European Math









Characteristic of European Middle Ages Mathematics:
Europe had accepted calculus and algebra from India and east counties until 900's. In India Aryabhata(475553) 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.
Monastic 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 research of mathematics besides the research by babies of Catholic. Of the persons charitably credited with playing a role in the history of mathematics 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 π±. The work of Boethius about arithmetic and geometry had been used as a test book 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 Renaissance (1100's1400'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 Europe.
Europe in 1100's was the times of translation. The superior publication of Greek and Arabic mathematicians, Archimedes, Apollonius, Ptolemy, Menelaus and AlKhwarizmi translated to Latin in Arabia.
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 influenced 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. Liber abaci shows to be influenced by algebra
of AlKhwarizmi and Abu Kamil. 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 Fibonacci's
sequence.
1, 1, 2, 3, 5,...., x, y, x + y,.....
The Antagonism of
Commercial Against Monastic Mathematics :
Though IndianArabic 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 churchmen.
From this times the antagonism of progress against conservativeness appeared.
This antagonism has been known the fight between the abacuses and the algorisms. The
continuance of the antagonism proved that the algorisms won finally but they
waited until 1500's. The characteristic of the algorisms 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.
The 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 became
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 baby in Italy, wrote. This book
contains many examples and commercial mathematics, especially bookkeeping by
double entry.

NonEuropean 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.
Indian Mathematics: Greek mathematicians were good at geometry but they were not
at arithmetic and algebra because they didn't use signs.
But Indian mathematises actively used symbols and they made IndoArabian
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 unabletogetacquainted
friends. But, surprisingly. IndoArabian 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 convenient tools
for calculation (Indians wrote numbers on a small blackboard with bamboo pen
and white ink)
(2) It may sound paradoxical, but they 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. Written by Bhaskara is a good
example. The name of the book is his daughter'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 Europecentered mathematics developed only
in nonEuropean countries. It were Europeans who used this IndoArabian
mathematics but it developed so lively in Gupta Dynasty which had a great power
in military, politics and culture from 4th to 12th century.
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 mathematics. When a slave state, Saracen Empire, was formed, commerce
and trade developed. 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 mathematics. Arabian
merchants introduced Indian arithmetic and algebra into their commerce. On recent
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 Arabia 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 land. So we can say
that mathematics in Arabia served as a setoff for astronomy as in China and
India. AlKhwarizmi 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 influenced.
'Algorithm' today named after him means a
certain process of calculation.