The main reason is accounting. Examples:

Somebody wants to exchange goods. He has 9 sheep but he needs chickens. How is he going to handle the problem? He does not understand the concept of "nine" but he represents his possessions with a small stone for each animal.

Now, a sheep is worth several chickens. How to negotiate this? Representing the sheep's "price in chicken!"

Later, people realized that stones (or watever represented the object of interest) did not represent well and they also needed to keep track of several other things.

For small transactions, the hands worked as a "calculator" (base 10). The Mayans used base 20 (fingers and toes). Other civilizations used different numerical bases.

The abacus and other equivalent systems facilitated accounting.

With the advent of writing, somebody created symbols for the quantities and the operations.

The Arabs and other civilizations claim the invention of the positional system. The Arab introduced the zero.

Best wishes.

The genesis of mathematical concepts from the creation of the human mind.

As stated in the following link:

https://www.e-onec.com/2014/05/blog-post_3.html

Thanks Baidaa Mohammed Ahmed

The first surviving examples of geometrical and algebraic calculations derive from Babylon and Egypt in about 1750 BC.

Read more:http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=aa50#ixzz5x7BmMSbU

Refer this...

https://www.researchgate.net/post/What_is_the_origin_of_mathematics

Very interesting question! And answers too!

Mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction".

Reference

Heath (1931). "A Manual of Greek Mathematics". Nature. 128(3235): 5. Bibcode:1931Natur.128..739T. doi:10.1038/128739a0.

Interesting question.

Thanks @ Ajit kumar Roy

Thanks Devi Parameswari.C

Thanks Diary R. Sulaiman

Thanks Mila Ilieva

Thanks Sadanand Pandey

Thanks Suad Mohammed Heil

The main reason is accounting. Examples:

Somebody wants to exchange goods. He has 9 sheep but he needs chickens. How is he going to handle the problem? He does not understand the concept of "nine" but he represents his possessions with a small stone for each animal.

Now, a sheep is worth several chickens. How to negotiate this? Representing the sheep's "price in chicken!"

Later, people realized that stones (or watever represented the object of interest) did not represent well and they also needed to keep track of several other things.

For small transactions, the hands worked as a "calculator" (base 10). The Mayans used base 20 (fingers and toes). Other civilizations used different numerical bases.

The abacus and other equivalent systems facilitated accounting.

With the advent of writing, somebody created symbols for the quantities and the operations.

The Arabs and other civilizations claim the invention of the positional system. The Arab introduced the zero.

Best wishes.

Base 20? I saw that in a documentary.

From 3000 BC the Mesopotamian states of Sumer, in iraq with Ancient Egypt began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.

Mathematics science remains the finest science and excellence and that is the result of the nature of its subjects and methods consistent with them, which results in rigorous facts impressed many philosophers and scientists. The origin of mathematical concepts is that the overlap and complementarity between the mind and experience can not be denied the role of each of them in the emergence of mathematical concepts.

The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today .

In Babylonia mathematics developed from 2000 BC. Earlier a place value notation number system had evolved over a lengthy period with a number base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to be the foundation of more high powered mathematical development.

Thanks Vania Vieira Estrela

Thanks Suely MM Dias

Thanks Zainab Raheem

Thanks Amal Saadoon Majeed

Thanks Ali Alhayany

This article talks about numerical bases. The Yoruba also worked with base 20!

http://mentalfloss.com/article/31879/12-mind-blowing-number-systems-other-languages

Thanks Vania Vieira Estrela

Following