For centuries the dispute between the algorithmic and the abacist system went on and then finally in the 18th century, the abacist system was totally disappeared! some links on the history of maths…
This picture depicts that dispute.
This woodcut from the Margarita Philosophica of Gregorius Reisch, published in Freiburg 1503, shows “Arithmetica” watching a competition between an “abacist” and an “algorist”. Judging from the clothes of the two competitors, the abacist is a monk and the algorist a worldly scholar. Arithmetica appears to favour the algorist; her own clothes are covered in Indian numerals, and she looks approvingly at the algorist’s progress