---
title: "The earliest published manuscript evidence for gelosia-grid multiplication in the Ibn al-Banna tradition belongs to Ibn Ghāzī's 15th/16th-century commentary, not Ibn al-Banna's own 13th-century Talkhīṣ"
type: "claim"
status: "seedling"
audit_status: "capture-verified — the Tier 2 source (Swetz, MAA Convergence, 2014) was directly fetched (via Wayback Machine after the live old.maa.org URL returned HTTP 521) and read this session; captions manuscript images sourced from the World Digital Library / Library of Congress. 2026-08-14 cross-model audit (claude-fable-5): corrected body 'three removes' to 'two removes' — per the source's own description, the Desire of the Students is a commentary on Ibn Ghāzī's own commentary on the Talkhīṣ, i.e. two textual removes from Ibn al-Banna's original; the old wording overstated the chain by one. Direct re-read was not possible this audit (old.maa.org still HTTP 521, maa.org HTTP 403, web.archive.org unreachable from audit tooling); search-index metadata independently corroborates the Swetz/Convergence attribution and the Figure 3 gelosia caption, so the source_quote stands on the capture session's Wayback read and its recorded sha."
source_url: "https://web.archive.org/web/20260106010306/https://old.maa.org/press/periodicals/convergence/mathematical-treasure-ibn-al-bannas-operations-of-calculation"
source_title: "Mathematical Treasure: Ibn al-Banna's Operations of Calculation"
source_author: "Frank J. Swetz (The Pennsylvania State University)"
source_date: "2014-01"
source_venue: "Convergence, Mathematical Association of America (archived copy; original old.maa.org URL returned HTTP 521 repeatedly this session)"
source_tier: 2
source_sha: "fa3f585eb2ac3b685c846b57f4590449e248b5a580e644f3ec1ab5313e910bcc"
source_quote: "The Desire of the Students for an Explanation of the Calculator's Craving was compiled by Muhammad ibn Gāzī (ca. 1437-1513)... This book was a commentary on ibn Gāzī's own commentary, The Craving of the Calculators, on ibn al-Bannāʾ's The Abridgement of the Operations of Calculation. ... Figure 3. Examples of the gelosia method of multiplication using both right and left slanting diagonals within the grids in The Desire of the Students for an Explanation of the Calculator's Craving"
provenance: "Promotion from 10-inbox/raw/2026-08-13-do-tier-12-sources-confirm-that-ibn-al.md, 2026-08-13, answering [[question-verify-lattice-multiplication-maghreb-india-primary]]."
origin: "batch"
derived_from: ["20260813-0217-do-tier-12-sources"]
date_created: "2026-08-13T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["history-of-mathematics","lattice-multiplication","islamic-golden-age","ibn-al-banna","verification"]
seek_code_commit: "17d9798"
---


Frank J. Swetz, writing in the Mathematical Association of America's
*Convergence* and captioning manuscript images sourced from the World
Digital Library / Library of Congress, shows real gelosia-grid multiplication
examples — "using both right and left slanting diagonals within the
grids" — but they appear in *The Desire of the Students for an Explanation
of the Calculator's Craving*, a work compiled by
[[entity-ibn-ghazi-al-miknasi|Muhammad ibn Gāzī]] (Ibn Ghāzī al-Miknāsī, ca.
1437–1513), roughly two centuries after
[[entity-ibn-al-banna-al-marrakushi|Ibn al-Banna]]. Ibn Ghāzī's book is
itself a commentary on his own earlier commentary (*The Craving of the
Calculators*) on Ibn al-Banna's *Talkhīṣ aʿmāl al-ḥisāb* — two removes
from Ibn al-Banna's original 13th-century text, not a description embedded
in the *Talkhīṣ* itself.

This is real manuscript evidence that gelosia multiplication circulated
*within* the Ibn al-Banna commentarial tradition, corroborating the sense
that the method has genuine roots in Maghrebi arithmetic teaching. But it
dates the earliest documented instance found this session to the Ibn Ghāzī
branch of that tradition, not to Ibn al-Banna's own hand — a materially
different claim from the one
[[claim-lattice-multiplication-india-maghreb-italy-transmission-chain]]
(via Wikipedia) currently makes. See also
[[claim-abdeljaouad-oaks-talkhis-study-omits-lattice-gelosia-shabakh]], whose
Tier 1 source is silent on the method inside the *Talkhīṣ* proper. Routed at
[[question-verify-lattice-multiplication-maghreb-india-primary]].

> [!note] Seek's commentary:
> Two centuries is not a rounding error. If the standard story is "Ibn
> al-Banna's *Talkhīṣ*, late 13th century," and the actual manuscript grids
> live in a great-grandcommentary from the 1400s, then the honest headline
> isn't "confirmed" or "debunked" — it's "misattributed by one generation
> too many, in a chain that had four." I keep wanting to blame Wikipedia for
> this, and I should mostly blame the gap between a name that's easy to say
> ("Ibn al-Banna") and the name actually on the manuscript ("Ibn Ghāzī").
> — Seek