Arabic achievements in the History of Mathematics
We know very little of Arabic mathematics, and take it for granted that most of mathematics that we use today has been developed by the western civilisations. It is however due to the hard work and love of mathematics that Arabic scholars have shown during the Middle Ages that we have preserved works of Greek mathematicians. We also use numerals which they brought to the Middle East from India, including the sign for zero.
The beginning of great activity in mathematical arts begun in or around 786AD under the Caliph Harun al-Rashid, who was the fifth Caliph of the Abbasid dynasty. Al-Rasid encouraged and sponsored translation of all Greek texts that could be found into Arabic. Among them were the Elements of Euclid.
This trend continued after al-Rashid died. The next Caliph, al-Ma’mun (son of al-Rashid) continued in his father’s footsteps and went even further. He established the famous House of Wisdom in Baghdad, which was re-established in our time (only to be almost totally destroyed through the recent wars there).
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The House of Wisdom became an institution famous for its learning and scholarship on mathematics, astronomy and geography. It was here that the Elements of Euclid were translated as well as the works of Archimedes, Apollonius, Diophantus, Menelaus and Ptolemy.
Probably one of the most important achievements of Arabic mathematics is the work of al-Kwarizmi and his work on what we today call algebra. Following his work there ensued a flurry of mathematical research on algebra, and a number of Arabic scholars invented very many important concepts that were later incorporated, or sometimes rediscovered by European mathematicians from the 16th century onward.
Some other important achievements were findings by Thabit ibn Qurra who around 850 made a number of important discoveries in number theory and wrote Book on the determination of amicable numbers which contained general methods to construct them. Ibn Qurra knew the pair of amicable numbers 17296 and 18416.
Later on, in or around 990 al-Karaji gave a version of, what we now call Pascal's triangle, in his book on algebra Al-Fakhri .
From 12th century Arabic mathematical opus started to reach the western culture. 1142 sees the translation of Euclid's Elements from Arabic into Latin by Adelard of Bath. Two years later Gherard of Cremona began translating other Arabic works (and Arabic translations of Greek works) into Latin. He introduced Arabic numerals in his translation of Ptolemy's Almagest. The name of 'sine' also comes from this translation.