Golden Scholars

Mathematics of the Islamic World: An Encyclopedic Reference

Between roughly 750 and 1600 CE, scholars working across the Islamic world, from Córdoba to Samarkand, produced one of the most consequential bodies of mathematical work in history. They created algebra as an independent discipline, transmitted and completed the decimal positional number system, transformed trigonometry from a tool of astronomy into a branch of mathematics, developed decimal fractions and high-precision computation, and preserved, corrected, and extended the Greek geometric tradition. When this material reached medieval Europe through translation, it supplied much of the foundation on which Renaissance and early modern mathematics was built.

This reference compiles the contributions of more than fifty of these scholars, organizes their work thematically, traces the transmission of their results into Europe, and follows the threads that connect their discoveries to the mathematics practiced today.

How to Use This Site

If you want people: start with the Scholars Master Index, which lists every figure alphabetically with dates and specialties, then follow links into the era chapters where each scholar has a structured entry.

If you want ideas: the Thematic Chapters each follow one branch of mathematics (algebra, trigonometry, arithmetic, geometry, number theory, astronomy, optics) across the whole period.

If you want the story of influence: the Transmission section explains how this mathematics reached Europe, and the Legacy section connects it to modern practice.

If you want orientation: the Timeline gives the whole arc on one page, and the Glossary defines recurring terms.

A Note on Names, Dates, and Accuracy

Medieval biographical data is often incomplete. Birth and death years given as "c." (circa) reflect genuine scholarly uncertainty, not imprecision in this compilation. Names are given in simplified transliteration, with common Latinized forms (Algorismi, Alhazen, Geber) noted where they matter for the European story. Claims that remain debated among historians of mathematics, such as the exact route by which the Tusi couple reached Copernicus, are flagged as debated rather than stated as settled fact. See About This Project for methodology and sourcing standards.

The Short Version

If the entire subject had to be compressed into five sentences:

1. Al-Khwarizmi's ninth-century Baghdad treatise on al-jabr founded algebra as a discipline and, in Latin translation, gave Europe both the word algebra and the word algorithm.
2. Scholars from al-Uqlidisi to al-Kashi built decimal arithmetic, including decimal fractions, into the complete computational system the modern world runs on.
3. Abu al-Wafa, al-Biruni, Nasir al-Din al-Tusi and others turned trigonometry into an independent mathematical science, introducing the tangent function and the law of sines along the way.
4. Ibn al-Haytham founded mathematical optics and used what is now called mathematical induction-style reasoning and fourth-power summation formulas that anticipate integral calculus techniques.
5. Through the translation centers of Toledo and Sicily, and through Fibonacci's Liber Abaci, this mathematics entered Europe and became the substrate of the Renaissance mathematics that leads directly to the modern subject.