Numbers and paper: contributions that travelled

Each record separates what one community brought from what another took up. As you read, name separately the origin, the people who carried it and the place where it was taken up.

In the preface of his algebra, al-Khwarizmi describes the decimal build of numbers himself. He found, he says, that everything people need of reckoning is number, and that all numbers are composed of one. The spoken numbers from one to ten follow the pattern of one; then ten is doubled and tripled as one was, giving twenty and thirty up to a hundred; then a hundred is doubled and tripled up to a thousand; and so the thousand is repeated at every order, to the furthest number that can be grasped ². The TDV encyclopaedia describes this passage as a short account of how number is expressed in a positional system with base ten ³.

The Arabic original of al-Khwarizmi's book on Indian reckoning is lost ³, so the museum holds no preface of that book. His algebra has one. In it he says he wrote with the encouragement of the caliph al-Ma'mun, whose love of learning and closeness to scholars he praises ⁴, and that he made it "comprehensive of the fine and the weighty in reckoning" for what people need in their inheritances, bequests, partitions, judgements and trade, in measuring land, digging canals, geometry and the like ⁵. The book opens with a sermon praising God and blessing the Prophet ﷺ ⁴.

The museum's record of papermaking in Baghdad gives two accounts. Osman Ersoy, in the TDV encyclopaedia, attributes the proposal for a paper workshop in Baghdad to al-Fadl ibn Yahya al-Barmaki in 178 AH/794–795, under Harun al-Rashid ⁶. Jonathan Bloom, in Iranica, supports manufacture in Baghdad by the late eighth century without independently confirming that year or proposer ⁷. The record notes that no contemporary foundation document or workshop accounts were read for it ⁶. The museum gives no verdict between the two.

Al-Khwarizmi says he wrote for the reckoning people require in their inheritances, bequests, trade and the measuring of land ². The record also says the numerals and the decimal system are Indian, and that Indian reckoning was in Baghdad before him ³. For a person who needs to reckon in trade or in dividing an inheritance, does it matter more who first invented the numerals or that a clear book taught how to use them, and why?

• Algorism: how each place takes its value from its position, and why the record calls al-Khwarizmi's work transmission and not invention.
• The Algebra of al-Khwarizmi: how the book opens and which chapters it holds.
• Establishing papermaking in Baghdad: what the record knows about a craft that came from outside Baghdad, and what it does not know.
• Al-Fadl ibn Yahya al-Barmaki: the proposer named in the story of the Baghdad paper workshop.