The story of algebra

This lesson asks you to research an algebraic concept, tell the story of its development and use in a specific culture, and describe its relevance today. The museum offers the story of algebra in al-Khwarizmi's book as the Cairo editors tell it; other cultures and today's uses are for your class to bring. ¹

Gather from the page what the editors say about algebra before al-Khwarizmi, then what they say about him. Place both on a timeline and ask where the word al-jabr falls on it.

The Cairo editors of al-Khwarizmi's book, Ali Mustafa Mosharafa and Muhammad Mursi Ahmad, open with a survey of algebra before him ². They name the Ahmes (Rhind) papyrus of about 1700 BCE, with a first-degree equation in one unknown and a special sign for the unknown ³; Babylonian tables of squares and cubes ⁴; Greek geometric solutions of second-degree equations, and a first analytic solution that can be affirmed with Heron of Alexandria ⁴; Diophantus, who did not study the types systematically as al-Khwarizmi did ⁵; and Indian rules from Aryabhata to Brahmagupta and Mahavira ^{6 7}. Their conclusion is that all these developments led towards algebra in its proper sense, each country being influenced by its neighbours ^{7 8}.

Al-Khwarizmi gives his reason in the preface of his book. It opens with praise of God and a blessing on the Prophet ﷺ, then reflects on those who write learning for later generations: one who reaches what no one had drawn out before him, one who explains what the ancients left obscure, or one who finds a flaw in a book, repairs it and thinks well of its author ⁹. He says that the caliph al-Ma'mun's love of learning and closeness to scholars encouraged him ⁹, and that he wrote for what people need in their dealings, such as inheritances and trade ¹⁰.

Who was first? The Cairo editors report that Ibn Khaldun names al-Khwarizmi the first to write on algebra, with Abu Kamil after him, and that al-Qazwini says he was the first to translate algebra for the Muslims ¹¹. The TDV encyclopaedia reports that historians generally agree that algebra became an independent science with him ¹². It also sets out why some modern historians doubt that his book was the first: it calls itself a summary, al-Khwarizmi does not claim to be first, its terms are already mature, and there was a book by Ibn Turk and a lost book by Sanad ibn Ali on the subject ¹². The museum's record of algebra gives both views.

The Cairo edition is based on a manuscript in the Bodleian Library, Oxford, written in Cairo and finished on 19 Muharram 743 AH, about five hundred years after the author's death; to the editors' knowledge it is the only surviving copy ^{13 14}. They say the Latin translation by Robert of Chester differs from the Arabic in many places ¹³. The margins carry glosses that the editors take to be explanations added when the book was taught ¹⁵, and they corrected obvious copying errors without notice ¹⁶. Ask how much a single late copy can tell us about the earlier history the editors survey.

The Cairo editors call al-Khwarizmi the founder of algebra, yet the TDV encyclopaedia records why some historians doubt that his was the first book. Take a position and answer the strongest objection to it: is “founder of algebra” the right title for him?

• Algebra (al-jabr): the editors' survey of algebra before and after al-Khwarizmi.
• Algebra, the invention: who invented it, and the views of Ibn Khaldun and TDV.
• The Book of al-Jabr and al-Muqabala: the preface, the chapters, the single surviving copy and the editions.
• al-Khwarizmi: what is known of his life, and what is not.

Read Algebra (al-jabr). Draw a timeline of five stops in algebra before and after al-Khwarizmi as the record names them, and write your research question beneath it.