Omar Khayyam

Key Accomplishments

• Classified and solved cubic equations geometrically using intersections of conic sections
• Led the reform of the Persian calendar, producing the remarkably accurate Jalali calendar
• Made important contributions to the theory of parallels (Euclid's fifth postulate)
• Composed the "Rubaiyat," one of the most beloved collections of poetry in world literature

The Full Story

Ghiyath al-Din Abu al-Fath Umar ibn Ibrahim al-Khayyam was born in 1048 CE in Nishapur, one of the great cities of Khorasan. He studied under leading scholars of his time and gained the patronage of the Seljuq vizier Nizam al-Mulk, whose court at Isfahan became the center of Khayyam's most productive years.

Khayyam's most significant mathematical work, "Risala fi al-Barahin ala Masa'il al-Jabr wal-Muqabala" (Treatise on Demonstration of Problems of Algebra), completed around 1070, was a systematic classification and geometric solution of cubic equations. He identified nineteen types of cubic equations and provided geometric solutions using the intersection of conic sections, an approach that would not be surpassed until the algebraic solutions of del Ferro and Cardano in the 16th century. He also made important contributions to the understanding of Euclid's parallel postulate.

In 1079, Sultan Malik-Shah commissioned Khayyam to lead a team of astronomers in reforming the Persian calendar. The resulting Jalali calendar was extraordinarily accurate, with a year length of 365.2424 days, closer to the true solar year than the Gregorian calendar introduced 500 years later. It forms the basis of the modern Iranian calendar.

In the West, Khayyam is cherished for his "Rubaiyat" (Quatrains), meditative poems on the themes of mortality, the fleeting nature of time, and the pleasures of existence. Edward FitzGerald's 1859 English translation transformed these verses into one of the most popular works of poetry in the English language. Khayyam died in 1131 in his native Nishapur, revered as both a supreme mathematician and a poet of profound insight.

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Sources

• [1]Roshdi Rashed and Bijan Vahabzadeh, "Omar Khayyam: The Mathematician" (Mage Publishers, 2000)
• [2]Ali Dashti, "In Search of Omar Khayyam" (Routledge, 2012)
• [3]Victor J. Katz, "A History of Mathematics: An Introduction" (Pearson, 2008)