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Muhammad Al-Khwarizmi
One of the first Directors of the House of Wisdom in Bagdad in the early 9th Century was an outstanding Persian mathematician called Muhammad Al-Khwarizmi. He oversaw the translation of the major Greek and Indian mathematical and astronomy works (including those of Brahmagupta) into Arabic, and produced original work which had a lasting influence on the advance of Muslim and (after his works spread to Europe through Latin translations in the 12th Century) later European mathematics.
Al-Khwarizmi wrote texts in mathematics, astronomy, and geography that introduced algebra and Hindu-Arabic numerals to the West. His most famous works include Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing) and his treatise on arithmetic.
The word “algebra” comes from al-jabr meaning “restoration” or “completion,” referring to the method of moving a subtracted term to the other side of an equation to balance it.
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“Al-Khwarizmi – The Father Of Algebra”. 2021. storyofmathematics.com. https://www.storyofmathematics.com/islamic_alkhwarizmi.html.
“Al-Khwarizmi: The Father Of Algebra”. 2022. Medium. https://mathladyhazel.medium.com/al-khwarizmi-the-father-of-algebra-2bc1207b9c69.
Suggested Reading
Passey, Debbie. 2024. “Why Are Algorithms Called Algorithms? A Brief History of the Persian Polymath You’ve Likely Never Heard Of.” The Conversation. May 9. https://theconversation.com/why-are-algorithms-called-algorithms-a-brief-history-of-the-persian-polymath-youve-likely-never-heard-of-229286.
Al-Khwārizmī made important contributions to mathematics, geography, astronomy and trigonometry. To help provide a more accurate world map, he corrected Alexandrian polymath Ptolemy’s classic cartography book, Geographia.
He produced calculations for tracking the movement of the Sun, Moon and planets. He also wrote about trigonometric functions and produced the first table of tangents.
Al-Khwārizmī was a scholar in the House of Wisdom (Bayt al-Hikmah) in Baghdad. At this intellectual hub, scholars were translating knowledge from around the world into Arabic, synthesising it to make meaningful progress in a range of disciplines.
Gorodin, Michael. “The Genius Who Invented Algebra”. 2023. ynetnews. https://www.ynetnews.com/health_science/article/hyww0gmas.
Al-Khwarizmi was the first to refer to general “Algebraic objects”: an equation, a variable and more. Before his time there were only problems and solutions. He already spoke of general types of problems, which he turned into abstract objects themselves, which we study and talk about today, without referring to the private cases given by Al-Khwarizmi.
Today we take it almost for granted that this is one of the main things mathematics does. But until al-Khwarizmi it was simply not true. To him, the equation was not simply an excuse to deal with a numerical problem, it was the main objective of mathematical research.
Al-Khwarizmi’s first step was followed by a long line of algebra practitioners, who studied equations further and further, increasing the level of algebraic complexity. Later they set sail to the abstract and built additional mathematical objects, more general and more abstract, which allowed mathematics to soar to new heights. But it all started at the House of Wisdom in Baghdad.
Gullapalli, Kalyan. 2023. “Al-Khwarizmi: The Father of Algebra”. LinkedIn. October 12. https://www.linkedin.com/posts/kalyangullapalli_rediscoveringbharat-activity-7118037560878112768-7AXF.
Muhammad ibn Musa al-Khwarizmi (Muhammad, the son of Musa, from the village of Khwarazm), simply called Al-Khwarizmi, was a 9th century CE Persian mathematician, astronomer & geographer. He is considered to be ‘The Father of Algebra.’ Let’s understand why!
Space Daily Editorial Team. “The word algebra comes from the title of a book called Al-Jabr, written around the year 820 by a Persian mathematician named Muhammad ibn Musa al-Khwarizmi at the House of Wisdom in Baghdad — and the word algorithm comes from the Latinized version of his name.” Space Daily, July 4, 2026. https://spacedaily.com/d-the-word-algebra-comes-from-the-title-of-a-book-called-al-jabr-written-around-the-year-820-by-a-persian-mathematician-named-muhammad-ibn-musa-al-khwarizmi-at-the-house-of-wisdom-in-baghdad/.
Two of the most substantially used words in the current global vocabulary of mathematics and computing come from the same 9th-century Persian scholar working in the same Baghdad library across approximately the same twenty-year period between 813 and 833 CE.
“Why Algorithms Are Called Algorithms, And How It All Goes Back To The Medieval Persian Mathematician Muhammad Al-Khwarizmi”. 2022. Open Culture. https://www.openculture.com/2022/04/why-algorithms-are-called-algorithms.html.
In recent decades, a medieval Persian word has come to prominence in English and other major world languages. Many of use it on a daily basis, often while regarding the concept to which it refers as essentially mysterious. The word is algorithm, whose roots go back to the ninth century in modern-day Greater Iran. There lived a polymath by the name of Muhammad ibn Musa al-Khwarizmi, whom we now remember for his achievements in geography, astronomy, and mathematics. In that last field, he was the first to define the principles of “reducing” and “balancing” equations, a subject all of us came to know in school as algebra (a name itself descended from the Arabic al-jabr, or “completion”).
Hypatia Of Alexandria
Adair, Ginny. “Hypatia.” Biographies of Women Mathematicians. Accessed March 30, 2026. https://mathwomen.agnesscott.org/women/hypatia.htm.
The life of Hypatia was one enriched with a passion for knowledge. Hypatia was known more for the work she did in mathematics than in astronomy, primarily for her work on the ideas of conic sections introduced by Apollonius. She edited the work On the Conics of Apollonius, which divided cones into different parts by a plane. This concept developed the ideas of hyperbolas, parabolas, and ellipses. With Hypatia’s work on this important book, she made the concepts easier to understand, thus making the work survive through many centuries. Hypatia was the first woman to have such a profound impact on the survival of early thought in mathematics.
“Hypatia Of Alexandria”. 2021. Medium. https://himnickson.medium.com/hypatia-of-alexandria-94bb7797919c.
In a time of religious warfare, Hypatia was an outspoken pagan who was also one of the first women to study math, astronomy, and philosophy. Her life is little remembered, but her tragic death at the hands of Christian fanatics is well-known.
Suggested Reading
“Hellenistic”. 2021. storyofmathematics.com. https://www.storyofmathematics.com/hellenistic.html.
By the middle of the 1st Century BCE and thereafter, however, the Romans had tightened their grip on the old Greek empire. The Romans had no use for pure mathematics, only for its practical applications, and the Christian regime that followed it even less so. The final blow to the Hellenistic mathematical heritage at Alexandria might be seen in the figure of Hypatia, the first recorded female mathematician, and a renowned teacher who had written some respected commentaries on Diophantus and Apollonius. She was dragged to her death by a Christian mob in 415 CE.
Cuna, Jason. “What Ancient Event Has Been Recorded In History That Alerts The World To Human Wickedness?” 2023. Quora. https://qr.ae/prlBjl.
In the name of religion, she [Hypatia] was stripped naked and brutally butchered using ostraka (shards of “roof tiles” or “oyster shells”). Before her horrific ordeal ended, her eyeballs had been gouged, her body had been torn into pieces, her limbs had been dragged through the town to a place called Cinarion, where her remains had finally been set on fire.
Plevris, Vagelis. “Hypatia: The Mathematician We Made A Myth.” Medium, August 18, 2026. https://vplevris.medium.com/hypatia-the-mathematician-we-made-a-myth-482bfe7b8bf5.
There is something painful about Hypatia’s survival in memory. We know the violence. We know the accusation. We know the political tension around her death. We know how later centuries used her image. But the daily substance of her teaching, the exact words she wrote beside a difficult passage of Diophantus or Ptolemy, mostly escapes us.
This does not make her less of a mathematician. It reminds us how mathematics survives. It survives through named discoveries, but also through unnamed labor. It survives because someone copies a text carefully. Someone corrects an error. Someone explains a difficult passage to a student. Someone draws the diagram again. Someone keeps a tradition alive in a city where power is shifting and institutions are unstable.