was already a sign of something more abstract and general. Understanding this difference has led to a qualitative change in the process of thinking and to the development of the brain and human consciousness. Moreover, it happened when the primitive hunting society has passed to a sedentary lifestyle, people have come out of the caves and have started to build houses and started to develop trade.

So ten digits we use today are known as Hindi-Arabic numbers and are imported into Europe in the 12th century by the Italian mathematician Leonardo Pisano, who got his education in North Africa. Arab digits, which we use today, are modifications of these signs. The sign for "zero" was invented in India; initially in its place was used pebble or point.

Thousands of years ago there were no numbers to represent two or three. Instead fingers, rocks, sticks or eyes were used to represent numbers. There were neither clocks nor calendars to help keep track of time. The sun and moon were used to distinguish between 1 PM and 4 PM. Most civilizations did not have words for numbers larger than two so they had to use terminology familiar to them such as flocks of sheep, heaps of grain, or lots of people. There was little need for a numeric system until groups of people formed clans, villages and settlements and began a system of bartering and trade that in turn created a demand for currency.

Paper and pencils were not available to transcribe numbers. Other methods were invented for means of communication and teaching of numerical systems. Babylonians stamped numbers in clay by using a stick and depressing it into the clay at different angles or pressures and the Egyptians painted on pottery and cut numbers into stone. Numerical systems devised of symbols were used instead of numbers.

Anthropologists tell us that in Suma, in about 4,000 BCE, Sumerians used tokens to represent numbers, an improvement over notches in a stick or bone. A very important development from using tokens to represent numbers was that in addition to adding tokens you can also take away, giving birth to arithmetic, an event of major significance.The Sumerian’s tokens made possible the arithmetic required for them to assess wealth, calculate profit and loss and even more importantly, to collect taxes, as well as keep permanent records. The standard belief is that in this way numbers became the world’s first writings and thus accounting was born.

More primitive societies, such as the Wiligree of Central Australia, never used numbers, nor felt the need for them.We may ask, why then did the Sumerians on the other side of the world feel the need for simple mathematics? The answer of course, was because they lived in cities which required organizing. For example, grain needed to be stored and determining how much each citizen received required arithmetic.

Egyptians loved all big things, such as big buildings, big statues and big armies. They developed numbers of drudgery for everyday labor and large numbers for aristocrats, such as a thousand, ten thousand and even a million.The Egyptians transformation of using “one” from counting things to measuring things was of great significance.

Their enthusiasm for building required accurate measurements so they defined their own version of “one.” A cubit was defined as the length of a mans arm from elbow to finger tips plus the width of his palm. Using this standardized measure of “one” the Egyptians completed vast construction projects, such as their great pyramids, with astonishing accuracy.

The Chinese had one of the oldest systems of numerals that were based on sticks laid on tables to represent calculations.

From about 450 BC the Greeks had several ways to write their numbers, the most common way was to use the first ten letters in their alphabet to represent the first ten numbers. To distinguish between numbers and letters they often placed a mark  by each letter.

Two and a half thousand years ago, in 520 BCE, Pythagorus founded his vegetarian school of math in Greece. Pythagorus was intrigued by whole numbers,noticing that pleasing harmonies are combinations of whole numbers. Convinced that the number one was the basis of the universe, he tried to make all three sides of a triangle an exact number of units, a feat which he was not able to accomplish. He was thus defeated by his own favorite geometrical shape, one for which he would be forever famous.

His Pythagorean theorem has been credited to him, even though ancient Indian texts, the Sulva Sutras (800 BCE) and the Shatapatha Brahmana (8th to 6th centuries BCE) prove that this theorem was known in India some two thousand years before his birth.

Later in the third century BCE, Archimedes, the renowned Greek scientist, who loved to play games with numbers, entered the realm of the unimaginable, trying to calculate such things as how many grains of sand would fill the entire universe. Some of these intellectual exercises proved to be useful, such as turning a sphere into a cylinder. His formula was later used to take a globe and turn it into a flat map.

Romans invading Greece were interested in power, not abstract mathematics. They killed Archimedes in 212 BCE and thereby impeded the development of mathematics. Their system of Roman numerals was too complicated for calculating, so actual counting had to be done on a counting board, an early form of the abacus.

Although the usage of the Roman numeral system spread all over Europe and remained the dominant numeral system for more than five hundred years, not a single Roman mathematician is celebrated today. The Romans were more interested in using numbers to record their conquests and count dead bodies.

The Roman numerical system is still used today although the symbols have changed from time to time. The Romans often wrote four as IIII instead of IV, I from V. Today the Roman numerals are used to represent numerical chapters of books or for the main divisions of outlines.  Even nowadays use so-called Roman numerals, for example from one to ten, and also for larger numbers: I, II, III, IV, V, VI, VII, VIII, IX, X. Suppose that each of us uses Arabic and Roman numbers in many areas of their lives.

Separately we will illustrate in tables different numerical systems.

Finger numerals were used by the ancient Greeks, Romans, Europeans of the Middle Ages, and later the Asiatics. Still today you can see children learning to count on our own finger numerical system.

Odd and even numbers.

In our real lives, we ​​use the idea of odd and even numbers in many occasions. For example, when we want to classify or to group things, and when we want to split objects into equal parts. It is important to remember that even numbers are divisible by two and as a result, they give whole numbers. Odd numbers can also be divided into two, but do not give whole numbers. I suppose this information it might be useful for practical reasons.

The number "pi".

Hardly in our real life we will ever use our knowledge of the number "π, pi". However, it is a number that draws attention to itself with many things and such information may be useful to us to impress someone with our mathematical knowledge. The earliest data on the number "pi" can be found in ancient Egypt and Babylon, which means this number has a long history. The number "pi" "π" is a mathematical constant that is the ratio between the length of a circle and its diameter. It is famous for the fact that it never ends. The number π is approximately equal to 7.22 or 3.14 to within the third significant digit.
The numerical value of π, rounded up to the 100th decimal place, is
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679...

*   *   *   *

In the picture below, we can see bones that are between 20 000 and 30 000 years old. They have marks on them that are the first way of counting of primitive hunting societies. These tallies are a certain indication of counting and they mark a defining moment in human development.

(Elena S Lyubenova)