Muhammad al-Khwarizmi
Who Named Algebra And The Algorithm · Mathematician & Astronomer · c. 780–850
The Baghdad scholar whose book on restoring and balancing gave algebra its name, its method, and the diagram for completing the square still printed in schoolbooks.
Who was al-Khwarizmi?
Muhammad ibn Musa al-Khwarizmi worked in Baghdad in the first half of the ninth century, at the House of Wisdom under the caliph al-Ma'mun, where Greek, Persian and Indian works were being translated and where he had charge of the library. His algebra — al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala, the Compendious Book on Calculation by Restoring and Balancing, written around 820 — is the first systematic treatment of linear and quadratic equations. He works entirely in words: there are no symbols, no letters standing for numbers and no equals sign, and because he recognises no negative quantities he has to sort every equation into six separate types so that no case is left out. Al-jabr, restoring, is moving a subtracted quantity across; al-muqabala, balancing, is cancelling like quantities from both sides. For each type he gives the procedure AND a geometric justification: he draws the square, adds the rectangles along its sides, and shows exactly what has to be supplied to complete the figure. That is completing the square, and it is the same diagram taught today. In a second book he set out calculation with the Indian numerals, including zero, which is the route by which they reached Europe; the Latin form of his name, Algoritmi, became the word algorithm, and al-jabr became algebra. He also produced astronomical tables and a revision of Ptolemy's geography with corrected coordinates for hundreds of places.
Major achievements
- Wrote the first systematic solution of linear and quadratic equations, around 820
- Gave the geometric proof of completing the square that is still taught
- Classified quadratics into six types so that no case could be omitted
- Transmitted the Indian numerals and zero to the Islamic world and thence to Europe
- Produced astronomical tables and a corrected geography of the known world
Life in brief
- c. 780 — Born: In or near Khwarazm, south of the Aral Sea.
- c. 820 — The House of Wisdom: Working in Baghdad under al-Ma'mun, with charge of the library.
- c. 820 — Al-jabr wa'l-muqabala: The six types of equation, the two operations, and the completed square.
- c. 825 — The Indian numerals: A treatise on calculation with them, including zero.
- c. 830 — Geography: Ptolemy's world revised, with corrected coordinates for hundreds of places.
- c. 850 — Died: In Baghdad, with his methods already spreading westwards.
Explore the life of al-Khwarizmi — five chapters
- The House of Wisdom — Baghdad, translation, and a library to run
- Restoring and Balancing — Two operations, and the words that became algebra
- The Square With Rectangles Along Its Sides — A diagram still drawn twelve hundred years later
- Bringing the Zero West — A second book, and the route by which digits reached Europe
- Tables, Coordinates and the Shape of the Earth — The other half of the working life
Read the five-chapter life of Muhammad al-Khwarizmi →
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