The reigns of Harun al-Rashid (786 – 809) and his successors fostered an age of great intellectual achievement. In large part, this was the result of the schismatic forces that had undermined the Umayyad regime, which relied on the assertion of the superiority of Arab culture as part of its claim to legitimacy, and the Abbasids' welcoming of support from non-Arab Muslims. It is well established that the Abbasid caliphs modeled their administration on that of the Sassanids. Harun al-Rashid's son, Al-Ma'mun (whose mother was Persian), is even quoted as saying:
“The Persians ruled for a thousand years and did not need us Arabs even for a day. We have been ruling them for one or two centuries and cannot do without them for an hour.”
A number of medieval thinkers and scientists living under Islamic rule played a role in transmitting Islamic science to the Christian West. They contributed to making Aristotle known in Christian Europe. In addition, the period saw the recovery of much of the Alexandrian mathematical, geometric and astronomical knowledge, such as that of Euclid and Claudius Ptolemy. These recovered mathematical methods were later enhanced and developed much further by other Islamic scholars, notably by Persian scientists Al-Biruni and Abu Nasr Mansur.
Algebra was also pioneered by Persian Scientist Muhammad ibn Musa al-Khwarizmi during this time in his landmark text, Kitab al-Jabr wa-l-Muqabala, from which the term algebra is derived. He is thus considered to be the father of algebra. The terms algorism and algorithm are also derived from the name of al-Khwarizmi, who was responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian subcontinent.
Ibn al-Haytham (Alhazen) developed an early scientific method in his Book of Optics (1021). The most important development of the scientific method was the use of experiments to distinguish between competing scientific theories set within a generally empirical orientation, which began among Muslim scientists. Ibn al-Haytham is also regarded as the father of optics, especially for his empirical proof of the intromission theory of light. Bradley Steffens described Ibn al-Haytham as the “first scientist” for his development of scientific method.
Medicine in medieval Islam was an area of science that advanced particularly during the Abbasids' reign. During the ninth century, Baghdad
Astronomy in medieval Islam was advanced by Al-Battani, who improved the precision of the measurement of the precession of the Earth's axis. The corrections made to the geocentric model by al-Battani, Averroes, Nasir al-Din al-Tusi, Mo'ayyeduddin Urdi and Ibn al-Shatir were later incorporated into the Copernican heliocentric model. The astrolabe, though originally developed by the Greeks, was perfected by Islamic astronomers and engineers, and was subsequently brought to Europe .
Muslim chemists and alchemists played an important role in the foundation of modern chemistry. Scholars such as Will Durant and Alexander von Humboldt regard Muslim chemists to be the founders of chemistry. In particular, Jabir ibn Hayyan (Geber) is considered the "father of chemistry". The works of Arab chemists influenced Roger Bacon (who introduced the empirical method to Europe , strongly influenced by his reading of Arabic writers), Isaac Newton, among many others. A number of chemical processes such as distillation techniques and the production of alcohol were developed in the Muslim world and then spread to Europe .
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