Numerical Systems

This section is about the many numerical systems, since mesopotamia until the binary system.

We are accustomed to numbers. Everyday we pass by a number on the streets, we have to remember our documents number, our address and so on. But how natural is the process of counting.

In mathematics counting is the same thing as associating a set A to a set B through a function. For example, the set A might be your fingers and the set B a colection o objects.

The Mayas

The Mayas were a civilization that lived around the year 2000 b.C. in the Yucatan peninsula.

It comes naturally to us to count from 1 to 10 using our fingers. It seems that the Mayas decided to use their toes as well. It is not known for sure why they chose a base 20 system for their calculations, but perhaps it was because of the astronomy it required. We know that 20 is a multiple of 2, 5 and 10, maybe that’s why having three multiples is an advantage in any number system especially when a number has to divide angles of 360, 180, 90, 45 (inclined plane), 15, 5 degrees.

As we can see in the figure above, the Mayas used a circle for the unitary value (uinals) and the bar worth 5 uinals[1]. But what about zero?


[1] Salyers, Gary D. “The Number System of the Mayas.” Mathematics Magazine, vol. 28, no. 1, 1954, pp. 44–48. JSTOR, Accessed 25 Jan. 2023.

[2] BLUME, ANNA. “Maya Concepts of Zero.” Proceedings of the American Philosophical Society, vol. 155, no. 1, 2011, pp. 51–88. JSTOR, Accessed 25 Jan. 2023.


unknown Mayan (Mayan cultural designation). Uxmal. 8th-11th centuries. JSTOR, Accessed 25 Jan. 2023.