Al-Khwarizmi is best known for his contribution to the field of mathematics, particularly for his work that became the basis for algebra. His influential book "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala," which translates to "The Compendious Book on Calculation by Completion and Balancing," is considered one of the foundational texts in algebra. It introduced systematic solution techniques for linear and quadratic equations and provided a clear mathematical language that would influence mathematics for centuries.
Therefore, the correct response is: His work became the basis for algebra.