**Gerbert of Aurillac** or **Pope Syvester II** was a talented French mathematics teacher who popularised the Indo-Arabic numerals.

- Even the date of his birth that we have given as 946 as simply a guess based on later known dates.
- However, the majority of historians believe that he was born in either 945 or 946.
- The fact that nothing is known of his parents would certainly suggest that they were poor people and not of any status.
- Gerbert was educated at the monastery of Saint-Gerald at Aurillac, a Benedictine monastery which had been founded around 60 years before Gerbert entered it in 963.
- At the monastery, Gerbert learnt literature, theology, history, and philosophy, but would not have studied any mathematics and only a very little logic.
- The year 967 was one of great importance for Gerbert since in that year he gained the opportunity to learn mathematical skills which were almost totally lacking throughout Europe.
- The abbot of the monastery, Gerauld, asked Count Borrell whether there were scholars of the arts in Spain and, when he replied that there were many men of learning, Gerauld persuaded Count Borrell to take one of his students back to Barcelona with him so that he might profit from the learning there.
- There he lived in the cathedral school of Vich, close to Barcelona, for three years.
- Bishop Atto was in charge of the cathedral school of Vich and he was officially Gerbert's teacher during these years but it was not from Atto that Gerbert learnt about the leading Islamic scholarship of the day.
- We know about Gerbert's studies in Spain from a number of sources, the most important of which was written by Richer of Saint-Remi, a student of Gerbert's, who wrote Historia Francorum around 996.
- Count Borrell took Gerbert to Rome in 970 and there he met pope John XIII.
- And because music and astronomy were completely ignored in Italy at that time, the pope through a legate promptly informed Otto, king of Germany and Italy, that a young man of such quality had arrived, one who perfectly mastered mathematics and who was capable of teaching it effectively to his men.
- What particular skills had Gerbert acquired while in Spain?
- It is noteworthy that arithmetic and music are only very briefly mentioned at the beginning and that geometry is described in a short paragraph at the end, while the rest of the account is devoted to a description of astronomical tools fabricated by Gerbert in order to introduce his disciples to astronomy.
- These tools portray an ingenious and original method of familiarizing students with the names and positions of the zodiacal constellations and with planetary astronomy and also of providing a basic knowledge of how to tackle problems of positional astronomy.
- This was as good a position as any scholar could ever hope to have and one might have expected Gerbert to make full use of the opportunity.
- The reason he wanted to go to Rheims was that Garamnus, perhaps Europe's leading logician, was there and he had offered to teach Gerbert logic in exchange for Gerbert teaching him music and mathematics.
- Once Gerbert was settled in Rheims, he quickly impressed Archbishop Adalbero of Rheims who appointed him to take charge of the cathedral school in Rheims.
- Gerbert designed the syllabus and quickly made this school into perhaps the leading European centre of learning of its time.
- Some of Euclid's propositions occur further on; but the major portion of the work is concerned with finding the area of figures and fields, the heights of mountains, the widths of rivers, and such like questions, which are generally considered the province of mensuration or trigonometry today.
- At Rheims Gerbert also taught his students how to use astronomical instruments and, with a breadth of learning which covered the full range of academic subjects, he taught his students the classic Latin authors Terence, Cicero, Virgil, Lucan, Persius, Juvenal and Statius.
- Here it was that Gerbert's powers found their fullest play in inventions of all kinds for the simplification of the subject and the advancement of science.
- So astonishing was his skill, that the simple folk of his day, in sheer bewilderment, accepted without question the belief that his knowledge was universal ...
- It is to be noticed that Gerbert was the first to introduce into the schools instruments as an assistance to the study of arithmetic, astronomy, and geometry.
- In arithmetic he first introduced the abacus, a tablet divided lengthwise into twenty-seven parts, on which the student moved about the nine numerical signs, which Gerbert caused to be cut out in horn to the number of one thousand.
- A blank space was left to replace the figure 0, which was unknown to Gerbert.
- Cumbrous as his methods appear to us, they must have been a great advance upon the ignorance of the end of the ninth century, and must also have been of the utmost service in teaching the proper use of arithmetic.
- It is worth noting that we have not made mention of any great advances in Gerbert's teaching of theology.
- His belief was that his teaching had to give his students skills to help them lead their lives and, as a consequence, he had little regard for much of the abstract theological arguments which were undertaken by most in the Church.
- Remember to that we are here describing a man who went on to become pope! It was at Rheims that Gerbert was ordained by Archbishop Adalbero.
- The reputation that Gerbert gained soon caused others to be jealous and attempt to undermine his reputation.
- One such was Otric, the head of the school at Magdeburg, who attempted to damage Gerbert by sending one of his own students to study with Gerbert in Rheims and bring copies of his lectures back to Magdeburg.
- The student, apparently, made some errors in the notes he took back and Otric thought he had evidence to bring down Gerbert so reported the errors to Otto II.
- He summoned Gerbert and Otric to Ravenna in 980 and set up a contest between the two men to be judged by himself and the most learned men at court.
- Gerbert was declared a clear winner and returned to Rheims with an even higher reputation.
- This important monastery had been badly run for many years and was in need of major reform.
- Gerbert was a talented teacher whose passion in life was scholarship and teaching, but he had neither the administrative skills nor the desire to turn round the failing monastery.
- After a year of arguments with the monks, Gerbert gave up the unequal struggle to reform the St Columban monastery and he returned to Rheims where he was enthusiastically reinstated as head of the school.
- Procure the 'Historia' of Julius Caesar from Lord Adso, abbot of Montier-en-Der, to be copied again for us in order that you may have whichever books are ours at Rheims, and may expect ones that we have since discovered at Bobbio, namely eight volumes: Boethius 'On astrology', also some beautiful figures of geometry; and others no less worthy of being admired.
- You also know how many copyists there are here and there in the cities and countryside of Italy.
- At Rheims, Gerbert had been much more than a teacher and head of the cathedral school.
- Archbishop Adalbero died in 988 and he had made it known that he wanted Gerbert to be his successor.
- However, it appears that Gerbert did not want to become Archbishop of Rheims, and certainly there were others who did not want to see him in that role.
- Arnulf, a descendant of Charlemagne, became Archbishop but was almost at once accused of irregular practices.
- A council of French bishops and abbots was held in Rheims in 991 and, following a recommendation by the French King, Arnulf was dismissed and Gerbert appointed in his place.
- There followed a bitter wrangle, with claims that Arnulf had been improperly dismissed and certainly Gerbert was faced with almost impossible difficulties in carrying out his duties.
- In 995 a synod was held which dismissed Gerbert and reinstated Arnulf.
- Pope Gregory V become pope in 996 and, two years later, he appointed Gerbert to be Archbishop of Ravenna.
- In the following year, 999, pope Gregory V died and Gerbert was elected pope.
- He found that the unfortunate circumstances of the time, the animosity of the Romans towards him, and the swift approach of death were more than able to paralyze his own worthy projects and high endeavours, and the powerful protection of the Emperor.
- He was the first Frenchman to become pope and the Romans certainly considered that the position of pope should not go to a "foreigner".
- Finally we look at a letter that Gerbert wrote to his friend Adalbold shortly before he was elected pope.
- Gerbert then goes on to answer a problem that Adalbold has posed.
- In an equilateral triangle with base 30 feet and height 26 feet Adalbold knows two ways of finding the area.
- Gerbert correctly tells his friend that half the base times the height, giving 390 square feet, is the correct method.
- However, his explanation is far from convincing! There are a number of points worth making.
- (i) The triviality of the problem gives a good indication of the low level of European mathematics in the year 1000.
- The 30th triangular number is indeed an equilateral triangle of dots with 1 in the first row, 2 in the second, up to 30 in the third.
- (iii) Finally, we note that an equilateral triangle with base 30 feet has height 25.98 feet so the height of 26 feet is a good approximation.
- Gerbert's fame as a mathematician lies not in any mathematical achievement but rather in his enthusiasm to teach the topic and to popularise the use of Indo-Arabic numerals and the abacus in Europe at a time when, for Europeans, mathematical understanding was at a low ebb.

Born 946, Belliac, (now St-Simon) Auvergne, France. Died 12 May 1003, Rome (now Italy).

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**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive