Nasir al-Din al-Tusi

1201-1274

Arab Mathematician and Astronomer

In 1259, Nasir al-Din al-Tusi persuaded the Mongol conqueror Hulagu Khan (c. 1217-1265) to establish an observatory at Maragheh in what is now Azerbaijan. The Maragheh observatory became a center of learning, producing information such as the tables contained in al-Tusi's Zij-i ilkhani. Al-Tusi was not merely concerned with mathematics in its applied form, however; in fact, he is often given credit as the first thinker to use pure trigonometry.

Al-Tusi, also known as Muhaqqiq-i Tusi, Kwaja-yi Tusi, and Khwaja Nasir, was born in the town of Tus in northeastern Iran. His father was a jurist in the Shi'ite Islamic sect, and al-Tusi received a strong religious education supplemented with teachings, provided by his uncle, in logic, physics, and mathematics. As a teenager he studied philosophy, medicine, and mathematics in the Persian city of Nishapur.

From at least the time of al-Tusi's early teen years, his homeland had been in a state of turmoil, threatened from without by the prospect of Mongol invasion and from within by the Assassins. The latter, a radical political-religious group and perhaps the world's first formally organized terrorist organization, invited al-Tusi to join their numbers as a scholar under their protection. Whether this "invitation" was in fact a command is not known, nor is it clear whether al-Tusi, who threw in his lot with the Assassins after 1220—when he would have been only about 20 years old—did so voluntarily.

Under the protection of the Assassins in their various strongholds, al-Tusi continued his mathematical and scientific scholarship until Hulagu's forces stormed the Assassins' redoubt in 1256. Again, it is not clear whether al-Tusi betrayed his allies, or simply regarded Hulagu as someone liberating him from kidnappers—though in fact he had been with the Assassins for more than three decades by then. In any case, the Mongols slaughtered the Assassins, and al-Tusi suddenly found himself under the care of Hulagu, who greatly admired his scholarship.

When the dust of the invasion settled and Hulagu established his capital at Maragheh, al-Tusi suggested the idea of the observatory, which met with the new khan's hearty approval. It took three years to construct and prepare the observatory, during which time the Mongols brought in Chinese astronomers to assist their Persian counterparts. The completed observatory included a large copper wall quadrant, an azimuth quadrant, and other instruments designed by al-Tusi, and a library containing books on all manner of scientific pursuits. In fact the observatory was far more than simply a place for observing stars, and became a center for inquiry in mathematics, various sciences, and philosophy.

Another product of the Maragheh observatory was al-Tusi's Zij-i ilkhani, or "Ilkhanic Tables." (Hulagu had given himself the title "il-Khan.") Written in Persian and translated into Arabic later, the book contained 12 years' worth of observations on the planets. In another astronomical work, al-Tusi developed a mathematical principle that came to be known as the "Tusi-couple," which enabled him to describe motion in uniform terms, regardless of whether that motion was linear or circular.

This in turn led to new hypotheses on the movement of planets, which some scholars consider the most important contribution to the understanding of the planetary system between the time of Ptolemy (c. 100-170) and that of Copernicus (1473-1543). It is possible that the latter may in fact have modeled his own use of a similar method on the Tusi couples.

Al-Tusi's Treatise on the Quadrilateral was perhaps the first mathematical work in history to treat trigonometry as a discipline in its own right, rather than as a mere application of astronomy. He also wrote on nth roots of an integer, and provided commentaries or revisions to Arabic versions of works by a variety of ancient Greek mathematical and scientific figures. Other writings by al-Tusi addressed logic, medicine, minerals, and ethics. He died on June 26, 1274, near Baghdad.

JUDSON KNIGHT