In the 960s, a French monk named Gerbert of Aurillac came to Barcelona under the protection of its Count. The Count met him while traveling, stopping in the Benedictine monastery of Aurillac, and was so impressed with the young man’s intellect that he got permission to carry him south for further advanced study. Gerbert lived for a number of years in a Benedictine monastery in the Pyrenees, studying the scholarship that was now at its height in the Muslim Golden Age (which was ending during his lifetime).
Gerbert studied philosophy, a new field that was opened up by Arabic scholars reading and commenting on Aristotle, and theology. But he also mastered the quadrivium, a set of four academic disciplines that the Greeks had seen as closely related. Mathematics was the foundation, although in Greek mathematics, arithmetic was the junior partner. Mathematics meant the measured relationship of things (such as lines) to each other. It began with Euclid’s geometry, but it continued into studies of 3-dimensional figures like cones. The other related fields were music and astronomy.
Music was seen as a mathematical field because tones could be measured relative to each other, like lines or angles. Although they did not yet measure pitch by hertz, they knew that the 8-note scale represented something real in physics. We can now say that a violin is tuned to A = 440 hz, while the A one octave lower is tuned to 220. Medieval music knew this, without the numbers attached. Similarly, astronomy was about the relationship of measurements between stars and planets over time.
By the late 900s, Mozarabic culture in Cordoba was at its height. Christian bishops spoke Arabic and dressed in Arab fashions; Christians and Jews wrote Arabic treatises and poetry. We aren’t sure if Gerbert traveled to Cordoba or beyond; some legends place him even in Morocco. At the very least, he used his perch in the Pyrenees to obtain Arabic language skills and books.
Gerbert accompanied the Count of Barcelona on pilgrimage to Rome in 969. (That’s a significant year that we’ll loop back to shortly, but its events did not affect Gerbert in Rome.) In Rome, he met the new German Emperor, Otto I. Otto was looking for a tutor for his son, the future Otto II, so he hired Gerbert on the spot. This brought Gerbert north to Aachen.
Otto I, a descendant of Charlemagne, had ambitions to pull Germany out of the shadows. He himself had married an Anglo-Saxon princess and then a widowed Queen of Italy, the boy Otto’s mother. Italy was the crown jewel of the German empire, and it was always in danger of slipping away. That’s why Otto II needed a world-class education; eventually he married a Byzantine princess, which also made peace with Byzantine claims to Italy.
After Otto II grew up, Gerbert became the head teacher at the cathedral school in Reims, France. This was before the establishment of any of Europe’s universities; the school of Bishop Hincmar was one of the first ambitious, modern schools. Gerbert brought its curriculum up to date and began teaching Arabic mathematics. He also introduced a new kind of abacus that, in simplified form, became the “counting board” of European merchants. (Hence our term “counter” for the place next to the cash register.)
At Reims, Gerbert improved and innovated to create a hydraulic pipe organ. It was certainly part of his music curriculum, since a pipe organ is clearly based on mathematics. He also created an armillary sphere, a sort of globe of the skies. This was part of bringing in the latest in astronomy from Arabic treatises.