Mayans were among the few ancient civilisations who were able to not only devise an advanced numbering system but also had a concept of zero. This enabled the Mayans to have an elaborate mathematical system. The chief use to which the Mayan put their mathematical system was in observing astronomical bodies and in maintaining records of their movements.
Later, the Mayans also used mathematics together with astronomy in creating an exceptionally accurate calendar. In recording larger computations, Mayans made use of a well-formulated base-20 numbering system. This system was frequently used in calculating dates falling in future and computed with the help of the Long Count cycle of the Mayan calendar.
Mayans settled down to an agricultural lifestyle sometime around 1800 B.C. Since the Mayans lived in a region where annual rainfall was unpredictable, astronomy was considered critical in foreshadowing the turning of seasons and the expectations of harvest. It was because of astronomy that the earliest mathematics notions and ideas blossomed among the Mayans. According to later historical evidence, Mayans were already making use of the concept of zero by 36 B.C. which suggests that it was invented a lot earlier. The Mayan calendar also dates back to the pre-Classic period which means that Mayans had a sophisticated mathematical understanding which was needed in creating the calendar.
The concept of zero is an integral part of a complete mathematical system. It is a unique factor in the historical development of mathematics in different civilisations. Most ancient civilisations simply didn’t have a concept of zero and consequently, didn’t use it. Mayans were unique in that they were able to understand the notion of zero fairly early on and formulated a symbol to denote it. An empty shell was used to denote zero in Mayan numerical system. According to historical researchers, there is a possibility that the concept of zero was already in use in the previous Olmec civilisation and that the Mayans borrowed it from them. However, this theory is not definitively substantiated.
The development of mathematics in different ancient civilisations came with unique symbols to represent different figures. The Mayans also developed a sophisticated system of symbols to correspond to the numerology. In Mayan numerical system, zero was represented by an empty shell. 1 was represented by a single dot, 2 by two dots and so on until five was represented by a straight line. Five became a basic consolidating unit in the Mayan system, so that ten was represented by two straight lines, 15 by three lines and so on. For larger numbers, however, Mayans made use of a base-20 system.
For numbers less than 20, Mayans made use of the above-mentioned numerical symbols. But for numbers exceeding 20, a different representation was used. 20 itself became a unit in its own being and was represented by a dot. The difference between a regular dot and a dot representing 20 was that the latter was placed vertically above the rest of the numbers. So for instance, 22 was represented by a dot represented 20 and two dots representing 2 below it. It was using this base-20 system that Mayans were able to make huge computations and pen down astronomical calculations of extraordinary length, often related to dates in the future.
It is believed that Mayan mathematics was born directly as a consequence of Mayan astronomy. Mayans were keen observers of astral bodies. They kept track of the movements of Sun, Moon, Venus and other observable bodies. Astronomical knowledge was exclusively limited to the priestly class in the Mayan society. Mayans built special observatories where the priests would closely monitor these celestial movements and estimate the coming of rainy season and other natural events. Mathematics probably evolved when Mayans felt the need to pen down and record their astronomical observations for subsequent generations.
Mayans had an elaborate calendar which was one of the most accurate to have been created by any ancient civilisation. The calendar had a lunar cycle, a solar cycle and Long Count cycle. Mayans were able to create such an accurate calendar thanks to their brilliant knowledge of astronomy and their skill in mathematics. It was because of their mastery of mathematics that they frequently calculate dates thousands or even millions of years in the future with perfect accuracy. These dates were then penned down in elaborate mathematical notations, sometimes covering multiple lines to represent a single date.
The Long Count cycle of the Mayan calendar was meant to compute very large periods of time. A single cycle of the calendar represented more than 5000 years and Mayans were able to accurately predict different days on any given date within this time period. It was a common practice among the Mayans to predict different future dates using Long Count. These dates were computed and then penned using the elaborate base-20 numerical system. However, the base-20 system used for Long Count computations was slightly modified so that it changed value in the third value, a feature which doesn’t occur in regular base-20 computations. Mayans probably came up with this feature to visibly distinguish Long Count computations from any other mathematical calculations.
Mayans were among the few ancient civilisations who developed not only an elaborate mathematical system but also understood the concept of zero. This enabled the Mayans to create an elaborate and accurate calendar using solar and lunar cycles, and an additional Long Count. Since the Mayans had a very active interest in astronomy since the pre-Classic period and astronomy played a vital role in the agrarian Mayan society, it is quite possible that mathematics among the Mayans grew from astronomy. Extant Mayan sources reveal that Mayan mathematics was most frequently put to use in computing future dates on the Mayan Long Count calendar and in penning down these dates using a base-20 numerical system. This base-20 numerical system was specifically used by the Mayans to pen down exceptionally larger numbers.