Short answers, pulled from the story.
Science in the medieval Islamic world refers to the scientific knowledge developed and practiced during the Islamic Golden Age, roughly between 786 and 1258, under dynasties including the Abbasid Caliphate of Baghdad, the Umayyads of Córdoba and rulers across Persia. It encompassed astronomy, mathematics, medicine, optics, chemistry, geography, botany and physics.
Key figures include Al-Khwarizmi, who founded algebra as an independent discipline; Ibn al-Haytham (Alhazen), who transformed the study of optics; Al-Razi, who identified smallpox and measles; Avicenna (Ibn Sina), who wrote The Canon of Medicine; Al-Biruni, who measured the Earth's radius; and Jamshid al-Kashi, who calculated pi to seventeen significant figures.
Islamic mathematicians developed algebra as an independent field, contributed to trigonometry, and were instrumental in adopting and transmitting the Hindu-Arabic numeral system that is used worldwide today. Al-Khwarizmi presented the first systematic solution of linear and quadratic equations, Omar Khayyam solved all thirteen forms of cubic equations geometrically, and Jamshid al-Kashi is credited with the law of cosines and calculated pi correctly to seventeen significant figures.
Copernicus used astronomical tables compiled by Al-Battani when developing his own work. The concept of inertia, which Ibn Sina articulated in his Book of Healing, was later described as "impetus" by Jean Buridan around 1295-1363. Works by pharmacologists such as Masawaih al-Mardini and Ibn al-Wafid were printed in Latin more than fifty times. Ibn al-Haytham's Book of Optics remained influential in the West for centuries.
Ibn al-Haytham (Alhazen), born in 965, rejected Greek theories of vision and proposed in his Book of Optics that vision occurs because light rays form a cone with its vertex at the centre of the eye. He argued that light reflects from surfaces in different directions, causing objects to appear as they do, and was an early advocate of the scientific method, insisting hypotheses must be proved by experiment or mathematical evidence.
Islamic science survived the initial Christian reconquest of Spain, including the fall of Seville in 1248. After the completion of the Spanish reconquest in 1492, the Islamic world entered an economic and cultural decline. Work in the arts and sciences continued under the subsequent Ottoman Empire (c. 1299-1922) and Safavid Empire (1501-1736).