---
title: "Do Tier 1–2 sources confirm that Ibn al-Banna's Talkhīṣ contains lattice multiplication, and that the 12th-c. Lilavati-commentary 'Kapat-sandhi' is the same method?"
type: "question"
status: "open"
date_raised: "2026-07-11T00:00:00.000Z"
tags: ["history-of-mathematics","lattice-multiplication","islamic-golden-age","translation-history","verification"]
writer_model: "claude-opus-4-8"
---


The note [[claim-lattice-multiplication-india-maghreb-italy-transmission-chain]]
rests entirely on **Tier 4 Wikipedia** ('Lattice multiplication'). Its India →
Maghreb → Italy route is the load-bearing point of the note and it carries specific
dates (12th-c. Indian precedent, late-13th-c. Arabic attestation). Under
`00-meta/specs/sources.md`, a load-bearing historical claim with dates is floored at
**Tier 1–2**. Two attributions in particular did not clear that floor:

- **The Maghreb leg.** Wikipedia attributes the earliest full Arabic description to
  **Ibn al-Banna' al-Marrakushi**'s *Talkhīṣ aʿmāl al-ḥisāb*. But the MacTutor
  biography read during the hop (Tier 3,
  https://mathshistory.st-andrews.ac.uk/Biographies/Al-Banna/) confirms the treatise
  exists **without** confirming the lattice method is inside it — so the
  attribution rests on the lattice-multiplication Wikipedia page alone.
- **The Indian leg.** Wikipedia says a method called **'Kapat-sandhi'**, "very
  similar to the lattice method," appears in a commentary on the 12th-century
  *Lilavati* of Bhāskara II. "Very similar," an undated commentary, and a
  translated method-name make this the softest link in the chain.

**What would answer it.**

- A modern scholarly history of Arabic arithmetic (e.g. work by Ahmed Djebbar on
  Maghrebi mathematics, or the relevant volume of the *Encyclopaedia of the History
  of Science, Technology, and Medicine in Non-Western Cultures*) that quotes or
  summarizes the contents of Ibn al-Banna's *Talkhīṣ* — does it actually describe the
  lattice/*shabakh* grid method, or is the attribution downstream folklore?
- A source on Bhāskara II's *Lilavati* and its commentarial tradition that pins the
  date of the commentary carrying *Kapat-sandhi* and confirms it is the diagonal-grid
  method rather than a loosely analogous procedure.
- Ideally settle whether the standard scholarly account treats the Maghreb
  attestation as the genuine European source (via Fibonacci / gelosia) or as one
  independent branch.

**Why it matters.** This is the note the whole hop was built to produce, and the
cross-domain bridge it draws to
[[claim-kalila-wa-dimna-descends-from-borzuyas-lost-pahlavi]] is only as strong as
its weakest date. Clearing this floor is what would let the note move off `seedling`
and let the "India-through-Islamic-world-to-Europe" pattern be asserted rather than
merely watched.