Mathematics
Muslim mathematicians excelled in geometry, as can be seen in their graphic arts, and it was the great Al-Biruni (who excelled also in the fields of natural history, even geology and mineralogy) who established trigonometry as a distinct branch of mathematics. Other Muslim mathematicians made significant progress in number theory.
It is interesting to note that Islam so strongly urges mankind to study and explore the universe. For example, the Holy Qur'an states:
"We (Allah) will show you (mankind) Our signs/patterns in the horizons/universe and in yourselves until you are convinced that the revelation is the truth." [Qur'an, 41:53]This invitation to explore and search made Muslims interested in astronomy, mathematics, chemistry, and the other sciences, and they had a very clear and firm understanding of the correspondences among geometry, mathematics, and astronomy.
The Muslims invented the symbol for zero (The word "cipher" comes from Arabic sifr), and they organized the numbers into the decimal system - base 10. Additionally, they invented the symbol to express an unknown quantity, i.e. variables like x.
The first great Muslim mathematician, Al-Khawarizmi, invented the subject of algebra (al-Jabr), which was further developed by others, most notably Umar Khayyam. Al-Khawarizmi's work, in Latin translation, brought the Arabic numerals along with the mathematics to Europe, through Spain. The word "algorithm" is derived fr
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