Which mathematician-astronomer ran the House of Wisdom and named algebra?

Muhammad ibn Musa al-Khwarizmi, or simply al-Khwarizmi was a mathematician active during the Islamic Golden Age, who produced Arabic-language works in mathematics, astronomy, and geography. Around 820, he worked at the House of Wisdom in Baghdad, the contemporary capital city of the Abbasid Caliphate. One of the most prominent scholars of the period, his works were widely influential on later authors, both in the Islamic world and Europe.