Al-Khwārizmī and the Historical Roots of Algorithmic Method: Algorism, Algebra, and Computation

Last Updated June 23, 2026

Al-Khwārizmī and the Historical Roots of Algorithmic Method examines one of the most important figures in the long history of algorithms without reducing that history to a single inventor, word, culture, or moment. Muḥammad ibn Mūsā al-Khwārizmī belongs at the center of any serious history of algorithmic reasoning because his name became embedded in the word history of algorithm, his arithmetic work helped transmit Hindu-Arabic numeral calculation, and his algebraic writing helped systematize rule-governed problem solving with unknown quantities.

But al-Khwārizmī’s significance is not that he invented every algorithm. Procedures existed long before him in Babylonian calculation, Greek geometry, Indian numeration and combinatorics, Chinese mathematical traditions, administrative practice, astronomy, surveying, commerce, and law. His importance is more precise and more historically interesting. He helped make methods explicit, organized, teachable, portable, and transmissible. His works stand at a crucial junction where arithmetic, algebra, astronomy, geography, translation, pedagogy, and institutional knowledge came together.

The historical roots of algorithmic method therefore include both name and method. The word algorithm preserves a memory of al-Khwārizmī through algorism and Latin reception. The method history is wider: rule, case, procedure, demonstration, representation, calculation, correction, verification, and transmission. This article treats al-Khwārizmī not as a mythic origin point, but as a decisive historical bridge in the movement from practical procedure toward systematic computation.

This article introduces al-Khwārizmī, algorithm, algorism, algebra, al-jabr, al-muqābalah, Hindu-Arabic numerals, place-value calculation, arithmetic procedure, equation cases, unknowns, roots, squares, numbers, geometric demonstration, Arabic scientific culture, Abbasid Baghdad, translation movements, Latin reception, procedural method, mathematical pedagogy, historical roots, etymology, and algorithmic reasoning. It argues that al-Khwārizmī’s legacy is strongest when framed precisely: as a central figure in the history of algorithmic method, not as a slogan for the entire history of computation.

Why Al-Khwārizmī Matters

Al-Khwārizmī matters because he stands at the intersection of word history, mathematical method, institutional transmission, and modern memory. The word algorithm is historically connected to Latinized forms of his name through algorism. His work on calculation helped carry Hindu-Arabic numeral arithmetic into broader circulation. His algebraic treatise organized equation solving into cases and procedures. His astronomical and geographical work also belongs to a wider culture of tables, coordinates, prediction, and computational representation.

His importance is not merely linguistic. It is methodological. Al-Khwārizmī’s works show how mathematical knowledge can be written as teachable procedure: identify the kind of problem, apply a rule, transform the terms, find the result, and verify the answer.

Al-Khwārizmī matters because he helps us see algorithms as named, teachable, transmissible methods before modern computers.

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The Risk of Mythic Origin Stories

Al-Khwārizmī is often described as the “father of algebra” or the figure whose name gave us “algorithm.” These phrases can be useful when carefully explained. They can also mislead. A mythic origin story turns a complex history into a single heroic moment. It may imply that algorithms began with one person, that algebra was invented from nothing, or that medieval mathematical procedure was already modern computing.

A better story is more careful. Al-Khwārizmī systematized and transmitted important methods. He worked within a larger intellectual environment. His works drew from and contributed to multiple traditions. His legacy changed through translation, commentary, Latin reception, and later technical usage.

Al-Khwārizmī’s historical importance increases when myth is removed.

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Al-Khwārizmī in Abbasid Intellectual Context

Al-Khwārizmī worked in the intellectual world of Abbasid Baghdad, where translation, astronomy, mathematics, administration, geography, and philosophical inquiry were deeply connected. This context matters. His work did not emerge in isolation. It belonged to a culture in which scientific and mathematical knowledge moved across Greek, Syriac, Persian, Sanskrit, Arabic, and later Latin pathways.

Abbasid intellectual culture valued useful calculation and systematic scholarship. Astronomers needed tables. Administrators needed arithmetic. Jurists and families needed inheritance calculation. Merchants needed commercial arithmetic. Geographers needed coordinates. Mathematicians needed methods for unknown quantities. Al-Khwārizmī’s writings belong to this world of practical and theoretical procedure.

Al-Khwārizmī is best understood as part of a knowledge system where method had practical, scholarly, and institutional value.

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Algorism and Written Calculation

Algorism originally referred to techniques of calculation using Hindu-Arabic numerals. In Latin Europe, algorism became associated with written arithmetic using positional notation, rather than older habits based on Roman numerals, counting boards, or abacus methods. The term is historically linked to Latinized forms of al-Khwārizmī’s name.

This matters because written calculation is an algorithmic technology. Place-value notation does not merely record numbers; it supports procedures. Addition, subtraction, multiplication, division, extraction, and checking become systematic because the representation itself helps organize the method.

Algorism shows that algorithmic method depends on representation as much as on steps.

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Hindu-Arabic Numerals and Place Value

The Hindu-Arabic numeral system transformed calculation because it made written arithmetic more compact, scalable, and teachable. Al-Khwārizmī’s role was not to invent the numeral system from nothing, but to help transmit and explain methods associated with it in Arabic mathematical culture and, through later Latin reception, into Europe.

Place value is algorithmically powerful because the same procedure can operate position by position. A digit’s meaning depends on location. Operations can be broken down into repeated local transformations. That is why written arithmetic is a major ancestor of computational method.

Place value is one of the great historical infrastructures of algorithmic calculation.

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Algebra as Rule-Governed Problem Solving

Al-Khwārizmī’s algebra is central because it presents mathematical problems as cases that can be solved by rules. The reader does not simply receive isolated answers. The reader learns procedures for transforming a type of problem into a solvable form. This is one reason his algebraic work remains important for algorithmic reasoning.

The algebraic tradition associated with al-Khwārizmī uses verbal descriptions rather than modern symbolic notation. That does not make it non-algorithmic. It makes it verbally procedural. The method identifies squares, roots, numbers, unknowns, and cases, then prescribes transformations.

Algebra shows algorithmic method as organized transformation of unknown quantities.

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Al-Jabr, Al-Muqābalah, and Transformation

The terms al-jabr and al-muqābalah are often interpreted as restoration and balancing or comparison. They describe operations that transform an equation into a more useful form. This is central to algorithmic method: a problem is not solved by merely observing it; it is changed step by step while preserving its meaning.

Restoration can move or repair deficient terms. Balancing can reduce like terms or compare sides. Together they help normalize a problem so a known rule can be applied. This is a deep ancestor of modern symbolic manipulation, equation solving, and state transformation.

Al-jabr and al-muqābalah are not just historical terms; they name a procedural logic of transformation.

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Unknowns, Roots, Squares, and Numbers

Al-Khwārizmī’s algebraic method depends on a vocabulary of mathematical objects. The unknown is the quantity to be found. The root is the base unknown. The square is the product of the root with itself. The number is the known amount. These terms organize problem structure before symbolic notation.

This vocabulary is important because it makes the unknown thinkable. A missing quantity becomes an object that can be classified and transformed. A problem no longer consists only of known numbers; it consists of relationships among known and unknown quantities.

Naming the unknown is one of the conceptual roots of algorithmic algebra.

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Geometric Demonstration and Correctness

Al-Khwārizmī’s algebra is not merely a list of tricks. It is connected to demonstration. Geometric reasoning helps justify procedures such as completing the square. A root may be represented as a line segment. A square may be represented as an area. Completing the square becomes a visual and constructive proof that the procedure works.

This matters for algorithm history because correctness is part of algorithmic method. A procedure must not only produce an answer; it must produce the right answer under defined conditions. Demonstration, examples, and verification are early forms of correctness control.

Algorithmic method requires both steps and standards for why the steps work.

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Astronomy, Geography, and Tabular Method

Al-Khwārizmī’s importance is not limited to algebra and arithmetic. He also worked in areas such as astronomy and geography, where tables, coordinates, calendars, and numerical correction played central roles. These fields reveal another side of algorithmic method: structured data and repeatable calculation.

Astronomical and geographical tables are not programs, but they are computational tools. They organize values so users can predict, locate, compare, and calculate. A table can encode procedure by telling the user where to look, what value to combine, and how to adjust or interpret a result.

Tables show that algorithmic method can live in organized data as well as in verbal rules.

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Translation, Latin Reception, and the Word Algorithm

Al-Khwārizmī’s legacy changed through translation. Arabic mathematical texts and Arabic-mediated knowledge entered Latin Europe through translation, commentary, teaching, and practical use. His name was Latinized, and through algorism it became linked to written calculation. Over centuries, algorithm came to mean a general method of computation.

This is why word history must be separated from method history. The word algorithm carries al-Khwārizmī’s name, but the concept of algorithm broadened through later mathematical, logical, and computational developments. Translation preserved a memory, but reception transformed its meaning.

The word algorithm is a historical fossil of transmission, not a complete explanation by itself.

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From Algorism to Algorithm

The movement from algorism to algorithm shows how a term can broaden over time. Algorism referred to arithmetic using Hindu-Arabic numerals. Algorithm later came to mean a more general procedure for computation. In modern computer science, algorithm has an even more formal meaning involving finite, effective, rule-governed procedures.

This semantic shift matters because it preserves continuity and difference at the same time. The modern word remembers al-Khwārizmī. But the modern concept also depends on later developments: symbolic algebra, formal logic, computability, programming languages, data structures, complexity theory, and machine execution.

The word’s journey is itself a lesson in historical method.

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Algorithmic Method Before Modern Computing

Al-Khwārizmī helps show that algorithmic method existed before modern computing. His works belong to a world of human readers, manuscripts, tables, examples, and verbal procedures. Yet they display features central to algorithmic reasoning: formalized problem types, rules, transformations, ordered steps, representation, verification, and practical application.

This should not be confused with programming. Al-Khwārizmī did not write code. But his work shows how procedures can be made explicit enough to travel, be taught, and be reused. That is one of the historical roots of computation.

The point is not to modernize al-Khwārizmī, but to recognize algorithmic method in historical form.

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What Al-Khwārizmī Did Not Do

A responsible history also says what al-Khwārizmī did not do. He did not invent the Hindu-Arabic numeral system from nothing. He did not invent all step-by-step procedures. He did not create modern symbolic algebra. He did not develop computability theory. He did not program computers. He did not create artificial intelligence.

These limits do not weaken his legacy. They protect it from distortion. His real importance lies in systematization, exposition, transmission, and method. He helped make arithmetic and algebraic procedures historically durable. That is enough to make him one of the great figures in the history of algorithmic reasoning.

Precision is the best way to honor al-Khwārizmī’s place in history.

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Mathematics, Computation, and Modeling

Al-Khwārizmī’s historical role can be modeled as a layered relationship:

Algebraic method can be modeled as:

Algorism can be modeled as:

Historical caution can be modeled as:

These formulas use modern notation to clarify historical structure. They are interpretive models, not claims that ninth-century authors used this notation.

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Python Workflow: Al-Khwārizmī Method Map

The Python workflow below creates a dependency-light interpretive map of al-Khwārizmī’s contribution to algorithmic method. It scores themes by arithmetic method, algebraic procedure, representation, transformation, proof relation, transmission, etymology, institutional adoption, historiographic caution, and modern resonance, then writes reproducible CSV and JSON outputs.

# al_khwarizmi_algorithmic_method_map.py
# Dependency-light workflow for mapping al-Khwārizmī's role in algorithmic method.

from __future__ import annotations

from dataclasses import asdict, dataclass
from pathlib import Path
from statistics import mean
import csv
import json
from datetime import datetime, timezone

ARTICLE_ROOT = Path(__file__).resolve().parents[1]
TABLES = ARTICLE_ROOT / "outputs" / "tables"
JSON_DIR = ARTICLE_ROOT / "outputs" / "json"


@dataclass(frozen=True)
class KhwarizmiMethodConfig:
    article: str = "al_khwarizmi_and_the_historical_roots_of_algorithmic_method"
    core_threshold: float = 0.80
    high_method_threshold: float = 0.86


def timestamp_utc() -> str:
    return datetime.now(timezone.utc).isoformat()


def write_csv(path: Path, rows: list[dict[str, object]]) -> None:
    path.parent.mkdir(parents=True, exist_ok=True)
    if not rows:
        path.write_text("", encoding="utf-8")
        return
    fieldnames = sorted({key for row in rows for key in row.keys()})
    with path.open("w", newline="", encoding="utf-8") as handle:
        writer = csv.DictWriter(handle, fieldnames=fieldnames, extrasaction="ignore")
        writer.writeheader()
        writer.writerows(rows)


def write_json(path: Path, payload: object) -> None:
    path.parent.mkdir(parents=True, exist_ok=True)
    path.write_text(json.dumps(payload, indent=2, sort_keys=True), encoding="utf-8")


def khwarizmi_themes() -> list[dict[str, object]]:
    return [
        {"theme_id": "algorism_written_calculation", "arithmetic_method": 0.98, "algebraic_procedure": 0.76, "representation": 0.98, "transformation": 0.88, "proof_relation": 0.78, "transmission": 0.98, "etymology": 0.98, "institutional_adoption": 0.94, "historiographic_caution": 0.92, "modern_resonance": 0.98},
        {"theme_id": "algebra_case_based_method", "arithmetic_method": 0.86, "algebraic_procedure": 0.98, "representation": 0.92, "transformation": 0.98, "proof_relation": 0.92, "transmission": 0.94, "etymology": 0.88, "institutional_adoption": 0.92, "historiographic_caution": 0.92, "modern_resonance": 0.98},
        {"theme_id": "al_jabr_al_muqabalah_transformation", "arithmetic_method": 0.82, "algebraic_procedure": 0.98, "representation": 0.90, "transformation": 0.98, "proof_relation": 0.90, "transmission": 0.94, "etymology": 0.92, "institutional_adoption": 0.92, "historiographic_caution": 0.92, "modern_resonance": 0.96},
        {"theme_id": "unknown_root_square_number", "arithmetic_method": 0.82, "algebraic_procedure": 0.96, "representation": 0.94, "transformation": 0.94, "proof_relation": 0.90, "transmission": 0.92, "etymology": 0.84, "institutional_adoption": 0.90, "historiographic_caution": 0.94, "modern_resonance": 0.96},
        {"theme_id": "geometric_demonstration_correctness", "arithmetic_method": 0.72, "algebraic_procedure": 0.92, "representation": 0.90, "transformation": 0.92, "proof_relation": 0.98, "transmission": 0.86, "etymology": 0.72, "institutional_adoption": 0.86, "historiographic_caution": 0.92, "modern_resonance": 0.94},
        {"theme_id": "astronomy_geography_tables", "arithmetic_method": 0.90, "algebraic_procedure": 0.68, "representation": 0.96, "transformation": 0.82, "proof_relation": 0.80, "transmission": 0.92, "etymology": 0.70, "institutional_adoption": 0.90, "historiographic_caution": 0.90, "modern_resonance": 0.92},
        {"theme_id": "latin_reception_word_algorithm", "arithmetic_method": 0.92, "algebraic_procedure": 0.86, "representation": 0.92, "transformation": 0.86, "proof_relation": 0.76, "transmission": 0.98, "etymology": 0.98, "institutional_adoption": 0.96, "historiographic_caution": 0.98, "modern_resonance": 0.98},
        {"theme_id": "myth_correction_precise_legacy", "arithmetic_method": 0.82, "algebraic_procedure": 0.82, "representation": 0.82, "transformation": 0.82, "proof_relation": 0.82, "transmission": 0.90, "etymology": 0.92, "institutional_adoption": 0.88, "historiographic_caution": 0.98, "modern_resonance": 0.96},
    ]


def score_theme(row: dict[str, object], config: KhwarizmiMethodConfig) -> dict[str, object]:
    method_score = mean([
        float(row["arithmetic_method"]),
        float(row["algebraic_procedure"]),
        float(row["representation"]),
        float(row["transformation"]),
        float(row["proof_relation"]),
        float(row["transmission"]),
        float(row["etymology"]),
        float(row["institutional_adoption"]),
        float(row["historiographic_caution"]),
        float(row["modern_resonance"]),
    ])

    if method_score >= config.core_threshold and max(float(row["arithmetic_method"]), float(row["algebraic_procedure"])) >= config.high_method_threshold:
        interpretive_status = "core_khwarizmi_algorithmic_method_thread"
    elif method_score >= config.core_threshold:
        interpretive_status = "major_khwarizmi_algorithmic_method_thread"
    else:
        interpretive_status = "supporting_khwarizmi_algorithmic_method_thread"

    return {
        "theme_id": row["theme_id"],
        "arithmetic_method": round(float(row["arithmetic_method"]), 6),
        "algebraic_procedure": round(float(row["algebraic_procedure"]), 6),
        "representation": round(float(row["representation"]), 6),
        "transformation": round(float(row["transformation"]), 6),
        "proof_relation": round(float(row["proof_relation"]), 6),
        "transmission": round(float(row["transmission"]), 6),
        "etymology": round(float(row["etymology"]), 6),
        "institutional_adoption": round(float(row["institutional_adoption"]), 6),
        "historiographic_caution": round(float(row["historiographic_caution"]), 6),
        "modern_resonance": round(float(row["modern_resonance"]), 6),
        "method_score": round(method_score, 6),
        "interpretive_status": interpretive_status,
    }


def interpretation_cautions() -> list[dict[str, str]]:
    return [
        {"caution": "do_not_claim_al_khwarizmi_invented_all_algorithms", "meaning": "His name is central to algorithm word history, but procedural reasoning is broader and older."},
        {"caution": "do_not_reduce_his_legacy_to_etymology", "meaning": "His arithmetic and algebraic methods matter beyond the word algorithm."},
        {"caution": "do_not_ignore_indian_numeration", "meaning": "Hindu-Arabic numerals and place value have their own history."},
        {"caution": "do_not_project_modern_code_backward", "meaning": "Al-Khwārizmī used verbal and geometric procedures, not programming languages."},
        {"caution": "do_not_describe_him_as_only_preserving_knowledge", "meaning": "Transmission, organization, exposition, and systematization are creative intellectual acts."},
    ]


def main() -> None:
    config = KhwarizmiMethodConfig()
    themes = khwarizmi_themes()
    scored = [score_theme(row, config) for row in themes]
    cautions = interpretation_cautions()

    summary = {
        "article": config.article,
        "timestamp_utc": timestamp_utc(),
        "themes_reviewed": len(scored),
        "core_threads": sum(1 for row in scored if row["interpretive_status"] == "core_khwarizmi_algorithmic_method_thread"),
        "major_threads": sum(1 for row in scored if row["interpretive_status"] == "major_khwarizmi_algorithmic_method_thread"),
        "supporting_threads": sum(1 for row in scored if row["interpretive_status"] == "supporting_khwarizmi_algorithmic_method_thread"),
        "mean_method_score": round(mean(float(row["method_score"]) for row in scored), 6),
        "cautions": len(cautions),
        "interpretation": "Al-Khwārizmī should be studied as a decisive bridge in algorithmic method: algorism, algebra, transformation, representation, transmission, and careful historical memory.",
    }

    write_csv(TABLES / "khwarizmi_themes.csv", themes)
    write_csv(TABLES / "khwarizmi_algorithmic_method_map.csv", scored)
    write_csv(TABLES / "interpretation_cautions.csv", cautions)
    write_csv(TABLES / "khwarizmi_method_summary.csv", [summary])

    write_json(JSON_DIR / "khwarizmi_method_config.json", asdict(config))
    write_json(JSON_DIR / "khwarizmi_algorithmic_method_map.json", scored)
    write_json(JSON_DIR / "interpretation_cautions.json", cautions)
    write_json(JSON_DIR / "khwarizmi_method_summary.json", summary)

    print("Al-Khwārizmī algorithmic method map complete.")
    print(TABLES / "khwarizmi_method_summary.csv")


if __name__ == "__main__":
    main()

This workflow turns al-Khwārizmī’s role into a structured interpretive artifact: algorism, algebra, transformation, representation, proof, transmission, etymology, institutional adoption, and historical caution can be analyzed together.

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R Workflow: Historical Roots Diagnostics

The R workflow reads the generated CSV outputs, summarizes al-Khwārizmī method themes, visualizes dimensions, and writes an additional diagnostic table.

# al_khwarizmi_algorithmic_method_summary.R
args <- commandArgs(trailingOnly = FALSE)
file_arg <- grep("^--file=", args, value = TRUE)

if (length(file_arg) > 0) {
  script_path <- normalizePath(sub("^--file=", "", file_arg[1]), mustWork = TRUE)
  article_root <- normalizePath(file.path(dirname(script_path), ".."), mustWork = TRUE)
} else {
  article_root <- getwd()
}

setwd(article_root)

tables_dir <- file.path(article_root, "outputs", "tables")
figures_dir <- file.path(article_root, "outputs", "figures")
dir.create(tables_dir, recursive = TRUE, showWarnings = FALSE)
dir.create(figures_dir, recursive = TRUE, showWarnings = FALSE)

map_path <- file.path(tables_dir, "khwarizmi_algorithmic_method_map.csv")
summary_path <- file.path(tables_dir, "khwarizmi_method_summary.csv")

if (!file.exists(map_path)) {
  stop(paste("Missing", map_path, "Run the Python workflow first."))
}

method_map <- read.csv(map_path, stringsAsFactors = FALSE)
summary <- read.csv(summary_path, stringsAsFactors = FALSE)

png(file.path(figures_dir, "khwarizmi_method_dimensions.png"), width = 1200, height = 850)
score_matrix <- t(as.matrix(method_map[, c("arithmetic_method", "algebraic_procedure", "representation", "transformation", "proof_relation", "transmission", "etymology", "institutional_adoption", "historiographic_caution", "modern_resonance")]))
barplot(score_matrix,
        beside = TRUE,
        names.arg = method_map$theme_id,
        las = 2,
        ylim = c(0, 1),
        ylab = "Interpretive Score",
        main = "Al-Khwārizmī and the Historical Roots of Algorithmic Method")
legend("bottomright",
       legend = rownames(score_matrix),
       cex = 0.68,
       bty = "n")
grid()
dev.off()

png(file.path(figures_dir, "khwarizmi_method_score_by_theme.png"), width = 1000, height = 750)
barplot(method_map$method_score,
        names.arg = method_map$theme_id,
        las = 2,
        ylab = "Method Score",
        main = "Al-Khwārizmī Method Score by Theme")
grid()
dev.off()

r_summary <- data.frame(
  themes_reviewed = summary$themes_reviewed[1],
  core_threads = summary$core_threads[1],
  major_threads = summary$major_threads[1],
  supporting_threads = summary$supporting_threads[1],
  mean_method_score = summary$mean_method_score[1],
  cautions = summary$cautions[1],
  diagnostic_note = "Al-Khwārizmī should be studied as a decisive bridge in algorithmic method: algorism, algebra, transformation, representation, transmission, and careful historical memory."
)

write.csv(r_summary, file.path(tables_dir, "r_khwarizmi_method_diagnostic_summary.csv"), row.names = FALSE)
print(r_summary)

The R layer makes the interpretive structure visible: arithmetic method, algebraic procedure, representation, transformation, proof, transmission, etymology, institutional adoption, historical caution, and modern resonance can be compared across themes.

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GitHub Repository

The companion repository contains reproducible workflows, synthetic interpretive data, outputs, calculators, documentation, and multilingual examples for this article.

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A Practical Method for Studying Al-Khwārizmī

A careful study of al-Khwārizmī asks how name, method, text, translation, and later memory relate without collapsing them.

This method lets al-Khwārizmī’s contribution remain central without making it simplistic.

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Common Pitfalls

The first pitfall is saying al-Khwārizmī invented algorithms. The second is reducing him to the etymology of a word. The third is ignoring Indian numeration and broader Islamic-world transmission. The fourth is calling him a computer scientist.

A strong account of al-Khwārizmī is precise, generous, and historically layered.

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Why Al-Khwārizmī Still Matters

Al-Khwārizmī still matters because he helps modern readers see algorithms as historical objects. They are not only computer programs. They are methods that must be represented, taught, executed, checked, transmitted, trusted, and interpreted. His arithmetic and algebraic works stand near the roots of written calculation and rule-governed problem solving that later became part of the history of computation.

He also matters because his legacy requires careful historical reasoning. His name gave us one of the most important words in modern technical life. But the word’s history is not the whole history of algorithms. His works helped transmit and systematize major procedures. But he did not invent all procedure. His legacy is neither trivial nor total.

The best way to honor al-Khwārizmī is to place him exactly where he belongs: at a decisive historical junction between arithmetic, algebra, method, translation, and computation. AI belongs in the toolkit, not in control.

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Related Articles

• The History of Algorithms: From Procedure to Computation
• Ada Lovelace and the Analytical Engine
• Al-Khwārizmī, Algorism, and the Procedural Imagination
• Al-Jabr wa’l-Muqābalah: Algebra as Rule-Governed Problem Solving
• Why Origin Stories of Algorithms Need Care

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Further Reading

• MacTutor History of Mathematics (n.d.) ‘Al-Khwarizmi’. University of St Andrews.
• Online Etymology Dictionary (n.d.) ‘Algorithm’.
• Zarepour, M.S. (2022) ‘Arabic and Islamic Philosophy of Mathematics’. Stanford Encyclopedia of Philosophy.
• Rashed, R. (2009) Al-Khwārizmī: The Beginnings of Algebra. London: Saqi.
• Oaks, J.A. (2015) The Algebra of Mohammed ben Musa. Cham: Springer.
• Berggren, J.L. (2007) Mathematics in Medieval Islam. Princeton: Princeton University Press.
• Rashed, R. (1994) The Development of Arabic Mathematics: Between Arithmetic and Algebra. Dordrecht: Kluwer.
• Chabert, J.-L. (ed.) (1999) A History of Algorithms: From the Pebble to the Microchip. Berlin: Springer.

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References

• Berggren, J.L. (2007) Mathematics in Medieval Islam. Princeton: Princeton University Press.
• Chabert, J.-L. (ed.) (1999) A History of Algorithms: From the Pebble to the Microchip. Berlin: Springer.
• MacTutor History of Mathematics (n.d.) ‘Al-Khwarizmi’. University of St Andrews. Available at: https://mathshistory.st-andrews.ac.uk/Biographies/Al-Khwarizmi/.
• Oaks, J.A. (2015) The Algebra of Mohammed ben Musa. Cham: Springer.
• Online Etymology Dictionary (n.d.) ‘Algorithm’. Available at: https://www.etymonline.com/word/algorithm.
• Rashed, R. (1994) The Development of Arabic Mathematics: Between Arithmetic and Algebra. Dordrecht: Kluwer.
• Rashed, R. (2009) Al-Khwārizmī: The Beginnings of Algebra. London: Saqi.
• Zarepour, M.S. (2022) ‘Arabic and Islamic Philosophy of Mathematics’. Stanford Encyclopedia of Philosophy. Available at: https://plato.stanford.edu/entries/arabic-islamic-phil-math/.

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