First, it was advocated by Mei, a mathematician in the Qing Dynasty during the Eastern Han Dynasty and the Southern and Northern Dynasties. The basis is that Xu Yue, a mathematician in the Eastern Han Dynasty, wrote a book "Numerology Legacy", which recorded 14 algorithms, and the thirteenth algorithm was called "abacus calculation", and said: "abacus calculation, control of four seasons, latitude and longitude three talents." Later, Zhen Luan, a mathematician in the Northern Zhou Dynasty, commented on this passage: "Stereotyped writing is divided into three points, the upper and lower points are the pearl of stopping traveling, and the middle point is positioning. There are five beads in each position, and the upper bead is different from the lower four beads. There are five beads of different colors on the top and one on the bottom. To the next four beads, so the cloud' controls the four seasons'. Its beads swim between the three parties, so the cloud' latitude and longitude three talents' is also. " These characters are considered to be the earliest records of abacus calculation. However, some scholars believe that the abacus described in this book is at best a counting tool or a simple calculation board that can only be added and subtracted, which is different from the abacus that appeared later.
Second, the Yuan and Ming Dynasties advocated by Qing Dynasty scholar Qian Dating, that is, abacus appeared in the middle of the Yuan Dynasty and was widely used in the late Yuan and early Ming Dynasties. In the Yuan Dynasty, Tao's "Record of Dropping out of Farming in the South Village" (Volume 29) and "Well Beads" quoted a proverb at that time to describe servants, saying: "Anyone who brings a servant will beat the pearls when he first comes, and will not speak automatically; Say abacus beads for a while, and move as soon as you say it; For a long time, the Buddha's top bead, the word all day long, although it can't be moved. " Later generations called this "three-bead drama language." Comparing a veteran handmaiden to an abacus bead can be stirred, which shows that abacus was very popular at that time. In Liu Yin's Collected Works of Mr. Mu Jing at the end of Song Dynasty and the beginning of Yuan Dynasty, there is a five-character quatrain entitled Abacus: "Don't stop singing the song of bread unless you dance with Weng Shang. How difficult is it to raise funds? " This is also clear evidence that abacus appeared in the Yuan Dynasty. As for the Ming Dynasty, Luban Mu Jing, compiled during Yongle period, had specifications and dimensions for making abacus, and there were also some books introducing the usage of abacus, such as Zhu Zhu Algorithm by Xu Xinlu and Tong Zong by Cheng Dawei, so abacus was widely used in the Ming Dynasty, which is beyond doubt.
With the discovery of new historical materials, the third theory of abacus originated in Tang Dynasty and was popular in Song Dynasty. The basis is as follows: First, in the famous painting The Riverside Scene at Qingming Festival in Song Dynasty, there was a drugstore with an abacus on the counter. After enlarging the picture, the abacus experts in China and Japan confirmed that the object in the painting is a renju abacus similar to the abacus used in modern times. 2. 192 1 A wooden abacus bead was unearthed in Julu County, Hebei Province. Submerged by water and soil for 800 years, it is still drum-shaped with holes in the middle, which is no different from modern abacus beads. Third, Liu Yin was born in the late Song Dynasty and early Yuan Dynasty. His abacus poems are more accurate than describing things in the Yuan Dynasty. Similarly, Tao's "Three Beads Play" shows that there are abacus in Yuan people's proverbs, and it also reflects that "Fa prevailed in Song Dynasty" ("Algorithm unifies clans" in the Summary of Sikuquanshu). Fourthly, there are nine files of abacus figures in the textbooks of Mongolian studies in the early Yuan Dynasty. Since it was already a training content in the early Yuan Dynasty, it can be seen that it is an ordinary thing, and its appearance can at least be pushed to the Song Dynasty. In addition, the abacus in Song Dynasty was mature, and it was not as clumsy or rough as new things. Therefore, many mathematicians believe that the birth of abacus can be pushed to the Tang Dynasty. Due to the constant wars in the Five Dynasties and Ten Kingdoms before the Song Dynasty, the development of science, technology and culture was relatively slow, so it was unlikely that abacus was born at this time. The Tang Dynasty was a prosperous time in China's history, with developed economy and culture, and needed new calculation tools. At this time, the abacus was invented, which is very likely.