Who was al-Khwarizmi and why does algorithm come from his name?
Muhammad ibn Musa al-Khwarizmi was a Persian scholar working in Baghdad in the early ninth century, and two of the most common words in mathematics and computing descend from his name and his work.
Algorithm comes from al-Khwarizmi itself. His treatise on calculating with Hindu-Arabic numerals was translated into Latin as Algoritmi de numero Indorum — "al-Khwarizmi on the Hindu numerals" — and the Latinised form of his name came to mean a step-by-step calculation procedure, then any defined procedure at all.
Algebra comes from the title of his other major work, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala. Al-jabr refers to the operation of moving a subtracted quantity to the other side of an equation — literally "restoring" or "completing".
The algebra book is the more significant contribution. It set out systematic methods for solving linear and quadratic equations, presented as general procedures rather than as solutions to individual problems. That generality is what makes it algebra rather than arithmetic, and it is why he is often called a founder of the discipline. The work was written for practical use, addressing inheritance division, surveying and trade.
His other book was instrumental in spreading the decimal positional number system westward — the system of digits and place value that replaced Roman numerals in Europe, without which most later mathematics would be unworkable.
He worked at the House of Wisdom in Baghdad, a major centre of translation and scholarship, and also produced work on geography and astronomy.
The numerals themselves originated in India, which the Latin title acknowledges.