Muhammad ibn Musa al-Khwarizmi

Few details survive about al-Khwarizmi's life (c. 780–850), but his output during the Islamic Golden Age reshaped mathematics. Between 813 and 833, he compiled Al-Jabr, the first systematic treatment of linear and quadratic equations, demonstrating solutions by completing the square with geometric proof. By treating algebra as its own field and formalizing "reduction" and "balancing" — moving terms across the equals sign, canceling like quantities — he earned the title founder of algebra; the English word comes from his book's shorthand title, al-jabr, "completion." His textbook on Indian arit…