Final answer:
Al-Khwarizmi developed the concept of algebra through his work on quadratic equations and his influential book, which established algebra as a distinct mathematical field.
Step-by-step explanation:
Muhammad ibn Musa al-Khwarizmi developed the concept of algebra through his seminal work on the subject which included dealing with quadratic equations. His most famous book on the topic is 'The Compendious Book on Calculation by Completion and Balancing', written around 820 AD, which laid the groundwork for algebra as a discipline. This treatise provided an evolutionary synthesis of knowledge that drew from prior mathematical work, including Greek and Indian sources, but it was al-Khwarizmi's original contributions that essentialized algebraic thinking. His work allowed for the systemic solving of linear and quadratic equations by methods that he termed 'completion' and 'balancing', effectively founding algebra as a unified mathematical discipline separate from geometry or arithmetic. While al-Khwarizmi's work was informed by other cultures, including Indian mathematics which provided the decimal system and the concept of zero, it was his creation of algebra that was his most notable contribution.