The Hindu-Arabic number system was invented in India around the year 500 AD, and during the Early Middle Ages spread throughout Arabic-speaking world, but it did not spread quickly throughout Europe:
Crossley examined 1398 manuscripts created between the years 1200 and 1500 to see how much use of the Hindu-Arabic numerals, and found that throughout this period Roman numerals were still largely preferred. For the 13th century, only 7% of manuscripts had the new numbers, rising to 17% for the 14th century and 47% for the 15th century. He also found that in many instances where writers were mixing the two systems, sometimes within the same number – for example, one sometimes found M (for 1000) followed by Arabic numerals.
That crazy, mixed-up example sounds like a superior system, like a more readable scientific notation, where you succinctly clarify the order of magnitude (M = 103) and then rattle off the significant digits.
The new and old systems continued side by side, but in different domains:
Roman numerals were used in academia where universities taught about abstract properties: square numbers, triangular numbers, etc. Hindu-Arabic numerals were used for the practical world of commerce. This occurred in special, so-called abacus schools where merchants and their employees were taught the new Hindu-Arabic numerals. Such schools were prevalent in Italy. Since they were intimately involved with sometimes quite complicated calculations, the commercial use ultimately led to the development of algebra. It was not until the sixteenth century that the two domains came together. At that time academia at last embraced the study of methods of calculation, in particular algebra, while retaining its theoretical concern with abstract properties of numbers.