Before the Rubaiyat, Khayyam solved cubic equations
English readers met Omar Khayyam through Edward FitzGerald’s 1859 quatrains. In his own century he was the mathematician who gave a general geometric solution for all third-degree polynomials and timed the solar year so precisely that the Jalali calendar still underpins Persia’s year nearly a millennium later.
The polymath later called Omar Khayyam entered the world in Nishapur, a busy Seljuk Khorasan city, in 1048. Bayhaqi, who knew him personally, left a Gemini horoscope that modern readers fix as 18 May 1048; whether “Khayyam” truly recalls tent-making kin remains debated. He memorised large stretches of the Quran, studied under Mawlana Qadi Muhammad and Abu’l-Hasan al-Anbari—including Ptolemy’s Almagest—and sat with Imam Muwaffaq Nishaburi among noble pupils. Around 1068 he worked in Bukhara’s Ark library; around 1070 in Samarkand he opened his Algebra treatise under judge Abu Tahir, while Karakhanid Shams al-Mulk Nasr placed him in honour beside the throne.
Peace with Sultan Malik-Shah in 1073–4 brought a summons via Nizam al-Mulk. From 1074 Khayyam led Isfahan observatory work that closed in 1079 with a year-length of 365.24219858156 days—within a whisker of later measured values. That campaign shaped the Jalali solar calendar and its thirty-three-year intercalation, ancestor of the Persian calendar still used. Surviving treatises include the Euclid commentary finished December 1077, the quadrant essay, and Algebra likely of 1079. He offered the first general geometric attack on all cubics (positive roots) by conic intersections, and analysed acute, obtuse, and right summit angles of the Khayyam–Saccheri quadrilateral—ideas that reached Europe through Tusi, Wallis, and Saccheri’s 1733 Euclid book.
After Malik-Shah and Nizam al-Mulk died, Khayyam lost court favour, pilgrimaged to Mecca amid charges of unorthodoxy, briefly served Sultan Sanjar, then withdrew to Nishapur. He died there on 4 December 1131; disciple Nizami Aruzi later found the tomb under pear and apricot blossom, matching a rose-scattering prophecy Khayyam had voiced in Balkh. Rubāʿiyāt attributed to him conquered Victorian taste via FitzGerald—yet his own age first celebrated the calendar and the cubics.
Source: Omar Khayyam
