Raynaldus as mathematician

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. It reached into Western Europe by the end of the 10th century, and started getting more use in the 13th century. In his article “Old-Fashioned versus Newfangled: Reading and Writing Numbers, 1200-1500,” math historian John Crossley (Monash University, Australia, Studies in Medieval and Renaissance History, Third Series, Volume 10 2013) explains that even by the end of the Middle Ages many writers had difficulty understanding how numbers worked, and preferred using Roman numerals. With Roman numerals they would know that the various characters had a fixed amount. If they saw a V it would be five, X would be ten, and M that would mean one thousand.

“With minor exceptions, Roman numerals do not change their meanings when they change their place, but Hindu-Arabic numerals do.. When we encounter 3 in 437 or in 3,145,872, it means two different things. The distinctive feature of Hindu-Arabic numbers is their place notation, independent of the form of the numerals 0,1,…9.

The concept of place notation, along with new forms/symbols for numbers, proved difficult for medieval Europeans to understand, so changing over to the new system was slow. Crossley examined manuscripts from 1200 to 1500 to determine use of the Hindu-Arabic numerals, and found that in the 13th century, only 7% of manuscripts had the new numbers, rising to 17% for the 14th century and 47% for the 15th century. The impetus for changing to the Hindu-Arabic numbers in medieval Europe seems to have come from businessmen. Progressive and successful merchants such as those in our novels would have had to learn a major new approach to numbers

“Roman numerals were used in universities that taught about abstract properties ( square numbers, triangular numbers, etc.) and Hindu-Arabic numerals were used for commerce. They were taught in so-called abacus schools where merchants were taught the new Hindu-Arabic numerals. Such schools were prevalent in Italy. Since they were sometimes involved with quite complicated calculations, the commercial used ultimately led to the development of algebra. It was not until the 16th century that time academia embraced the study of methods of calculation, in particular algebra, while retaining its theoretical concern with abstract properties of numbers.”