Historical Profiles
Twelve mathematicians. Every claim sourced.
The four olympiad subjects the Academy teaches, algebra, geometry, number theory, combinatorics, have a deep, documented lineage in the mathematical tradition of the Arab world and beyond. This archive is where that lineage lives on the site, one scholar per page, with citations you can check.
This is a working reference document. Every entry lists the scholar's dates and places of work, principal treatises, and the specific relevant to olympiad mathematical results attributable to them. The primary sources drawn on across the archive are the MacTutor History of Mathematics archive at St Andrews, Britannica's biographical entries, and Roshdi Rashed's 2021 critical edition of Al-Samaw'al's Al-Bāhir (De Gruyter, Scientia Graeco-Arabica). Named modern scholars , Hogendijk, Woepcke, Rashed, Berggren, are cited by name where their work is at issue. A full editorial policy and corrections page governs everything published here.
The archive, so far
Twelve entries. Every scholar in the Continuum, on their own page.
The Mathematical Heritage is the site's narrative history of this tradition, a single readable arc from Al-Khwārizmī to al-Kāshī. The archive is its evidence layer: one scholar per page, every claim traceable to a named source. Continuum and archive are now fully symmetric, all twelve scholars appear in both, in the same chronological order.
- 01 Al-Khwārizmī Systematic classification and geometric solution of the six standard quadratic forms; the treatise that gave algebra its name.
- 02 Thābit ibn Qurra A general theorem generating families of amicable numbers; a Pythagorean theorem generalisation for arbitrary triangles.
- 03 Al-Battānī The Kitāb al-Zīj: a working spherical trigonometry manual, sine and versed sine tabulated to three sexagesimal places, a corrected value for the length of the tropical year, and the first firm reading of the motion of the solar apogee.
- 04 Abū al-Wafāʾ al-Būzjānī Sine, cosine, tangent, cotangent, secant, cosecant treated together as one system; sine tables to nine sexagesimal places; a spherical law of sines whose priority is contested and preserved as contested.
- 05 Al-Karajī The sum of cubes identity, an early inductive argument, and a symbolic algebra of powers of x pushed away from geometric figures.
- 06 Ibn al-Haytham A congruence system problem solved via what is now called Wilson's theorem; the geometric construction known as Alhazen's problem.
- 07 Al-Bīrūnī Rigorous trigonometric measurement of the Earth's radius; a career long standard of observational precision and careful error reporting.
- 08 Omar Khayyām A geometric classification and conic section solution of cubic equations; a critique of Euclid's parallel postulate that anticipates non Euclidean geometry; the Jalālī calendar with its eight in thirty three leap year cycle.
- 09 Al-Samaw'al al-Maghribī A closed form expression for the sum of the first n squares; a combinatorics problem recovering ten unknowns from 210 combination sum equations; the surviving detailed record of Al-Karajī's inductive method.
- 10 Sharaf al-Dīn al-Ṭūsī Existence conditions for the positive roots of cubics tied to a maximum value criterion, and a Ruffini Horner iteration for numerical roots, with the Rashed / Hogendijk reading of his method openly hedged.
- 11 Naṣīr al-Dīn al-Ṭūsī The first Arabic treatise to treat trigonometry as an autonomous subject, the Ṭūsī couple that decomposes linear motion into two circular motions, and the Marāgha observatory tradition.
- 12 Jamshīd al-Kāshī 2π computed to nine sexagesimal places (sixteen decimal places) from a polygon with 3 × 228 sides, and an iterative cubic equation method for sin 1°.
How to read this archive
Each entry follows the same structure. It opens with dates and geographic base, gives a short orientation of the scholar in their own historical setting, lists principal treatises with their sources, and then walks through the relevant to olympiad mathematics attributable to them. The final section on each page is a citation block: every URL used to build the page, listed openly so any claim can be checked.
The archive will grow. Any new entry added here will meet the same standard: verified through two sources dates, named scholar attribution for contested claims, hedges preserved where the underlying literature hedges. If you spot an error, the corrections process tells you how to report it.
Sources for this index page: MacTutor History of Mathematics biographies for Al-Khwārizmī, Thābit ibn Qurra, Al-Battānī, Abū al-Wafāʾ al-Būzjānī, Al-Karajī, Ibn al-Haytham, Al-Bīrūnī, Omar Khayyām, Al-Samaw'al, Sharaf al-Dīn al-Ṭūsī, Naṣīr al-Dīn al-Ṭūsī, al-Kāshī. Verified across sources against Britannica biographical entries for each scholar and, for Khayyām, the Stanford Encyclopedia of Philosophy.