25/01/2023

In Folha: Silvestre II's contributions to mathematics

Crédito: Freepik

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

Around 972, Gerbert of Aurillac was already considered the greatest intellectual in Europe. Tutor of the future Roman Emperor Otto II, he also became director of the Reims Cathedral School, one of the most advanced educational institutions on the continent, which, under his leadership, would reach the pinnacle of glory as a center of knowledge.

Among Gerbert's great contributions is the introduction to Europe of the decimal system, the Hindu-Arabic numeral system that we still use today. At the time, calculations were done using Roman numerals, which are very impractical for this purpose. Gerbert taught how to perform the four arithmetic operations much faster using abacuses.

Unfortunately, his teachings faced opposition from the powerful clergy, who monopolized knowledge of numbers and distrusted teachings from the Islamic world. Therefore, the abacus and decimal notation only became popular in Europe much later, starting with the publication of "Liber Abaci" by the Italian Leonardo Fibonacci in 1202.

Astronomy was another field in which Gerbert excelled. We owe him, in particular, the introduction of the astrolabe to the West, an extremely precise instrument for observation and calculation that would play a fundamental role in the Age of Discovery.

Gerbert also left behind important written works on music. One of his works explains how to calculate the length of organ pipes to cover a band of two octaves, which involves interesting mathematical problems.

In geometry, his lecture notes for students in Reims were the most advanced work on the subject in Europe for two centuries, only to be surpassed by the Latin translation of Euclid's "Elements" (from Arabic, since the original Greek was lost).

Alongside his work as a scholar and academic, Gerbert was also a significant player in the major political issues of his time. He was instrumental in Hugh Capet's ascension to the throne of France in 987. Four years later, he was rewarded with the appointment as Archbishop of Reims, but his opposition to Rome led to his excommunication and deposition.

He enjoyed the protection and friendship of the new Roman emperor, Otto III, who had also been his tutor. Otto appointed him archbishop of Ravenna in 998, and the following year had him elected pope.

Symbolically, he chose to be called Sylvester II, in honor of Pope Sylvester I, who had been a close collaborator of another Roman emperor, Constantine the Great.

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