¡ß Characteristic of European Middle Ages Mathematics:
Europe had accepted calculus and algebra from India and east counties until
In India Aryabhata(475-553) wrote the numeration system and the
astronomical observation theory on Aryabhattiya(449) in 600's.
Arabic camber was invented in India. Italian Fibonacci introduced arabic
number go Europe.
¡ÝMonastic Mathematics : We call the term the black Age from the middle of
400's to 1000's. In this times, the church controlled all the action and thinking
of humans. Thus, there was no reserch of mathematics besides the reserch by
abbies of Catholic.
Of the persons chariably cereited with playing a role in the history of
mathimatics during the Dark Ages, we might mention the martyred Roman
citizen Boethius, the British ecclesiastical scholars Bede and Alcuin, and the
famous French scholar and churchman Gerbert, who became Pope Sylvester
The work of Boethius about arithmetic and geometry had been used as a
testbook during many centuries.
Gerbert was known to spread indian - arabic number without 0 to Europe
and also he was known to make an abacus, a terrestrial globe, a celestial globe
and watch and establish the first school at France in Europe.
After that time, mathematics in Europe started to progress in the end of the
middle age and the early part of the Renessance (1100's-1400's). The
knowledge in this times was based on not Greek but Islam mathematics.
Arabic mathematics played an important part Greece(and India) with modern
¡Ý Europe in 1100's was the times of translation. The superior publication of
Greek and Arabic mathematicians, Archimedes, Apollonius, Ptolemy, Menelaus
and Al-Khowarizmi translated to latin in Arabia.
¡Ý Fibonacci and The 13th Century : In the early part of 1200's Leonardo
Fibonacci, the most talented mathematician in middle age, came on the stage.
He was a man reconstructed mathematics of the middle age. He was
interested in arithmetic in childhood influanced by his father, and he traveled
Egypt, Sicily, Greece, Syria and had a chance to meet east and Arabic
mathematics. Finally he came back home in 1202 and published the famous
Liber abaci shows to be influanced by algebara of Al-Khowarizmi and Abu
This book played an important part to introduce Indian - Arabic number to
Europe, and had many problems. In this book, the following sequence is called
1, 1, 2, 3, 5,...., x, y, x+y,.....
¡Ý The Antagonism of Commercial Against Monastic Mathematics :
Though Indian-Arabic a system of measuring by decimal notation spread
among the merchants, mathematicians persevere in Roman a system of
measuring against Indian - Arabic a system of measuring. They were
From this times the antagonism of progress against conservativeness
This antagonism has been known the fight between the abacists and the
algorists. The continuance of the antagonism proved that the algorists won
finally but they waited until 1500's.
The characteristic of the algorists was not only to calculus using 0 as a
number without Indian - Arabic numeration system but also not to use abacus.
At last, Indian calculation spread abroad become of the progress of
commerce and industry con fronted by the period of prosperity.
Italy and Spain in 1400's and England, France and Germany in 17c used
Indian - Arabic mathematics instead of Roman's.
¡ÝThe greatest mathematician in 1300's was Nicole Oresme born at Normandy
in 1323. He was a professor and became a bishop and died in 1382.
One of the books he wrote used a fraction and an exponent for the first time
(not modern expression), the other expressed coordinates as a point. It become
the origin of modern coordinates geometry.
This paper in the end of 1300's influenced Descartes and many Penessance
mathematicians. Luca Pacioli(1445 - 1509), a abby in Italy, wrote.
<Summa de Arithmetica> This book contains many examples and commercial
mathematics, especially bookkeeping by double entry.
¡ß Non-European Mathematics
We need to look over mathematics Arabia and India before moving to Middle
and Modern Ages.
That's why the two countries contributed to the development of the
european middle ages mathematics.
¡Ý Indian Mathematics :
Greek mathematicians were good at geometry but
they were not at arithmetic and algebra because they didn't use signs.
But Indian mathematians actively used symbols and they made
Indo-Arabian numbers. They also used decimal system.
Indian mathematicians thought about the negative numbers for the first time
and they made it a rule.
For example, Brahmagupta divided numbers into two : property(positive
number) and debt(negative number). But he didn't actually deal with 'negative
numbers' freely as 'positive numbers.'
He maybe thought that he could use 'negative numbers' in logical system
not in practical.
Bhaskara even said that 'negative numbers' were unable-to-get-acquainteo
friends. But, surprisingly. Indo-Arabian numbers were as quite complete as
people in other countries never dreamed it.
The reasons why this kind of numbers were made and the art of calculation
are as follows :
(1) They used very conveniend tools for calculation
(Indians wrote numbers on a small blackboard with bamboo pen and
(2) It may sound paradoxical, but whey didn't know how to
distinguish number from quality.
(3) Commerce developed in India earlier than other countries so
they needed the art of calculation.
Although their achievements, they exposed some faults.
Mathematics was for the nobilities so it tended to be games they, specially,
expressed mathematics in the form of verse, which brought about despising
the strict demonstration and inference.
<Lilabati> written by Bhaskara is a good example. The name of the book is
his dqughter's. It contained many meaningful contents but it is better known
as a representative sanskrit literary works.
It was Arabian who developed Indian mathematics' merit.
The field of algebra (equation) out of europe-centered mathematics
developed only in non-european countries.
It were europeans who used this Indo-Arabian mathematics but it developed
so lively in Gupta Dynasty which had a great power in military, politics and
culture from 4th to 12th century.
¡Ý Arabian Mathematics : Arabians ruled parts of North Africa and Europe
for 400 years since Mahomet(570?~632). They had new mathematics which
was mixed Greek and Indian mathematics, which made Islam lead an important
role in mathematics.
Islamic mathematics, thus, became the starting point of modern European
When a slave state, Saracenic Empire, was formed, commerce and trade
People needed convenient and accurate art of calculation.
Accurate maps were needed to Arabian merchant. Islamic
ceremony(praying toward Mecca) had a great influence on the Arabian
Arabian merchants introduced Indian arithmetic and algebra into their
On recept of Greek study, Arabians praised it so much and they translated
many Greek classics in Greek.
Finally, Arabians fused Greek logical geometry Indian arithmetic and algebra
and they renewed them.
Without Arabians' effort to preserve and study the Greek culture, important
Greek achievements about mathematics would disappeared. Arabian
mathematics, thus, had a great role in the history of mathematics.
Most people dealing with mathematics ub Arebia were astronomers because
commerce, administration, measurement, the way of making maps, astronomy
and the calendar method were needed to calculate and survey the area of a
So we can say that mathemtics in Arabia served as a setoff for astronomy
as in China and India.
Al-Khowarizmi was the most famous Arabian mathematician.
He wrote two books about algebra and Indian numbers. When the two
books were translated in Latin in 12th century, Europeans were quite
'Algorithm' today named after him means a certain process of calculation.