Mathematics in medieval Europe.
(Matematika ve středověké Evropě.)

*(Czech)*Zbl 1077.01006
Dějiny Matematiky / History of Mathematics 19. Prague: Prometheus (ISBN 80-7196-232-5). 445 p., open access (2001).

A more appropriate title of the book would be “Medieval Europe and Mathematics”. The authors tried first of all to evoke the emotional and political appeal of the medieval society which was far from being inclined to the rational mathematical line of thoughts. Only on this background, they follow the development of mathematical education and ideas – rather limited and closely tied to their ancient roots – by focusing on the most distinguished persons.

Patristics giving way to scholasticism, origins of monasticism and its achievements, passing attempts to re-create the Roman empire, struggles of Papacy for superiority are the items of the opening chapter entitled Middle Ages. They are illustrated by biographical sketches of Boëthius, Cassiodorus, Isidor of Seville, Bede the Venerable, Alcuin and Erigena.

The educational trends are examined in four chapters devoted to liberal arts, schools including the universities and to libraries. The separate chapters are dedicated to two outstanding medieval personages. Gerbert of Aurillac, who became a pope under the name of Sylvester II is famous not only for his learning and teaching abilities but also for his support of the Ottonian imperial attempts. His merits in mathematics include calculation techniques in the decimal system by means of abacus and the popular textbook of longstanding influence, the “Geometria”. Leonardo da Pisa-Fibonacci is widely known for his contributions to algebra, arithmetics, geometry and number theory. They are based on the knowledge of Chinese, Babylonian, Egyptian and Arabic mathematics and in the present book they are summarized and commented. The chapter on medieval numerical algorithms can be regarded as a widely extended supplement of the works of Gerbert and Fibonacci; it covers the development during the whole period of time till 1600.

The impact of Arabic mathematics on its development in medieval Europe can be hardly overestimated and a special chapter is reserved for it. In particular, also the effect of Arabic translations of Greek mathematical treatises is covered and the most important translators introduced; e.g. Abelard of Bath, Gherardo of Cremona, Robert of Chester etc.

The titles of the other chapters give at least some notion of other topics treated in the book. They are Physics and Astronomy in Middle Ages, Commentary on four images from Boëthius’ De arithmetica, Gothic architecture and geometry, Gothic window traceries.

Nearly all chapters are accompanied by numerous pieces from medieval books (original Latin versions or Czech translations) and by many excellent medieval drawings and engravings.

Patristics giving way to scholasticism, origins of monasticism and its achievements, passing attempts to re-create the Roman empire, struggles of Papacy for superiority are the items of the opening chapter entitled Middle Ages. They are illustrated by biographical sketches of Boëthius, Cassiodorus, Isidor of Seville, Bede the Venerable, Alcuin and Erigena.

The educational trends are examined in four chapters devoted to liberal arts, schools including the universities and to libraries. The separate chapters are dedicated to two outstanding medieval personages. Gerbert of Aurillac, who became a pope under the name of Sylvester II is famous not only for his learning and teaching abilities but also for his support of the Ottonian imperial attempts. His merits in mathematics include calculation techniques in the decimal system by means of abacus and the popular textbook of longstanding influence, the “Geometria”. Leonardo da Pisa-Fibonacci is widely known for his contributions to algebra, arithmetics, geometry and number theory. They are based on the knowledge of Chinese, Babylonian, Egyptian and Arabic mathematics and in the present book they are summarized and commented. The chapter on medieval numerical algorithms can be regarded as a widely extended supplement of the works of Gerbert and Fibonacci; it covers the development during the whole period of time till 1600.

The impact of Arabic mathematics on its development in medieval Europe can be hardly overestimated and a special chapter is reserved for it. In particular, also the effect of Arabic translations of Greek mathematical treatises is covered and the most important translators introduced; e.g. Abelard of Bath, Gherardo of Cremona, Robert of Chester etc.

The titles of the other chapters give at least some notion of other topics treated in the book. They are Physics and Astronomy in Middle Ages, Commentary on four images from Boëthius’ De arithmetica, Gothic architecture and geometry, Gothic window traceries.

Nearly all chapters are accompanied by numerous pieces from medieval books (original Latin versions or Czech translations) and by many excellent medieval drawings and engravings.

Reviewer: Ivan Saxl (Praha)

##### MSC:

01A35 | History of mathematics in Late Antiquity and medieval Europe |

01A30 | History of mathematics in the Golden Age of Islam |

01-06 | Proceedings, conferences, collections, etc. pertaining to history and biography |

00B25 | Proceedings of conferences of miscellaneous specific interest |