ISLAMIC MATHEMATICS
The first article we refer to is http://en.wikipedia.org/wiki/House_of_Wisdom . The House of Wisdom was a library and translation institute in the Abbasid era Baghdad, Iraq. The great scholars of the House of Wisdom (Arabic Bayt al-Hikma) included Al-Khwarizmi, the "father" of algebra, which takes its name from his book Kitab al-jabr. Caliph al-Mansur (reigned 754-775) built Baghdad and made it his capital. He founded a palace library modelled after the Sassanid Imperial Library. The secret of paper-making had been obtained from Chinese prisoners taken at the Battle of Talas (751).
The concept of library catalog was also introduced in the House of Wisdom and other medieval Islamic libraries, where books were organised into specific genres and categories.
Under caliph al-Mamun (reigned 813-833) the focus shifted from Persian to Greek texts. Al-Khwarizmi lived during this period. Another note on him is found at http://facstaff.uindy.edu/~oaks/MHMC.htm . The author of this article, Jeff Oaks, writes:
"Three major astronomical/geographical undertakings sponsored by al-Ma'mun were
the construction of observatories at Baghdad and Damascus, and the observations made there.
the calculation of the circumference of the earth based on the measurement of one terrestrial degree.
the construction of a world map.
In mathematics proper, algebra was invented to facilitate the calculations for the distribution of estates. The promulgation of Hindu numerals, together with algorithms for basic operations, also had practical consequences. Al-Khwarizmi wrote the earliest known treatises on both subjects."
Among the better known figures after al-Ma'mun's time was al-Farabi (870-950), who lived through the reign of six Abbasid caliphs. As a philosopher and scientist, he acquired proficiency in various branches of learning and is reported to have been an expert in different languages. He contributed considerably to science, philosophy, logic, sociology, medicine, mathematics and music. He came to be known as the 'Second Teacher' (al-Mou'allim al-Thani) Aristotle being the first. One of the important contributions of Farabi was to make the study of logic more easy by dividing it into two categories viz., Takhayyul (idea) and Thubut (proof). His work, aimed at the synthesis of philosophy and Sufism, paved the way for Ibn Sina's work.
Ibn Sina (980-1037), by the age of ten, had memorised the Quran and most of the Arabic poetry which he had read. When he reached the age of thirteen he began to study medicine and by the age of sixteen began to treat patients. He also studied logic and metaphysics. He wrote about 450 works of which around 240 have survived. Of the surviving works, 150 are on philosophy while 40 are devoted to medicine. He also wrote on psychology, geology, mathematics, astronomy, and logic. The mathematical topics he wrote on include geometry and mechanics.
Along with all other libraries in Baghdad, the House of Wisdom was destroyed during the Mongol invasion of Baghdad in 1258. The Islamic legacy, however, continued in Spain until 1492 -- the year Columbus was sent to America; see http://wings.buffalo.edu/sa/muslim/Spain.htm .
A second wikipedia article which may be consulted is http://en.wikipedia.org/wiki/Islamic_mathematics .
The Contribution to Mathematics: Al-Khwarizmi's book included the solution of quadratic equations. He introduced the technique of completing the square. He did not invent algebra. it was already practiced by trade groups and was transmitted before his time. The solution of quadratics already appears in the work of Brahmagupta (598-665) who developed some algebraic notation and presented methods to solve quadratics in his book Brahmasphutasiddhanta.
Although al-Farabi is described as a mathematician, not much is known of his actual contribution to the subject.
Ibn-Sina attempted to give a proof of Euclid's fifth postulate. His work on mechanics involves a classification of mechanisms going beyond that of Heron (~10-75) of Alexandria. He is known to have corresponded with the astronomer al-Biruni, whom he sent several letters to in answers to questions posed on topics such as philosophy, astronomy and physics.
Al-Biruni made important contributions to geodesy and geography. He was a contemporary of Mahmud of Ghazni, and wrote a book India when brought to the country to make astronomical observations.
References
The wikipedia categories: History of Islamic Science | History of Iraq | Islamic Mathematics | Islamic Golden Age
http://www-groups.dcs.st-andrews.ac.uk/~history/Indexes/500_999.html
http://www.trincoll.edu/depts/phil/philo/phils/muslim/index.html
Also of interest
