The first findings or writings about the Mayan number system date back to the fourth century A.D. Evidence shows that the Mayan culture of Yucatan and Central America were extremely advanced not only in mathematics, but were believed to be geniuses when it came to time and calendars, astronomy, architecture, and commerce. It is believed that the Mayan culture was obsessed by time and numbers which studies have concluded based on drawings found on historical monuments. The Mayans were a thousand years in advance to Europe when it came to mathematics.
The Mayans used a vigesimal (base twenty) system of numeration with positional notation instead of the base ten decimal system used in today's standards. The Mayans used a system of dots and bars for counting. A dot (pebble) stood for one and a bar (stick or rod) stood for five. Depending on what level in the column the dots and lines were in would determine how many times it would need to be multiplied by twenty to give the right number. The Mayans wrote their numbers vertically instead of horizontally with the lowest denominations at the bottom, increasing as we move to the top.
The Mayans were the first to conceive a systematic use of a symbol for zero in the place-value system. They used this symbol long before others in different latitudes and more than a millennium before the concept ever arrived in Europe. The Mayan zero symbol was used to indicate the absence of any units of the various orders of the modified base-twenty system. This avoids confusing one place with another. Today we take for granted the existence of a symbol for zero but at the time this was certainly ingenious for the concept of zero to be understood. This concept happened only two or three times in the entire history of humanity!
The great advantage of the positional system is that you need only a limited number of symbols (the Mayans only had two, plus their symbol for zero) and you can represent any whole number, however big.