Short answers, pulled from the story.
The Islamic Golden Age lasted roughly between 786 and 1258. This period saw stable political structures that allowed trade and culture to flourish across a vast region stretching from Portugal to Central Asia.
Al-Khwarizmi lived during the eighth and ninth centuries and was instrumental in developing algebra as an independent discipline. He presented the first systematic solution of linear and quadratic equations using methods for simplifying equations based on Euclidean geometry.
Al-Razi lived between 865 and 925 and identified smallpox and measles while recognizing fever as part of the body's defenses. He wrote a twenty-three-volume compendium of Chinese, Indian, Persian, Syriac, and Greek medicine.
Ibn al-Haytham lived from 965 to 1040 and proposed in his Book of Optics that vision occurs by way of light rays forming a cone with its vertex at the center of the eye. He argued further that mathematics of reflection and refraction needed to be consistent with the anatomy of the eye and was an early proponent of the scientific method requiring hypotheses proved by experiments.
The Ottoman admiral Piri Reis lived from 1470 to 1553 and made a map of the New World and West Africa in 1513. He used maps from Greece, Portugal, Muslim sources, and perhaps one made by Christopher Columbus.