Maya mathematics constituted the most sophisticated mathematical system ever developed in the Americas. The Maya counting system required only three symbols: a dot representing a value of one, a bar representing five, and a shell representing zero. These three symbols were used in various combinations, to keep track of calendar events both past and future, and so that even uneducated people could do the simple arithmetic needed for trade and commerce. That the Maya understood the value of zero is remarkable - most of the world's civilizations had no concept of zero at that time.
The Maya used the vigesimal system for their calculations - a system based on 20 rather than 10. This means that instead of the 1, 10, 100, 1,000 and 10,000 of our mathematical system, the Maya used 1, 20, 400, 8,000 and 160,000.
Maya numbers, including calendar dates, were written from bottom to top, rather than horizontally. As an example of how they worked, three was represented by three dots in a horizontal row; 12 was two bars with two dots on top; and 19 was three bars with four dots on top. Numbers larger than 19 were represented by the same kind of sequence, but a dot was placed above the number for each group of 20. Thirty-two, for example, consisted of the symbols for 12, with a dot on top of the whole thing representing an additional group of 20. The system could thus be extended infinitely.
The Maya set of mathematical symbols allowed even uneducated people to add and subtract for the purposes of trade and commerce. To add two numbers together, for example, the symbols for each number would be set side by side, then collapsed together to make a new single number. Thus, two bars and a single dot representing 11 could be added to one bar for five, to make three bars and one dot, or 16.
The Maya considered some numbers more sacred than others. One of these special numbers was 20, as it represented the number of fingers and toes a human being could count on. Another special number was five, as this represented the number of digits on a hand or foot. Thirteen was sacred as the number of original Maya gods. Another sacred number was 52, representing the number of years in a "bundle", a unit similar in concept to our century. Another number, 400, had sacred meaning as the number of Maya gods of the night.
The Maya also used head glyphs as number signs. The number one, for example, is often depicted as a young earth goddess; two is represented by a god of sacrifice, and so on. These are similar to other glyphs representing deities, which has led to some confusion in decoding the glyphs. To further confuse things, number glyphs were sometimes compounds. The number 13, for example, could be written using the head glyph for 10 plus the head glyph for three. Numerical head glyphs could also be combined with the usual dots, bars and shells.
Mathematics was a sufficiently important discipline among the Maya that it appears in Maya art such as wall paintings, where mathematics scribes or mathematicians can be recognized by number scrolls which trail from under their arms. Interestingly, the first mathematician identified as such on a glyph was a female figure.
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