Nasir al-Din al-Tusi

By Julien Moreau

He was the most famous scholar in Persia, and the Mongols were coming. Nasir al-Din al-Tusi, born in 1201 in Tus, Khurasan, had built his reputation writing on everything — logic, ethics, theology, mathematics — and had taken refuge with the Ismailis in the mountain fortress of Alamut, where he directed their libraries. In 1256, Hulagu Khan's armies destroyed Alamut. Tusi did what brilliant men have always done at the edge of the sword: he changed patrons. He became the khan's scientific adviser, and he made the conqueror pay for the greatest observatory the world had ever seen.

Maragha, in northwestern Persia, rose around 1259: a hilltop complex with a great mural quadrant, armillary spheres, and a library said to hold 400,000 volumes, staffed by astronomers summoned from Damascus to China. Tusi directed it, and from its instruments came the Zij-i Ilkhani, the Ilkhanid Tables — star catalogs and planetary positions of unprecedented precision, computed for a thirty-year cycle and used across Asia for centuries.

But Tusi's deepest work was theoretical, and it solved a problem that had poisoned astronomy for fourteen hundred years. Ptolemy's models predicted the planets' positions, but only by cheating: the equant, a point off-center from which a planet's motion merely appeared uniform, violating the sacred principle of uniform circular motion. In his Tadhkira, the Memoir on Astronomy, Tusi offered the device now called the Tusi couple — a small circle rolling inside a circle twice its diameter, whose point traces a perfect straight line. Two uniform circular motions combine into linear oscillation: the equant could be discarded, and Ptolemy could be made honest.

In the same years he did something equally radical in mathematics. His Treatise on the Quadrilateral presented trigonometry — the sines, the spherical triangles — as a discipline independent of astronomy, the first such treatment anywhere. Sines, cosines, and the law of sines stood on their own feet for the first time.

The Maragha school's manuscripts traveled west through Byzantium, and here the story takes its famous turn: Copernicus, three centuries later, used the Tusi couple in De revolutionibus to solve the same equant problem, almost certainly from a Greek intermediary. The device that killed Ptolemy's astronomy was invented by a Persian in a Mongol observatory. Tusi died in 1274, still director of Maragha, and was buried in Baghdad — the scholar who taught the conquerors to look at the stars.

Impact on civilization

Al-Tusi reformed astronomy from the inside, proving Ptolemy's system could be purged of its contradictions without being abandoned — and in doing so forged the very tool Copernicus would use to overthrow it. The Tusi couple, generating straight-line motion from circles, is the most consequential geometric device between Apollonius and Kepler; it crossed from Maragha to Renaissance Europe and did quiet work inside the Copernican revolution. His founding of trigonometry as an independent science gave mathematicians their own subject, no longer a servant of stargazing. And Maragha itself — the research institute with its library, instruments, and international staff — became the template for every great observatory that followed, from Samarkand to Greenwich.