Muhammad ibn Musa al-Khwarizmi

Working in the House of Wisdom in Baghdad, al-Khwarizmi wrote the first systematic treatment of solving linear and quadratic equations by the operations of restoring and balancing — al-jabr. He also wrote the book that carried Hindu decimal numerals westward, and the Latin corruption of his name, algorismi, became 'algorithm'.

• Wrote The Compendious Book on Calculation by Completion and Balancing (c. 820), the founding text of algebra
• Introduced the Hindu-Arabic positional decimal system, including zero, to the Arabic-reading world
• Compiled the Zij al-Sindhind astronomical tables and revised Ptolemy's geography with corrected coordinates
• Described general procedures — step-by-step, input-to-output — that are the conceptual definition of an algorithm

Every equation solved in a school, every spreadsheet formula, every cryptographic key exchange and every line of executed code descends from his two contributions: symbolic equation-solving and procedural computation. The word 'algorithm' — the organising concept of the digital economy, from search ranking to machine learning — is literally his name. Decimal notation made double-entry bookkeeping and modern finance possible.

No reliable record of al-Khwarizmi's family or children survives; even his birthplace in Khwarazm is inferred from his name. Medieval Baghdad recorded scholars by their work, not their lineage.