Where do our numbers come from?

This lesson asks you to research one number concept, tell the story of how it was developed and used in a specific culture, and say why it still matters. The museum offers one such story, from the Islamic world of Baghdad and Damascus; the stories of other cultures and the current context are for your class to bring. ¹

Read the two stories side by side. Note what each says was inherited, and what the record says its maker did not invent. A research story names its sources.

Read how each story reaches us. Al-Khwarizmi's Arabic book of arithmetic is lost; the oldest witness that survives is a twelfth-century Latin translation in the Cambridge library ². B. Boncompagni published it in Rome in 1857, Kurt Vogel then published a facsimile of the manuscript in 1963, and André Allard a critical edition with a French translation in 1992 ². The book of al-Uqlidisi is a different case: the sources connect it with Damascus in 341/952–953 and distinguish its composition from the surviving copy dated 1157 ^{3 4}. Each story rests on a witness that is not the author's own page, a Latin translation in one case and a later copy in the other. Ask of each how far it stands from the author.

The record on algorism preserves no sentence in which al-Khwarizmi says why he wrote his book of arithmetic; its Arabic original is lost ². For his algebra it reports a stated purpose, the reckoning people require in their inheritances, bequests, trade and the measuring of land ⁵. For al-Uqlidisi, the biography reports that the author's introduction describes travel, reading and learning from arithmeticians he met, and it stresses the practical value the author attributes to Indian arithmetic ³. The record calls his account of his own travel and learning transmitted testimony, not an independently established itinerary ³.

Two dates stand beside al-Uqlidisi's book, 341/952–953 and 1157, and they can look like rival answers to the question "when was it invented?". The record says they date different acts, composition and copying, not competing attempts to identify an invention day ^{3 4}. The same care applies to the claim that matters: the record's narrow claim is an early surviving direct treatment of decimal fractions and operations with a units sign, improving older arithmetic ⁶.

For algorism the record keeps its witnesses apart: the algebraic introduction describes decimal structure, whereas the Latin translation witnesses a different book, the Indian reckoning; a gap in one cannot automatically be filled from the other ². The Encyclopaedia of Islam, as the record of al-Khwarizmi reports it, says the connections among the various mediaeval arithmetic works and al-Khwarizmi's own are not well established ⁷. For al-Uqlidisi the museum read Saidan's study in a print of an Encyclopedia.com page, and some arrays and formulae are actually missing from it; they are not recreated ^{6 4}.

Take a position and answer the strongest objection to it: which witness do you trust more for what its author wrote, a twelfth-century Latin translation of a lost Arabic book, or a surviving copy, dated 1157, of a book composed at Damascus in 341/952–953?

• Algorism: the lost original, the Latin translation and the editions.
• al-Uqlidisi's decimal-fraction methods: the units sign, the manuscript and the limits of what was read.
• al-Khwarizmi: the Encyclopaedia of Islam on the lost arithmetic and its Latin descendants.
• al-Uqlidisi: the book and the surviving copy.
• al-Khwarizmi's Book of Arithmetic: what the Cairo editors say about it.

Read Algorism (reckoning with Indian decimal numerals in al-Khwarizmi's book of arithmetic) and Al-Uqlidisi's decimal-fraction methods. Write a six-sentence story of one number idea, in order, then one last sentence saying why it matters to you today.