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scholarly referencemactutor-a-words
Earliest Known Uses of Some of the Words of Mathematics: A
- AUTHOR / EDITOR
- John Aldrich et al.
- YEAR
- 2026
- PUBLISHER
- University of St Andrews
- DOI
- Not recorded
- SOURCE TYPE
- scholarly reference
- EXTERNAL RECORD
- OPEN ORIGINAL ↗
012
CONTRARIAN TRUTH CLAIMS
RANKED REVEALS THAT CITE THIS SOURCE
RANK 14GRADE Asupports
Arithmetic put the “ithm” into algorithm without becoming its ancestor.
Arithmetic carries Greek arithmos “number.” Algorithm carries al-Khwārizmī's name; arithmos influenced its spelling, not its genealogy.
*h₂rei-
*h₂rei- → ἀριθμός → ἀριθμητική (τέχνη) → arithmetica → arsmetique / arismatike → arsmetike / arsmetrik → arithmetic
ALGORITHM section: influenced by Greek arithmosIndependently documents the spelling influence.
arithmetic dossier ↗truth record ↗89UNVEILING
RANK 73GRADE Asupports
Algorithm is the altered version; algorism came first.
The word began in al-Khwārizmī's geographic name. Greek arithmos later helped put “th” into algorithm without becoming its ancestor.
Khwārizm
Khwārizm → al-Khwārizmī → algorismus → algorisme / augorisme → algorisme / augrim → algorism
ALGORITHM entry: algorithm from algorism, influenced by Greek arithmosDocuments chronological priority and later spelling influence.
algorism dossier ↗truth record ↗86UNVEILING
024
SCHOLARLY DISAGREEMENT
DISPUTE POSITIONS THAT CITE THIS SOURCE
resolvedsupportsestablished
Was algorithm the original form and algorism a corruption?
No. Algorism is older. Algorithm is the later altered form, with its th commonly explained through Greek arithmos or arithmetic influence.
ALGORITHM entry: algorithm derived from algorism and influenced by Greek arithmosDocuments both chronological priority and later respelling.
resolvedcontextprobable
Is algorithm originally a Greek mathematical word?
No. The lexical line reaches the Arabic name al-Khwārizmī through Medieval Latin. Greek arithmos likely influenced the later spelling, but it is not the source of the name.
ALGORITHM entryRecords later influence from Greek arithmos on the modern spelling.
resolvedsupportsestablished
Was algorithm first used in 1699 or 1926?
Both dates describe different editorial claims. Oxford/MacTutor reports the spelling in 1699 for numeral calculation; Merriam-Webster gives 1926 for the currently defined finite-procedure sense.
ALGORITHM entryReports the 1699 spelling evidence and the 1926 technical-sense record.
resolvedcontextestablished
Are arithmetic and algorithm cognates?
No. Arithmetic descends through Greek arithmos “number.” Algorithm descends from al-Khwārizmī's name; arithmos influenced the later spelling rather than supplying the ancestor.
ALGORITHM and ARITHMETIC sectionsIndependently documents both histories and the influence statement.
036
CANONICAL RELATIONSHIP CLAIMS
EDGES THAT CITE THIS SOURCE
EDGE 83supportsprobable
algorithm → algorisme / augrim
Present-Day English → Middle English · alteration
- SOUND
- The older ending -ism was reshaped to -ithm, commonly explained through association with Greek arithmos “number.”
- MEANING
- Arithmetic or numeral procedure narrowed and generalized into a finite stepwise procedure.
- SCHOLAR / EDITOR
- Merriam-Webster · MacTutor editors
ALGORITHM entryReports influence from Greek arithmos.
EDGE 85supportsestablished
algorismus → al-Khwārizmī
Medieval Latin → Classical Arabic · eponymic borrowing
- SOUND
- The Arabic name al-Khwārizmī was heavily Latinized as Algoritmi / algorismus; the initial article was absorbed into the form.
- MEANING
- A scholar's geographic name came to denote the arithmetic associated with transmitted texts.
- SCHOLAR / EDITOR
- Merriam-Webster · MacTutor editors
ALGORITHM entryLatin arithmetic transmission.
EDGE 89supportsestablished
algebra → al-jabr
Medieval Latin → Classical Arabic · borrowing
- SOUND
- Arabic al-jabr was adapted into Medieval Latin algebra, retaining the article as part of the word.
- MEANING
- An operation of restoring a subtracted term—and a title phrase—came to name the mathematical discipline; a bone-setting sense also circulated.
- SCHOLAR / EDITOR
- Oxford · MacTutor editors
ALGEBRA entryExplains the equation operation.
EDGE 471contextestablished
arsmetike / arsmetrik → arsmetique / arismatike
Middle English → Old French · borrowing
- SOUND
- Middle English adapts Old French and Anglo-French forms; a folk association with ars metrica contributes the extra r in some spellings.
- MEANING
- The practical and learned counting discipline remains central.
- SCHOLAR / EDITOR
- Merriam-Webster · Etymonline · MacTutor editors
ARITHMETIC section: medieval spelling confusionsSupplies a history-of-mathematics account of the extra-r spellings.
EDGE 473supportsestablished
arithmetica → ἀριθμητική (τέχνη)
Latin → Ancient Greek · borrowing
- SOUND
- Latin arithmetica borrows and adapts Greek arithmētikē.
- MEANING
- The Greek counting art enters Latin education and mathematical vocabulary.
- SCHOLAR / EDITOR
- Merriam-Webster · MacTutor editors
ARITHMETIC section: Greek arithmetike passed into Latin as arithmeticaIndependently documents the learned borrowing.
EDGE 497supportsprobable
algorisme / augorisme → algorismus
Old French → Medieval Latin · borrowing
- SOUND
- Old French algorisme / augorisme adapts Medieval Latin algorismus with Romance vowel and ending changes.
- MEANING
- The learned arithmetic term enters vernacular calculation vocabulary.
- SCHOLAR / EDITOR
- Merriam-Webster · Etymonline · MacTutor editors
ALGORITHM entry: French algorisme from Latin algorismusIndependently documents the learned transmission.
042
LEXICAL ATTESTATIONS
WITNESSES REPORTED BY THIS SOURCE
algebraSOURCE-REPORTED
al-jabr
Source-reported title phrase in al-Khwārizmī's mathematical work
OPEN WITNESS 26 ↗algorithmSOURCE-REPORTED
algorithm
Source-reported English record for the algorithm spelling
OPEN WITNESS 23 ↗053
COMPARATIVE EVIDENCE
COGNATES, DESCENDANTS, AND RELATIVES
algorithm
Englishaltered descendant influenced in spelling by arithmetic
arithmetic
English / Greek lineagespelling influence, not a cognate
logistic
Ancient Greek / EnglishGreek calculation term contrasted with arithmetike
064
GEOGRAPHIC AND TEMPORAL CLAIMS
JOURNEY STAGES THAT CITE THIS SOURCE
stage 2supports
Iberian and Latin translation worlds
Describes al-jabr moving through Spain and Robert of Chester's circa-1140 Latin translation as Liber algebrae et almucabala.
ALGEBRA entry: Spanish transmission and Robert of Chester's Latin translation · regionalstage 2supports
Medieval Latin Europe
Documents the Latin arithmetic stage and century.
ALGORITHM entry: Medieval Latin algorismus and 12th-century transmission · broadstage 3supports
Medieval Latin Europe
Documents Latin transmission of al-Khwarizmi's arithmetic and the later augrim and algorisme forms used for Hindu-Arabic numeral calculation.
ALGORITHM entry: twelfth-century Latin translation and Middle English forms · regionalstage 1context
Ancient Greek linguistic world
Distinguishes Greek theoretical arithmetike from practical logistike.
ARITHMETIC section · broad073
NON-GENEALOGICAL CONNECTIONS
HISTORICAL CONTEXT, KEPT SEPARATE
shared historical agentsupports
ONE SCHOLAR, TWO DIFFERENT WORD HISTORIES
Algorithm descends from the Latinized personal name of al-Khwārizmī. Algebra descends from al-jabr in the title and terminology of his mathematical work. The words share a historical agent, not a lexical ancestor.
Merriam-Webster · MacTutor history of mathematics · establishedspelling influence not ancestrysupports
THE RESEMBLANCE IS REAL; THE COGNACY IS NOT
Arithmetic descends from Greek arithmos “number.” Algorithm descends from the name al-Khwārizmī, but its modern spelling was probably influenced by arithmetic or arithmos. Orthographic influence is historical evidence, not shared ancestry.
American Heritage Dictionary · MacTutor editors · establisheddescendant spelling influence not ancestrysupports
THE MISSING “TH” ARRIVED ONE GENERATION LATER
Algorism descends from al-Khwārizmī. Its altered descendant algorithm was reshaped under the influence of arithmetic or Greek arithmos. Arithmetic therefore explains a later resemblance without becoming algorism's ancestor.
American Heritage Dictionary · MacTutor editors · established084
WORD-FAMILY REUSE
DOSSIERS THAT DEPEND ON THIS SOURCE
7 entry-scoped citations map reviewed dossier paths onto the canonical claims above.