The abacus was invented during the Yuan Dynasty which lasted between 1206AD till 1368AD and then it was expanded and refined by the Ming Dynasty (1368AD-1644AD).
There have been archaeological proof of this as the writings of Tao Zongyi describes in his book that the new servants, unlike the older and more experienced ones were "just like abacus heads" and that they would not move unless they were made to move. This bears credence to the fact that the abacus was already widely used then.
