Short answers, pulled from the story.
Scholars place the life of Muhammad ibn Musa al-Khwarizmi between the years 780 and 850, and he was born in the region of Khwarazm which now straddles the modern borders of Turkmenistan and Uzbekistan. Some historical accounts suggest he may have been born just outside Baghdad under the epithet al-Qutrubbulli, though his name literally translates to from Khwarazm.
In the year 820, Muhammad ibn Musa al-Khwarizmi wrote a treatise titled Al-Jabr, or The Compendious Book on Calculation by Completion and Balancing. This work introduced the concept of algebra as an independent discipline dedicated to the solution of linear and quadratic equations using plain rhetorical prose.
The Latinized form of Muhammad ibn Musa al-Khwarizmi's name, Algorismus, became the root for the modern word algorithm when his text On the Calculation with Hindu Numerals was translated into Latin in the 12th century. This translation signified a step-by-step procedure for solving a problem and replaced the cumbersome Roman numerals and abacus-based methods that had dominated European commerce and science for centuries.
In the year 833, Muhammad ibn Musa al-Khwarizmi completed a monumental revision of Ptolemy's second-century Geography titled The Book of the Description of the Earth. He corrected the length of the Mediterranean Sea to nearly 50 degrees of longitude and redefined the Prime Meridian at the Fortunate Isles approximately 10 degrees east of the line used by Marinus and Ptolemy.
Muhammad ibn Musa al-Khwarizmi created astronomical tables known as the Zīj as-Sindhind which consisted of approximately 37 chapters and 116 tables containing data on the movements of the Sun, Moon, and the five planets known at the time. A Latin translation by the Spanish astronomer Maslama al-Majriti, likely translated by Adelard of Bath in 1126, survived in several manuscripts held in libraries across Europe.