Math began with counting. Counting is a basic need. Prehistoric men led a simple life. Their need for counting was limited. They had names only for the first few counting numbers. For a greater count, they had the notion of many.
They might have used more difficult ways of keeping a count than we use today. To keep count of animals, herdsmen might have marked each animal against their fingers or toes. Pebbles or sticks might have enabled them to keep an even greater count by matching.
At a later time in history, men started recording numbers. Chinese kept record of numbers by tying knots in strings. Herdsmen drew slashes in dust to keep track of number of animals in a herd. Some civilizations recorded slashes on clay or stones.
Even today we use slashes as tally marks for counting. // represents 2 and //// represents 4.
Roman system of numeration used more symbols than just a /. This made the number representation shorter. Numbers 1 to 10 in Roman numerals are written as I,II,III,IV,V,VI,VII,VIII,IX,X. V is the symbol for 5 and X the symbol for 10.
As men started living together as communities, their need for numbers increased. They were required to measure things like quantities of seeds and grain produced. Taxes were to be paid.
These elaborate counting needs required that numbers beyond the first few be given names for use. Besides counting, performing calculations like addition and subtraction faster also became important.
New systems of numeration developed in different parts of the world to make counting and calculations more efficient.
The sophisticated positional notation that we use today took centuries to develop. It is called the Hindu-Arabic system. The system not only makes it easy to represent numbers but also facilitates performing calculations on them.