Dark Age/Medieval/Renaissance Europeans used a "bead abacus" for computation, given the unwieldy nature of Roman numerals. This abacus was, in turn, derived from Roman models created to circumvent the same problem. The system was so complex that the operators possessed almost "supernatural" powers given the mysterious nature of the computations. The use of these kinds of abacuses persisted well after European contact with Arabic numerals -- even up to the time of the Reformation. (Christian) Europeans took a long time to come around to Arabic numerals, and their reluctance to shift towards modern mathematical computation styles likely handicapped math develop in the "west".[1]
I think that eventually a more transparent system like Arabic numerals would have been adopted, given the limitations of the Roman abacus for complex financial calculations. Maybe a Catholic edict forbidding use of Arabic numerals would have stalled development of a "new math", but the Reformation would have to be butterflied away given that newly Protestant nations might develop new mathematical advances forbidden in Catholic lands.
1. See Ifrah, Georges. "The Universal History of Numbers: From Prehistory to the Invention of the Computer" (Wiley, 2000)