History of Mathematics - Middle Ages


This film invites you to participate in the exciting developments in the ancient science of mathematics.

The main emphasis has been placed on the developments during the Middle Ages in Asia (the Orient) and Europe (the Occident). Many changes took place at that time and few of the written documents on the sciences in ancient Greece – particularly those on mathematics – were saved. But the scholars from Islamic countries discovered much of this cultural heritage and translated it into Arabic. In this way, a large portion of the ancient knowledge could be saved, further developed, and later translated into Latin.

In Europe, the Age of Migration and tribal wars initially blocked the spread of this ancient heritage. But eventually it returned to Europe with new advances from Islamic scholars.

In 64 minutes you will be introduced to the exciting and adventurous era of mathematical developments and the scholars of the Middle Ages.


In Europe the time span from around A.D. 500 until 1500 is called the Middle Ages.

For a better understanding of the developments of this time, we look first at the cultures of China and India.

Orient (32 min)


One of the oldest civilisations in the world arose in China. In China’s bureaucratic civil service, the officials had to learn about mathematics. Many developments originated in China: movable type for printing, paper production, the compass for navigation and architectural marvels like the Great Wall.


During the third millennium b.c. a great culture arose in Harappa and Mohenjo-Daro on the banks of the Indus River.

The main mathematical works were written between the second and sixteenth century a.d.

The playful way in which mathematical problems were formulated in verse is shown as an example. The discovery of zero and its use in the decimal system seems to have originally come from India. In the astronomical work “Siddhantas”, the mathematician Brahmagupta calculated with nine digits and zero back in the 7th century.


Until the late Middle Ages most of the main developments in the sciences came from the Islamic scholars.

The Abbasid caliphs – al-Mansur, Harun ar-Rashid and others – were great supporters of astronomy and mathematics.

Knowledge from the Indian and Greek-Hellenistic heritage was collected, translated into Arabic and further developed by Arabian and Persian scholars.

In his “Arithmetic” from the year 820 al Khwarizmi used the place-value decimal system with Indian digits. The terms “algorithm”, “algebra” and other terms were derived from his name and his work.

Ibn Sina was another of the great scientists of the Middle Ages. He was active in different areas. An astronomical instrument invented by him is shown in detail and explained. Astronomy was one of the most popular sciences at that time. Using astrolabes was common, the sextant of Ulugh Beg in Samarkand was an important part of the biggest observatory in those times.

A famous example of Middle East architecture is the Dome of the Rock in Jerusalem. Its structure is shown using computer animation. The design uses the numerical symbolism of the ancient Greeks, Romans and Gnostics.

Another example of an architectural dome leads us to the scientist al Kashi.

Chess plays an important role in a common tale about the mathematical basis for the Fibonacci Series.

The first universities of the world in medieval times were founded in Fez and Cairo in the 10th century.

Occident (32 min)


The Middle Ages started with the downfall of the Greek and Roman cultures. For several hundred years, Europe experienced a period of migration.

Only the church kept the knowledge of ancient Greek and Latin written works. But they did not come into use in those times. Many of the mathematical and other (including philosophical, literary and medical) achievements of the Greeks, Romans, Indians and Arabs were primarily brought to Europe through Moorish Spain from the 11th century on. Many works were translated in Toledo or Cordoba from Arabic into Latin.

The Vikings discovered America around the year 1000.

At the same time the church St Michael was built in Hildesheim, Germany. Today it is listed as a World Cultural Heritage Site by UNESCO. It was an early example of Romanesque architecture in the centre of Europe. The harmonic and mystic symbolism of the ancient Greeks was taken as a basis for the structural design of such churches.

The first universities in Europe were founded in Bologna and Paris in the 11th century.

Leonardo Pisano (also called Fibonacci) wrote a book on arithmetic and algebra, titled “Liber Abbaci” in 1202. He used the Hindu-Arabic place-value system of digits instead of Latin numerals. Using reproducing rabbits as an example, he came up with the Fibonacci Sequence, which was named after him.

The use of Roman numerals (or pebbles on lines) changed into the place-value decimal system with Indian-Arabic digits and zero.

With Gothic structures, a new, geometrical architectural style started in France in the 12th Century (Chartres, Reims, Amiens, Beauvais, Paris, …).

The black plague and the Inquisition, among other things, inhibited the development of knowledge.

With knighthood, the guilds, the foundation of universities and the Hanseatic League, the economy and knowledge boomed in Europe. Gutenberg used movable type for printing.

At the end of Middle Ages the age of discovery began. If the world was not flat, but round like a ball, there should be a passage to India to the west as well as one to the east. Following this idea, Columbus discovered America (again – 500 years after the Vikings), believing, he landed in India.

With the age of discovery, the Middle Ages ended, modern times had begun.

Trailer (ca. 4 min)

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You can choose between two versions:

- a PAL DVD for libraries, schools, colleges or universities, including permission for (non commercial) public viewing (49.00 euros)

- a PAL DVD for private use only, without permission for public viewing (14.90 euros)

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