Al-Khwarizmi

Muhammad ibn Musa al-Khwarizmi was a mathematician and astronomer associated with the House of Wisdom in Abbasid Baghdad. His treatise on al-jabr and al-muqābala presented algebra as a general method for solving whole classes of equations, abstracted from particular problems; the word 'algebra' comes from its title. A Latin version of his work on Hindu-Arabic numerals spread decimal place-value arithmetic in Europe, and the word 'algorithm' derives from the Latinised form of his name.

Key ideas

• Algebra solves general types of equations by systematic operations rather than case-by-case tricks.
• Restoration (al-jabr) and balancing (al-muqābala) reduce equations to standard forms.
• Decimal place-value notation makes calculation mechanical and teachable.
• Geometric demonstration can justify algebraic procedures.

Major works

• al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (The Compendious Book on Calculation by Restoration and Balancing, c. 820)
• Treatise on Hindu-Arabic numerals (survives in Latin as Algoritmi de numero Indorum)
• Zīj al-Sindhind (astronomical tables)

In the conversation

• Question What exactly was new about al-Khwarizmi’s algebra? Nur Aisyah Rahman · 4 replies

In the Journal

• Journal Not a warehouse: what the Baghdad translators actually did Layla Sfeir · 0 replies