Qutb al-Din al-Shirazi (1236-1311) was a Persian polymath of the Ilkhanid period whose contributions spanned astronomy, mathematics, medicine, philosophy, music theory, and geography. Born in Shiraz in the Fars region of present-day Iran, he studied under his father - a physician and Sufi - and later became a student of the renowned astronomer and philosopher Nasir al-Din al-Tusi at the Maragha observatory. Al-Shirazi is most often cited for his work in optics, particularly his explanation of the rainbow, and for his role in the transmission and development of the Maragha school's planetary models, which departed from strict Ptolemaic astronomy.

Al-Shirazi was born on 29 October 1236 in Shiraz to a family with a tradition of medicine and Sufism. His father, Zia al-Din Mas'ud al-Kazeruni, was a physician affiliated with the Suhrawardiyya Sufi order. Al-Shirazi studied medicine under his father and, following his father's death, traveled to the Maragha observatory in Azerbaijan, where he became a principal student of Nasir al-Din al-Tusi. He later served as a judge (qadi) in Malatya and Sivas under Ilkhanid administration, and traveled through Anatolia, Syria, and Egypt. He died on 7 February 1311 in Tabriz.

Al-Shirazi is credited, along with his student Kamal al-Din al-Farisi, with producing one of the earliest geometrically rigorous explanations of the rainbow. His account, drawing on Ibn al-Haytham's optics, described the refraction and internal reflection of sunlight within individual water droplets. Al-Farisi's own treatment in Tanqih al-Manazir is sometimes regarded as the more mathematically complete exposition of the two, which bears directly on the question of attribution. Historians of science have debated the relative contributions of al-Shirazi and al-Farisi, as well as the independence of this work from contemporaneous European investigations by Theodoric of Freiberg. A separate history of rainbow optics traces this line of inquiry.

At Maragha, al-Shirazi worked within a tradition that sought to resolve mathematical inconsistencies in Ptolemaic planetary theory - particularly the equant problem - without abandoning the general framework of geocentric, sphere-based cosmology. His major astronomical encyclopedia, the Nihayat al-Idrak fi Dirayat al-Aflak (The Limit of Comprehension in the Knowledge of the Heavens), and his al-Tuhfa al-Shahiyya presented alternative planetary configurations. Some historians of science have identified structural similarities between Maragha planetary models and those later used by Copernicus, and debate centers on whether these similarities reflect direct or indirect transmission or independent parallel development. That debate is addressed on the Maragha School and Copernicus Debate page.

Al-Shirazi produced a major commentary on Ibn Sina's Canon of Medicine and wrote on pharmacology, ethics, and Sufi thought. His geographical work, the Nuzhat al-Qulub, compiled information on the regions of the Islamic world and remains a reference for historians of medieval Islamic geography. He also wrote on music theory, contributing to the tradition of systematic classification of melodic modes.

There is broad scholarly consensus that al-Shirazi was a significant figure in medieval Islamic science and philosophy, and that the Maragha school represented a substantive development in mathematical astronomy. The extent of his specific influence on later European astronomy and on al-Farisi's optical work remains a matter of active historical inquiry rather than settled consensus.

Two areas of ongoing interpretive dispute are relevant to this article.

On the rainbow explanation, the primary question is whether al-Shirazi or al-Farisi deserves principal credit, given that al-Farisi's Tanqih al-Manazir presents a more detailed geometric treatment. A secondary question is whether the near-contemporary work of Theodoric of Freiberg in Europe was independent or reflects any common source. Most historians treat the two traditions as independent.

On the Maragha-Copernicus question, one camp holds that the mathematical devices shared between Maragha astronomers and Copernicus are too specific to be coincidental, implying some route of transmission - whether through Byzantine intermediaries, traveling scholars, or manuscript circulation. A competing view holds that similar mathematical problems independently generated similar solutions, and that no documentary evidence of transmission has been established. See Maragha School and Copernicus Debate for full treatment.

• Maragha Observatory - History
• Nasir al-Din al-Tusi
• Kamal al-Din al-Farisi
• Maragha School and Copernicus Debate
• Islamic Golden Age Astronomy
• Rainbow Optics - History
• Ibn Sina

1. Seyyed Hossein Nasr, Islamic Science: An Illustrated Study (World of Islam Festival Publishing, 1976).
2. F. Jamil Ragep, “Tusi and Copernicus: The Earth's Motion in Context,” Science in Context 14 (2001), pp. 145-163.
3. A. I. Sabra, “The Optics of Ibn al-Haytham,” Bulletin of the School of Oriental and African Studies 57 (1994).
4. E. S. Kennedy, “The Astronomical Tables of Qutb al-Din al-Shirazi,” Orientalia 34 (1965).
5. Carl Schoy and others cited in Edward Grant, Planets, Stars, and Orbs: The Medieval Cosmos (Cambridge University Press, 1994).
6. Hamd-Allah Mustawfi Qazvini (tr. G. Le Strange), Nuzhat-al-Qulub (Luzac, 1915) - cited for context on the medieval Islamic geographical tradition; note that Qazvini's work shares a title with al-Shirazi's own geographical encyclopedia but is a distinct text by a different author.