Thesis C examines when the now-dominant al-Ḫwārizmī narrative emerged. What is established is that it was first formulated in the 19th century as a mere conjecture. From the very beginning, its content was back-projected. This aligns with the results of Theses A and B (a functional understanding in the Middle Ages). It is certain that Joseph Reinaud was the first to mention the “true origin” in 1849. The conjecture was described as “proven,” however, only later by Moritz Cantor and colleagues.
Within Thesis C, the analysis reaches the following conclusions:
- Before 1849, there was no al-Ḫwārizmī eponym—not even the conjecture.
- The “rediscovery” of his person thus occurs 800 years after the Dixit Algorizmi.
- It was a period of few sources and poor dating methods for medieval manuscripts.
This last point helps explain how Reinaud’s conjecture could ultimately turn into the “proof” still claimed today. In the 19th century, many robust primary sources were missing that would have allowed a more realistic reconstruction. The result is therefore, in part, a product of missing information, filled in by speculation. On this basis, the eponym thesis first appears in 1849 and is presented about 15 years later by German authors as “proven.”
Boncompagni (1857) as catalyst, not “discoverer”
A contributing factor is Baldessare Boncompagni. In 1857 he republishes the Dixit Algorizmi and gives it the editorial title Algoritmi de numero indorum. His editorial practice (including Dixit Algoritmi with a “t”) increases the phonetic proximity to the modern spelling of algorithm. Boncompagni’s editions provide, for the first time, citable printed references and make the term algorithm popular again. He himself, however, does not establish an eponym. Still, the eponymic reading attaches closely in time to his publications, because they trigger a kind of “hype”: a sort of “discoverer competition” in the history of mathematics.
The “scholarly odyssey”: 1849 – 1871 produces the back-projection
19th-century context: manuscript hunting and “proof” rhetoric
The history of mathematics becomes institutionalized for the first time (journals, professorships). Because the source base for antiquity/the Middle Ages is thin, small clues are quickly inflated into “proofs.” Conversely, contradictions are more often “harmonized” than confronted. This fosters a climate in which a plausible narrative matters more than hard primary evidence.
The chain of key authors
The eponym is not started by Boncompagni, but by a Franco-German publication chain: first Reinaud (1849), then Wöpcke (1851), and then Cantor & Steinschneider (1865), Friedlein (1869), and Treutlein (1871). The culmination is Cantor’s lectures (1880/1894). These works form a “gravitational core” around which later texts orbit.
Core problem: who is “al-Ḫwārizmī” at all—and could medieval authors have meant him in the 12th century?
The analysis exposes a structural problem: al-Ḫwārizmī is a nisba, a geographical byname (“from Khwarazm/Chorasmia”). Several scholars bore it. For a medieval eponym, however, in the 12th century a specific individual would have had to be unambiguously known in al-Andalus/Europe under that byname.
Chronology tightens the problem further:
- On this account, Dixit Algorizmi predates the Latin translation of the algebra.
That means it is not even secure that the copyists knew the algebra author—let alone that they identified him primarily via the nisba.
Reinaud’s text even illustrates the competitive landscape with al-Bīrūnī, also linked to Khwarazm and in the 19th century sometimes more prominent in Europe than Ben Mūsā, and with Omar al-Khayyām, whose algebra title also fits and who could, in theory, have served as a closer temporal reference. The takeaway is: the mere possibility of multiple candidates makes any “proof” claims methodologically suspect.
Key stations of the back-projection
Ben Mūsā enters the picture late
Rosen first translates the algebra in 1831, but from an Arabic manuscript (1342), and he establishes in Europe primarily the name “Mohammed Ben Mūsā,” treating the byname “of Khowarezm” more as an aside. Consequence: until the mid-19th century, Europe lacks a stable naming practice that would phonetically link algorism to Ben Mūsā.
Reinaud (1849): a speculative starting point—and not even primarily about Ben Mūsā
Reinaud finds the word “Alchoarizam” in a 16th-century text (possibly even as a single handwritten marginal addition) and speculates: algorism might be named after the scholar who spread the numeral system. His first personal assignment points more toward al-Bīrūnī; only secondarily does he think of Ben Mūsā—and he stumbles over dating contradictions (940 fits neither). Importantly, Reinaud is also aware of the lexicographic situation (Old Spanish alguarismo), but he largely ignores it in practice in favor of the eponym approach.
Cantor (1865): “proof” from a nominative—despite an obvious counter-reading
Cantor discusses the “Salem Codex” (then misdated to the 12th century; today more likely around 1300). He declares the nominative algorizmus to be “proof” that a personal name must underlie it—and simultaneously asserts “forgetting.” But the text also contains the accusative algorizmum in an allegorical passage (seven kinds/gifts of the Holy Spirit), which supports a functional or allegorical reading. Cantor focuses on the nominative and suppresses the explosive implications of the full passage: the alleged “proof” reads like proof-by-suggestion.
Steinschneider (1865): the “empty eponym” gets filled with Ben Mūsā
In the same journal volume, Steinschneider sets up the equation: Algorizmi = Chowarezmi = Mohammed Ben Mūsā. He himself notes multiple candidates and risks of confusion (including Banū Mūsā), but he opts for Ben Mūsā without hard justification. The division of labor is clear: Cantor supplies the “proof that it’s an eponym,” Steinschneider supplies “which person.”
Friedlein (1869) & Treutlein (1871): expansion via a “forgetting thesis” and creative morphology
Friedlein increasingly turns Ben Mūsā into the iconic “Alkhärizmi” and tries to construct a name morphology via later texts (Algus/Algo). He selectively emphasizes, inserts sources in parentheses, and explains medieval functional interpretations as the result of “forgetting.” Treutlein adopts and intensifies this: early on, people allegedly spoke of algorism functionally because the eponym had been forgotten very early—so that almost all medieval sources would fall “after the forgetting.” Result: the thesis is immunized against counter-evidence (because every counter-example becomes a symptom of forgetting).
Fihrist / Karpinski / Dodge: later “pseudo-evidence” via editorial headings
Later literature suggests evidence in the Fihrist (10th c.) to show that Ben Mūsā was primarily “al-Ḫwārizmī.” The argument here is the opposite: translations apparently inserted headings/keyword labels that are not present in the original in that form, producing “facts by appearance.” This strengthens the narrative retroactively without truly improving the medieval primary record.
Overall conclusion of Thesis C
- The al-Ḫwārizmī eponym is reconstructible as a 19th-century creation in terms of source history (start 1849; canonization from 1865 onward).
- The “proof chain” rests heavily on clues, misdatings, selective readings, and the forgetting thesis as a universal explanation.
- Medieval sources (Theses A/B) primarily show a functional understanding (calculating art/dust reckoning) that clashes with a stable eponym.
- From the late 19th century onward, dictionaries/encyclopedias produce citogenesis: repetition replaces justification; later, digital lexica and AI amplify the echo.
Hence the partial result: the eponymic narrative is plausibly best assessed as a back-projection—without robust medieval primary evidence that would sustain an unambiguous binding to a specific person.
