Further questions to the historiography of Arabic (but not only Arabic) mathematics from the perspective of Romance abbacus mathematics: Contribution to the "9^ième Colloque Maghrébin sur l'Histoire des Mathématiques Arabes", Tipaza, 12-13-14 mai 2007

Since some years I have been engaged in a close reading of early Italian abbacus books and related material from the Ibero-Provençal orbit and in comparison of this material with Arabic mathematical writings. At the 7th North African Meeting on the History of Arab Mathematics in Marrakesh in 2002 I presented the first outcome of this investigation: namely that early Italian abbacus algebra was not influenced by the Latin algebraic writings of the 12th-13th centuries (neither by the translations of al-Khwa¯rizmı¯ nor by the works of Fibonacci); instead, it received indirect inspiration from a so far unknown link to the Arabic world, viz to a level of Arabic algebra (probably integrated with mu a¯mala¯t mathematics) of which very little is known. At the 8th Meeting in Tunis in 2004 mathematics) of which very little is known.

At the 8th Meeting in Tunis in 2004 I presented a list of linguistic clues which, if applied to Arabic material, might enable us to say more about the links between the Romance abbacus tradition and Arabic mu a¯mala¯t  teaching.

Here I investigate a number of problem types and techniques which turn up in some but not necessarily in all of the following source types:

- Romance abbacus writings,

- Byzantine writings of abbacus type,

- Arabic mathematical writings of various kinds,

- Sanskrit mathematical writings,

in order to display the intricacies of the links between these - intricacies which force us to become aware of the shortcomings of our current knowledge, and hence formulate questions that go beyond the answers I shall be able to present.