Al-Khwarizmi made significant contributions to the world of mathematics, most notably by laying the foundations for algebra. His work in the 9th century, particularly his book "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala" (The Compendious Book on Calculation by Completion and Balancing), introduced systematic methods for solving linear and quadratic equations, which fundamentally shaped the field of algebra. Therefore, the correct response is:
His work became the basis for algebra.