Numbers: Their Tales, Types, and Treasures.

Chapter 3: Numbers in History



In medieval Europe, mathematics had no part in the general knowledge, not even of learned people. Thus, the performance of simple arithmetic tasks was a matter for specialists. It was done by professionals, who did calculations for a living with the help of an abacus in the Roman tradition. The results were communicated with the help of Roman numerals, which were predominantly used throughout the Middle Ages.

A first chance to introduce Hindu-Arabic numerals to Europe came toward the end of the first millennium. The French monk and mathematician Gerbert d'Aurillac (ca. 946–1003 CE) was an important scientist of his time, and during a long visit in Spain, where the medieval Moors had established a large Islamic cultural domain, he studied mathematics from the Arabic scholars. According to legend, he traveled to Seville and Cordoba, gaining access to Islamic universities in the disguise of an Islamic pilgrim.

Gerbert later became the teacher of Emperor Otto III. In the year 999 he was elected to succeed Pope Gregory V. As pope, he took the name Silvester II. It was the only time in history that a leading mathematician became the pope.

Gerbert made the symbols 1 through 9 known as symbols on an abacus, but despite his influence he did not succeed in popularizing the Hindu-Arabic algorithms or the use of zero and the place-value system. The reception of the Hindu-Arabic numeral system met with considerable resistance from the Catholic Church and the conservative accountants. In some places the resistance lasted until the fifteenth century. Thus, it was the conservatism of medieval Europe and the Church that effectively blocked the early introduction of Hindu-Arabic mathematics to Europe. The nine Hindu-Arabic digits became known as “Arabic digits” among professional calculators (albeit without the symbol for zero because the symbols were exclusively used on an abacus where the zero is not needed). But the next few centuries would change that. Through the returning crusaders and the development of commercial routes, more and more information about a vastly superior Islamic culture reached Europe, where interest in the achievements of Arabic science grew steadily.

An important proponent of the Hindu-Arabic numeral system in Europe was the Italian mathematician Leonardo da Pisa (ca. 1170–1240 CE), the most important European mathematician of his time. Today, he is better known under the name Fibonacci, probably evolving from the Italian “filius Bonacci,” meaning “son of Bonacci.” Fibonacci traveled throughout the Mediterranean and Islamic North Africa, where he learned about Arabian mathematics, and, in particular, about the Hindu-Arabic numeral system being used there. In 1202 he wrote the book Liber Abaci (usually translated as “Book of Calculation”), introducing the “modus Indorum,” the method used by the Indians to write numbers. He thus made the advantages of the place-value system accessible to a larger audience in Europe. Fibonacci's word for 0 was cephirum, which turned into the Italian word zefiro, which later became the French zéro and the English zero. The Arabic word for zero was Sifr, which later developed into the English word cipher, as well as the German word Ziffer (meaning “digit”). This, then, takes us to our current number system, which is used extensively in today's technologically driven world.