The History and Evolution of Number Systems and Counting


The evolution of numbers developed differently with disparate versions, which include the Egyptian, Babylonians, Hindu-Arabic, Mayans, Romans, and the modern American number systems. The developmental history of counting is based on the mathematical evolution, which is believed to have been in existence before the counting systems of numbers started (Zavlatsky 124).

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The history of mathematics in counting started with the ideas of the formulation of measurement methods, which were used by the Babylonians and Egyptians, the introduction of the pattern recognition in number counting in pre-historical time, the organization concepts of different shapes, sizes, and numbers by the pre-historical people, and the natural phenomenon observance and universe behaviors. This paper will highlight the evolution history of counting by the Egyptians/Babylonians, the Romans, Hindu-Arabic, and the Mayans’ counting systems. Moreover, the paper will outline the reasons why Western counting systems are widely used contemporarily.

The Egyptians/Babylonians number system

The need for counting arose from the fact that the ancient people recognized the measurements in terms of more or less. Even though the assumption of numbers based its arguments on archeological evidence about 50,000 years ago, the counting system developed its background from the ancient recognition of more and less during routines activities (Higgins 87). Moreover, the need for simple counting by ancient people in history developed odd or even, more or less, and other forms of number systems that evolved to the current counting systems. The need for counting developed from the fact that people needed a way of counting groups of individuals through population increase by birth. In addition, Menninger asserts that the daily activities of the pre-historical people like cattle keeping and barter trade led to the need for counting and value determination (105).

For instance, in order to count cows, prehistoric people used sticks. The collection and allocation of sticks to count the animals helped in the determination of the total number of animals present. The mathematical history evolved from the marking of rows on bones, tallying, and pattern recognition, which led to the introduction of numbers. The bones and woods were marked, as shown below.

Wood and stones carvings.
Fig.1: Wood and stones carvings. (Ifrah and Bello198).

Moreover, the development of numbers evolved from spoken words by the pre-historical people. However, the pattern of numbers from one to ten has been difficult to trace. Fortunately, any pattern of numbers past ten is recognizable and easily traceable. For instance, eleven evolved from ein lifon, which was used to mean ‘one left’ over by the prehistoric people. Twelve developed from the lif, which meant “two leftovers” (Higgins143). In addition, thirteen was traced from three and four from fourteen, and the pattern continued to nineteen. One hundred is derived from the word “ten times” (Ifrah and Bello, 147). Furthermore, the written words used by the ancient people like notches on wood carvings, stones carvings, and knots for counting gave a solid base for the evolution of counting.

The counting of Boards was widely used by the Incas for record-keeping. The Incas used the “quip,” which helped the pre-historical people in recording their items in their daily life. The counting boards were painted with three different color levels. These were the darkest region, which represented the highest numbers, the lighter part representing the second-highest levels, while the white parts represented the stones compartments (Havil 127). In addition, the quip was used to do fast mathematical computations (Zavlatsky 154). Generally, the quip used knots on cords, which were arranged in a certain way to give certain numeral information. However, the quip systems of record keeping and information have been associated with several mysteries, which have not yet been established. Examples of how the knots looked are shown below

Knots and cords used by the Babylonians.
Fig.2: Knots and cords used by the Babylonians (Havil 187).

The Hindu- Arabic number system

This form is the common system of counting and numbers used in the 21st Century. In India, Al-Brahmi introduced the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 (Menninger 175). The Brahmi numerals kept changing with time. For instance, in the 4th to 6th Century, the numerals were as shown below.

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The numerical developments through centuries.
Fig.3 The numerical developments through centuries (Higgins 189).

Finally, the numerals were later developed to 1,2,3,4,5,6,7,8,9 with time. The earliest system of using zero developed from Cambodia. The evolution of the decimal points emerged during the Saka era, whereby three digits and a dot in between were introduced (Hays and Schmandt-Besserat 198). The Babylonians introduced the positional system, whereby the place value of the numerical systems was established. Moreover, the positional system by the Babylonians developed the base systems to the numerical, and the Indians later developed it further. The Brahmi numerals took different incarnations to develop, which resulted in the current number system (Higgins 204).

The Gupta numerals were one of the processes that the Hindu-Arabic number system passed to become the commonly used American number version. Currently, theories about the formation and development of the Gupta numerals remain debatable by researchers.

In addition, the Europeans adopted the Hindu-Arabic system through trading, whereby the travelers used the Mediterranean Sea for trade-interactions (Havil 190). The use of the abacus and the Pythagorean dominated the European number evolution. The Pythagorean used “sacred numbers” even though the two systems diminished after a short while. With time, the Europeans borrowed the Hindu-Arabic number system to invent their mathematical number systems establishment (Ifrah and Bello 207). However, the process through which the Europeans adopted the Hindu-Arabic system has not been established fully. It is believed that the Europeans adopted the Hindu-Arabic number system by relying heavily on it to build their current strong numerals (Higgins 210). For instance, the scope of the positional base system is quite large, which involved the conversion of different bases using numerical number 10.

The Mayan Numerical System

The Mayan civilization of counting and number systems developed in Mexico through ritual systems. The rituals were calendar calculations that involved two ritual systems, viz. one for the priests and the other for the common civilians (Higgins 217). For instance, the priestly calendar counting used mixed base systems, which involved numerical number multiples. The Mayan number systems form the base of mathematical knowledge. Moreover, the Mayan system of numbers used the positioning of numbers to allocate the place value of the combined digits (Havil 223).

The Mayans used the place value of numerical numbers, which were tabled to add and multiply numbers. Ultimately, the Hindu-Arabic and the Mayan number systems contributed highly to the evolution of numbers as opposed to the Egyptians/Babylonians number systems (Menninger 199). Nevertheless, the Western number system of counting and mathematics incorporated the strong features of all the other evolutions to get a standard solid number system. For instance, in the American system, which is commonly used in most countries, uses the decimal points, place value, base values, and the Roman numbers from 1 to 10 (Ifrah and Bello 225). The figure below represents a sketch of the tabled digits by the Mayans.

The tabulation of mathematical values used by Mayans for calculations.
Fig. 4: The tabulation of mathematical values used by Mayans for calculations (Havil 234).

The American version of numbers and counting used all the development features by the Mayans, Babylonians, Incas, Egyptians, and the Hindu-Arabic systems to develop a reliable and universally-accepted number system (Hays and Schmandt-Besserat 214). This aspect is outstanding as it makes the American system stand out of all the number systems and counting. Nevertheless, the commendable work of the Mayans, Babylonians, Egyptians, and the Indians cannot be underrated as, without them, the historical trace of counting and number systems would be impossible.


The historical trace of number systems and counting covers a wide scope of pre-historical archeological evidence. The tracing of the ancient times by the researchers pose a great challenge in trying to establish the counting and number systems. The research on the topic of number systems and counting has not yet been settled on the actual source information for evidence. Ultimately, the most effective number systems that led to the current dominant Western number system are the Mayans, Hindu, and the Babylonians systems relying on the Incas developments. The prehistoric remains left mathematical evidence as stones and wood carvings, which led to the evolution of counting, hence mathematical methodologies evolved. The methodology of research and arguments varies on the evolution of numbers. Consequently, there are no universally-accepted research findings on the mathematical and number systems evolution.

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Works Cited

Havil, Julian. The Irrationals: A Story of the Numbers You Cant Count on, Princeton: Princeton University Press, 2014. Print.

Hays, Michael, and Denise Schmandt-Besserat. The History of Counting, Broadway: HarperCollins, 1999. Print.

Higgins, Peter. Number Story: From Counting to Cryptography, Gottingen: Copernicus, 2008. Print.

Ifrah, Georges, and David Bello. The Universal History of Number: From Pre-history to the Invention of Computer, Hoboken: Wiley, 2000. Print.

Menninger, Karl. Number Words and Number Symbols; Cultural History of Numbers, Mineola: Dover Publications, 2011. Print.

Zavlatsky, Claudia. Africa Counts; Number and Pattern in Africa Cultures, Chicago: Chicago Review Press, 1999. Print.

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