Short answers, pulled from the story.
The year 786 marks the beginning of a period that historians call the Islamic Golden Age, starting with the reign of Caliph Harun al-Rashid. This era traditionally ends in 1258 when Mongol forces besieged Baghdad and destroyed the House of Wisdom.
The House of Wisdom library was established by Caliph al-Mansur in 825 and modeled after the academy of Jundishapur. Hunayn ibn Ishaq led this massive translation effort with salaries estimated to be equivalent to professional athletes today.
Ibn al-Haytham pioneered experimental science and argued that vision occurred when light traveling in straight lines reflects off an object into the eyes. He is described as the world's first true scientist for his work on optics and experimental methods.
Persian mathematician Muammad ibn Musa al-Khwazimi developed algebra and Hindu-Arabic numerals and has been described as the father or founder of algebra. Omar Khayyam identified foundations of analytic geometry and found general geometric solutions to cubic equations.
The earliest known Islamic hospital was built in 805 in Baghdad by order of Harun Al-Rashid. A major facility established in 982 by Buyid ruler Adud al-Dawla became one of the most important hospitals.