Omar Khayyam and the Jalali Calendar Reform (1079)

Omar Khayyam was a Persian mathematician and astronomer who led the team that created the Jalali calendar, a precise solar calendar introduced in March 1079 at the court of the Seljuk sultan Malik-Shah. He also made major advances in algebra and geometry. Yet in Europe and North America he is best known as the poet of the Rubaiyat, a reputation that rests largely on a Victorian English translation.

Background: Khayyam in the Seljuk world

Ghiyath al-Din Abu’l-Fath Umar ibn Ibrahim al-Khayyami was born in Nishapur in Khurasan, north-eastern Iran, in 1048, a few years after the Seljuk Turks took the region. His name may come from a family trade of tent-making. He studied the sciences of his day, including mathematics, astronomy and philosophy in the tradition of Avicenna.

In the early 1070s he worked in Samarkand under the patronage of a local judge, and there he wrote his most important mathematical work. Around 1074 he was invited to Isfahan by Malik-Shah and his powerful vizier Nizam al-Mulk, who wanted an observatory and a reformed calendar.

Why a new calendar was needed

The Islamic religious calendar is lunar, with twelve months of 29 or 30 days, about 354 days in all. It drifts through the seasons by around 11 days a year, so it is unsuitable for farming and for collecting taxes on harvests.

Iran also used an old Persian solar calendar of 365 days without leap years. Over centuries it had drifted badly: Nowruz, the Persian new year, no longer fell at the spring equinox. Tax dates tied to the calendar no longer matched the harvest, causing hardship and disputes.

The Jalali reform of 1079

Malik-Shah assembled a group of astronomers at Isfahan, with Khayyam as its leading figure. Other names recorded include Abu’l-Muzaffar al-Isfizari and Maymun ibn Najib al-Wasiti. They made observations over several years at an observatory whose exact location is not known.

The new calendar was named Jalali after Malik-Shah’s title, Jalal al-Din. Its era began on the spring equinox of March 1079, usually given as 15 March 1079 in the Julian calendar. The year began at Nowruz, the moment of the vernal equinox, and was divided into twelve months, with extra days added so that the calendar stayed in line with the solar year.

Leap days were placed according to the astronomers’ calculation of when the equinox fell. Later writers describe a cycle of eight leap years in every 33 years, which gives an average year of about 365.2424 days, extremely close to the true tropical year. Whether this exact rule was used from the start is debated, because the calendar was based on observation rather than a fixed formula.

By the numbers

How the calendar worked in practice

The Jalali year kept the old Persian month names, such as Farvardin, the first month of spring. In the form described by later astronomers, the year had twelve months of 30 days plus five extra days, with a sixth extra day in leap years. The modern Iranian calendar instead uses six months of 31 days, five of 30 and a final month of 29 or 30 days, a change made in 1925.

The key innovation was the starting point. Each year began on the day of the spring equinox as calculated by the astronomers, depending on whether the equinox fell before or after noon. This meant that Nowruz would always come at the start of spring, and festivals and tax dates tied to the farming year stayed in place.

The astronomers also needed accurate values for the length of the solar year and the motion of the sun, which required careful observation over several years. Later sources say the observatory produced a set of astronomical tables, the Zij-i Malikshahi, but only fragments of it survive. Because much of the original documentation is lost, modern reconstructions of the calendar depend on later Persian astronomers, who sometimes disagree about its exact rules and month lengths.

Khayyam the mathematician

Khayyam’s Treatise on Demonstration of Problems of Algebra, written around 1070, was a landmark. He classified equations up to the third degree and showed how each type of cubic equation could be solved geometrically by the intersection of conic sections such as circles, parabolas and hyperbolas. He hoped that an arithmetical solution might be found by later scholars; the general solution came only in sixteenth-century Italy.

In a commentary of 1077 on the difficulties in Euclid’s Elements, he examined the parallel postulate, which earlier mathematicians had tried to prove. His quadrilateral argument anticipates work by the Italian Giovanni Saccheri in the eighteenth century, part of the long path to non-Euclidean geometry.

After the patrons died

In 1092 Nizam al-Mulk was assassinated and Malik-Shah died weeks later. Funding for the observatory ended, and Khayyam lost favour at court. He spent time in Merv and other cities and eventually returned to Nishapur, where he died around 1131.

Medieval biographers describe Khayyam as a learned but reserved scholar, respected for his knowledge of philosophy, medicine and astronomy, and sometimes suspected by religious critics of freethinking. The writer Nizami Arudi, who met him in Balkh around 1112 and later visited his grave in Nishapur, left one of the earliest accounts of him, recalling Khayyam’s prediction that his tomb would lie where trees shed blossoms on it.

The Jalali calendar remained in use in Iran for centuries in various forms. In 1925 the Iranian parliament adopted the Solar Hijri calendar, which keeps the Jalali principle of beginning the year at the equinox and is still Iran’s official calendar, as it is in Afghanistan.

The Rubaiyat and the poet’s fame

A rubai is a Persian quatrain, a four-line poem. Hundreds of quatrains, many on wine, the brevity of life and doubt about the afterlife, have been attributed to Khayyam. The earliest attributions appear decades after his death, and later manuscripts added many more, so scholars cannot agree on which, if any, are his.

In 1859 Edward FitzGerald published the Rubáiyát of Omar Khayyám, a loose English rendering of 75 quatrains. It sold poorly at first, then became a Victorian favourite, went through several revised editions and inspired clubs, illustrated editions and countless quotations. The modern mausoleum in Nishapur, completed in 1963, honours both the poet and the scientist.

Timeline

• 1048: Omar Khayyam is born in Nishapur.
• c. 1070: He writes his treatise on algebra in Samarkand.
• c. 1074: He is invited to Isfahan by Malik-Shah and Nizam al-Mulk.
• 1077: Commentary on Euclid’s postulates.
• 1079, March: Era of the Jalali calendar begins at the spring equinox.
• 1092: Deaths of Nizam al-Mulk and Malik-Shah; the observatory declines.
• c. 1131: Khayyam dies in Nishapur.
• 1859: FitzGerald’s Rubaiyat is published in London.

Why it matters

The Jalali reform produced one of the most accurate calendars of the pre-modern world and shaped the calendar Iran still uses. Its leading astronomer, Omar Khayyam, was also a major mathematician, and his double fame as scientist and poet makes him one of the best-known figures of medieval Persia.