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“Al-Khayyámi.” Science and mathematics became his passions, and he spent most of his spare time on them. Eventually Nizam returned, secured a position in the government, and became administrator of affairs to the sultan Alp Arslan, with an office in Naishapur.
    Since Nizam was now rich and famous, Omar and Hasan claimed their rights under the pact. Nizam asked the sultan for permission to assist his friends, and when it was granted he honored the agreement. Hasan received a well-paid government job, but Omar merely wished to continue his scientific studies in Naishapur, where he would pray for the health andwell-being of Nizam. His old school friend arranged for Omar to be given a government salary, to free his time for study, and the deal was done.
    Hasan later tried to overthrow a senior official and lost his sinecure, but Omar continued serenely on and was appointed to a commission whose mandate was to reform the calendar. The Persian calendar was based on the movements of the sun, and the date of the first day of the new year was subject to change, which was confusing. It was just the job for a competent mathematician, and Omar applied his knowledge of mathematics and astronomy to calculate when New Year’s Day should fall in any given year.
    Around this time, he also penned the Rubaiyat , which loosely translates as “quatrains,” a poetic form. A rubai was a four-line verse with a rather specific rhyming pattern—more accurately, one of two possible patterns—and a rubaiyat was a collection of verses in this form. One verse makes a clear reference to his work on reforming the calendar:
    Ah, but my computations, People say,
Reduced the Year to better Reckoning? Nay,
’Twas only striking from the Calendar
Unborn To-morrow and dead Yesterday.
    Omar’s verses were distinctly nonreligious. Many of them praise wine and its effects. For instance:
    And lately, by the Tavern Door agape,
Came shining through the Dusk an Angel Shape
Bearing a Vessel on his Shoulder; and
He bid me taste of it; and ’twas—the Grape!
    There are wry allegorical references to wine, as well:
    Whether at Naishápúr or Babylon,
Whether the Cup with sweet or bitter run,
The Wine of Life keeps oozing drop by drop,
The Leaves of Life keep falling one by one.
    Other verses poke fun at religious beliefs. One wonders what the Sultan thought of the man he had put on retainer, and what the imam thought of the outcome of his teaching.
    Meanwhile, the disgraced Hasan, having been forced to leave Naishapur, fell in with a gang of bandits and made use of his superior education to become its leader. In the year 1090 those bandits, under Hasan’s command, captured Alamut castle in the Elburz Mountains, just south of the Caspian Sea. They terrorized the region, and Hasan became notorious as the Old Man of the Mountains. His followers, known as the Hashishiyun for their use of the drug hashish (a very potent form of cannabis), built six mountain fortifications, from which they would emerge to kill carefully selected religious and political figures. Their name was the origin of the word “assassin.” So Hasan managed to become rich and famous in his own right, as befitted a student of Mowaffak, though he was not, by this time, disposed to share his fortune with his old schoolmates.
    While Omar calculated astronomical tables and worked out how to solve the cubic, Nizam pursued his political career until, in a touch of exquisite irony, Hasan’s bandits assassinated him. Omar lived on to the age of 76, dying—so it is said—in 1123. Hasan died the following year, aged 84. The assassins continued to wreak political havoc until they were wiped out by the Mongols, who conquered Alamut in 1256.

    To return to Omar’s mathematics: Around 350 BCE the Greek mathematician Menaechmus discovered the special curves known as “conic sections,” which he used, scholars believe, to solve the problem