At the end of the analysis, an overall conclusion is drawn: all three theses—(A the al-ġubār word root, B functional medieval usage, C 19th-century back-projection)—are each plausible, well supported, and coherent (a “green light” for each). Thesis C is especially strongly evidenced: the eponym narrative is a speculative 19th-century back-projection and can be reconstructed as such.
How the theses interact on the timeline
- Starting point (8th/9th c.): al-Ḫwārizmī as an algebra author in Baghdad (Eastern Arabic world). Key point: no Latin algebra translation exists before the emergence of Dixit Algorizmi.
- Up to the 12th century, two Arabic “calculation worlds” coexist:
- Western Arabic: abacus-like sand/dust reckoning (ḥisāb al-ġubār)
- Eastern Arabic: the newer rule-based calculation with Indian numerals (ḥisāb al-hind) Thus al-ġubār could already function in the 11th century as a linguistic “anchor,” e.g., for alguarismo, so that the same mathematical term could carry different contents.
- Early 12th century: Dixit Algorizmi is produced. But: the author is unknown, there is no verifiable original, and there are many linguistic inconsistencies compared to algebra texts. That alone speaks against a straightforward attribution to al-Ḫwārizmī.
- Early 13th century: several works use algorismus explicitly in a functional sense, without an eponym—yet with contradictory valuations: Fibonacci negative, others positive. Key result: tracing algorismus back to sand/dust reckoning (ḥisāb al-ġubār) can explain all these contradictions; an eponymic reading cannot.
- 1509 onward (printing): “algorithmus” spreads in print, still functionally; algorismus/algorithmus then fall out of focus again until the mid-19th century.
- 1857 Boncompagni: a “rediscovery” occurs—his edition circulates a slightly altered form (Dixit Algoritmi) that phonetically fits the modern word “algorithm” better.
- 1865: first explicit eponym reference (the byname al-Ḫwārizmī), heavily supported by phonetic similarity; consolidation follows through further publications.
- 1869 onward (Cantor, Friedlein, Treutlein): the eponym is “manifested” by using the “forgetting thesis” to explain away medieval functional usage.
- 1874 Hankel: adopts the narrative but attributes it to Boncompagni (instead of those who constructed it). Lexica adopt it without evidence; worldwide diffusion follows.
- RAE as an exception: it considers a functional derivation more likely—not via an eponym, but via ḥisāb al-ġubār and Old Spanish alguarismo (“art of counting”).
- Fibonacci as a content stress test: his negative use of algorismus is especially well explained if it denotes an abacus-adjacent hybrid method (dust/lines/counting fields), while he praises “true” Indian place-value calculation.
Result: strong indications against the eponym
The analysis concludes that algorismus is not an eponym, but rather a method term linked to al-ġubār, already in the milieu of the Toledo translation school.
This becomes clear in the following contrast:
- Eponymic (Algorizmi = al-Ḫwārizmī): low historical-linguistic coherence, medium phonetic plausibility, low substantive plausibility, but very high diffusion.
- Functional (al-ġubār + -ismus = “doctrine” / dust board): high coherence, high phonetic and substantive plausibility, but low diffusion (because it is overshadowed by the eponym narrative).
Importantly, the functional derivation also clearly locates the origin in the Arabic world. It confirms the Arabic contribution twice over: as first-rate scholarly mathematics and as operationally used merchant arithmetic.
What “algorism” likely meant in the Middle Ages
On the basis of the overall results, a concrete medieval meaning is proposed:
Algorism in the Middle Ages was an abacus-like hybrid method. It could be carried out (also) with Indian numerals, on lines/sand/boards. It was visual-mechanical but also error-prone. It was a Europeanized implementation of Arabic ḥisāb al-ġubār.
Fibonacci thus plausibly distinguished:
- Negative: algorism = “abacus 2.0” (numerals as replacement counters, place value only formal/unstable—specifically not al-Ḫwārizmī)
- Positive: Indian = genuine place-value reckoning (ḥisāb al-hind) (conceptually stable, in line with al-Ḫwārizmī’s doctrine)
A final table (in the original analysis) then situates the result along dimensions (medium, place-value understanding, rule-governedness, error-proneness) and thus explains Fibonacci’s negative verdict on algorism while he simultaneously evaluates Indian reckoning positively.
“Irony”: the eponym authors themselves supply building blocks for al-ġubār
The final section highlights an irony: the founders of the eponym (Cantor/Treutlein/Friedlein) discuss gubār/gobar numerals and dust reckoning in detail, thereby documenting precisely the elements that support the functional derivation. At the same time, they reject that derivation because it does not fit the early fixed eponym narrative.
A further indication for the functional view is the later hybrid formation Algo-rithmus (1509):
The word symbolizes a possibility that Cantor mocks as an impossible combination of two linguistic worlds in medieval hybridizations—Arabic (Algo = shorthand for al-Ḫwārizmī) and Greek (rithmus = number).
What was claimed to be excluded for the time of Dixit Algorizmi thus appears historically attested later. The same principle is once tolerated as possible and once ridiculed as impossible.
Federico Corriente (1996): the origin of the RAE alternative
At the very end, the analysis identifies the real person behind the RAE wording:
It is the Spanish Arabist Federico Corriente (revision of Arabic loanwords, 1996). In a footnote (not adopted by the RAE), Corriente specifies how the word may have come about.
- al-Ḫwārizmī is not documented as the introducer of Arabic numerals; they would not have been known under his name either.
- The earliest meaning of alguarismo is said to be “the art of counting.” Corriente’s phonetic-semantic bridge therefore runs primarily via alguarismo.
- The only word currently named on the RAE pages, algorbarismo, was always a conjecture—hence the word “quizá” (“perhaps”).
- That “perhaps” therefore does not refer to the derivation from ḥisāb al-ġubār, but only to the intermediary term algorbarismo.
Later (1999), Corriente officially moves closer again to the consensus in the Diccionario de Arabismos, but at the same time points to bibliographic references that keep his alternative traceable. This can be read as a tactical retreat under consensus pressure. Corriente’s alternative nonetheless lives on in the RAE formulation—only without the explanatory footnote, which facilitates misunderstandings.
