Mayans were able to evolve a numbering system of their own which, they used mathematics extensively. Mathematics formed the cornerstone of the Mayan astronomy which in turn informed the Mayan religion, mythology and social customs. The number system used by the Mayans was fairly sophisticated. It included the concept of zero as well which was lacking in the classic-era mathematics of many other regions around the world. For larger numbers and computations, Mayans made use of a base-20 numbering system.
It is estimated that Mayans had evolved their number system well before the beginning of the Classic Period. Evidence extant from Mayan sites reveals that Mayans were using the concept of zero in their mathematics in 36 B.C. Researchers surmise that the concept had been developed a lot earlier than this date which also means that Mayan number system had largely developed before this date.
In the earliest evidence of mathematics among the Mayans, the number system was usually used to preserve large computations of astronomical dates, especially those related to Mayan mythology. It is entirely possible that Mayan number system evolved out of a need to store these huge date, some of them having been inscribed in Mayan sources over many lines.
Mayans had accurate representations for all basic numerical units. Zero, for instance, was represented by the symbol of a shell, 1 was represented by a single dot, 2 was represented by two dots and so on until at five the symbol changed again. A group of five was represented by a straight line. Ten was likewise represented by two straight lines.
To express numbers larger than 19, Mayans made use of a base-20 numbering system as opposed to the base-10 system which was developed and used in most other parts of the world. In total, the Mayan number system made use of only three symbols and the dot, the bar and the shell used to denote the zero. With these three symbols, Mayan laid the basis for a very advanced number system.
The base-20 numerical system was used by the Mayans to write down all larger numbers exceeding 19. Until 19, Mayans used the simply numerical representations as mentioned above. Larger numbers were written by representing 20 as a single dot and writing it above the other numbers. 21, for instance, would be represented by a dot representing 20 on the top and a dot representing one on the bottom. 44 would be represented by two dots representing 20 each on the top and five dots on the bottom. In this way, Mayans used multiple rows of dots representing 20’s to pen down even exceptionally large quantities.
Zero is of vital importance in the development of mathematics in the ancient civilisations because it heralded an advance over rudimentary numerical concepts. Researchers believe that although the earliest evidence of the use of zero in Mesoamerica is extant from Mayan sources, it is quite possible that zero was originally developed and used by the Olmec civilisation. Olmec predated the Mayans and were considered an ancestral civilisation to them. Most notable use of the zero concept in the Mayan culture was in the development of the Long Count in the famous Mayan calendar.
Long Count was one of the three cycles used in the Mayan calendar. Unlike the other two cycles, Long Count was used to denote very large periods of time. Mayans used a slight variation in the base-20 numerical system in the Long Count. Unlike regular base-20 numerical system, the Long Count changed its place in the third value. This modification essentially made it possible for the Mayans to express 360 with ease, thereby making it convenient to express the total number of days in a solar year. Since most Mayan dates dealing in large period were derived from the Long Count, nearly all of them have been found to be using this modified form of the base-20 system.
Mayan mythology was directly concerned with the astral bodies. This can be because of the agrarian basis of the society. Consequently, Mayan priests kept a close look at the movement of the astral bodies. They would watch the Sun and the Moon, the planet Venus as well as other stars. They built special observatories and tools to measure their movements.
With the help of very rudimentary tools, Mayans were able to trace the movement of the Sun and other astral bodies with exceptional accuracy. It is believed that the Mayan number system evolved when Mayans felt the need to record their observations. Having evolved and refined a mathematical system, it became possible for the Mayans to transmit the astronomical knowledge from one generation to the next in writing.
While astronomy is considered the need which gave birth to mathematics in the Mayan civilisation, calendrics is considered one of its outcomes. Mayan devised a very advanced calendar which was exceptionally accurate. This calendar was based on Mayan astronomical knowledge and their prowess in mathematics.
Because of their intimate and diligent practice of the number system, Mayan priests drew up multiple cycles for the calendar. These included the solar cycle called Haab, which was used for daily dates; the ritual cycle called Tzolkin which was used for religious rituals; and the Long Count, which utilised most of the mathematical knowledge of the Mayans and was used to record very large dates.
Mayan developed and evolved a fairly advanced mathematical system well before the Classic period of the Mayan civilisation. This included a numerical system which had a concept of zero and a neat representation for even very huge numbers. To express very large numbers, Mayans made use of a base-20 system in addition to the normal numbering conventions.
Mayan number systems played a critically important role in the preservation and transmission of the Mayan astronomical knowledge over the centuries. It was also very important in helping the Mayans create a very detailed and accurate calendar.
