The History of Mathematics: A Brief Course

4. EUROPE 59

at the monastery of St. Gerald in Aurillac. Throughout a vigorous career in the

Church that led to his coronation as Pope Sylvester II in the year 999 he worked for

a revival of learning, both literary and scientific. (He was not a successful clergyman

or pope. He got involved in the politics of his day, offended the Emperor, and was

suspended from his duties as Archbishop of Reims by Pope Gregory V in 998. He

was installed as pope by the 18-year-old Emperor Otto II in 999, but after only

three years both he and Otto were driven from Rome by a rebellion. Otto died

trying to reclaim Rome, and Sylvester II died shortly afterward.)

4.2. The high Middle Ages. By the midtwelfth century European civilization

had absorbed much of the learning of the Islamic world and was nearly ready to

embark on its own explorations. This was the zenith of papal power in Europe,

exemplified by the ascendancy of the popes Gregory VII (1073 1085) and Innocent

III (1198-1216) over the emperors and kings of the time. The Emperor Frederick I,

known as Frederick Barbarossa because of his red beard, who ruled the empire from

1152 to 1190, tried to maintain the principle that his power was not dependent on

the Pope, but was ultimately unsuccessful. His grandson Frederick II (1194-1250)

was a cultured man who encouraged the arts and sciences. To his court in Sicily he

invited distinguished scholars of many different religions, and he corresponded with

many others. He himself wrote a treatise on the principles of falconry. He was in

conflict with the Pope for much of his life and even tried to establish a new religion,

based on the premise that "no man should believe aught but what may be proved

by the power and reason of nature," as the papal document excommunicating him

stated.

4.3. Authors and works. A short list of European mathematicians prominent

in their time from the twelfth through sixteenth centuries begins in the empire of

Frederick II.

Leonardo of Pisa. Leonardo says in the introduction to his major book that he ac-

companied his father on an extended commercial mission in Algeria with a group of

Pisan merchants. There, he says, his father had him instructed in the Hindu-Arabic

numerals and computation, which he enjoyed so much that he continued his studies

while on business trips to Egypt, Syria, Greece, Sicily, and Provence. Upon his re-

turn to Pisa he wrote a treatise to introduce this new learning to Italy. The treatise,

whose author is given as "Leonardus Alius Bonaccij Pisani," that is, "Leonardo, son

of Bonaccio of Pisa," bears the date 1202. In the nineteenth century Leonardo's

works were edited by the Italian nobleman Baldassare Boncompagni (1821-1894),

who also compiled a catalog of locations of the manuscripts (Boncompagni, 1854).

The name Fibonacci by which the author is now known seems to have become

generally used only in the nineteenth century.

Jordanus Nemorarius. The works of Archimedes were translated into Latin in the

thirteenth century, and his work on the principles of mechanics was extended. One

of the authors involved in this work was Jordanus Nemorarius. Little is known

about this author except certain books that he wrote on mathematics and statics

for which manuscripts still exist dating to the actual time of composition.

Nicole d'Oresme. One of the most distinguished of the medieval philosophers was

Nicole d'Oresme, whose clerical career brought him to the office of Bishop of Lisieux

in 1377. D'Oresme had a wide-ranging intellect that covered economics, physics,

and mathematics as well as theology and philosophy. He considered the motion of