Abu Jafar Muhammad Ibn Muhammad Ibn al-Hasan Nasir al-Din al-Tusi was born in Tus (Khurasan) in 1201 A.D. He learnt sciences and philosophy from Kamal al-Din ibn Yunus and others. He was one of those who were kidnapped by Hasan bin Sabah's agents and sent to Almut, Hasan's stronghold. In 1256 when Almut was conquered by the Mongols, Nasir al-Din joined Halagu's service.
Halagu Khan was deeply impressed by his knowledge, including his astrological competency; appointed him as one of his ministers, and, later on, as administrator of Auqaf. He was instrumental in the establishment and progress of the observatory at Maragha. In his last year of life he went to Baghdad and died there.
Nasir al-Din was one of the greatest scientists, philosophers, mathematicians, astronomers, theologians and physicians of the time and was a prolific writer. He made significant contributions to a large number of subjects, and it is indeed difficult to present his work in a few words. He wrote one or several treatises on different sciences and subjects including those on geometry, algebra, arithmetic, trigonometry, medicine, metaphysics, logic, ethics and theology. In addition he wrote poetry in Persian.
In mathematics, his major contribution would seem to be in trigonometry, which was compiled by him as a new subject in its own right for the first time. Also he developed the subject of spherical trigonometry, including six fundamental formulas for the solution of spherical right-angled triangles.
As the chief scientist at the observatory established under his supervision at Maragha, he made significant contributions to astronomy. The observatory was equipped with the best possible instruments, including those collected by the Mongol armies from Baghdad and other Islamic centres. The instruments included astrolabes, representations of constellations, epicycles, shapes of spheres, etc. He himself invented an instrument 'turquet' that contained two planes. After the devoted work of 12 years at the observatory and with the assistance of his group, he produced new astronomical tables called Al-Zij-Ilkhani dedicated to Ilkhan (Halagu Khan). Although Tusi had contemplated completing the tables in 30 years, the time required for the completion of planetary cycles, but he had to complete them in 12 years on orders from Halagu Khan. The tables were largely based on original observations, but also drew upon the then existing knowledge on the subject. The Zij Ilkhani became the most popular tables among astronomers and remained so till the 15th century. Nasir al-Din pointed out several serious shortcomings in Ptolemy's astronomy and foreshadowed the later dissatisfaction with the system that culminated in the Copernican reforms.
In philosophy, apart from his contribution in logic and metaphysics, his work on ethics entitled Akhlaq-i-Nasri became the most important book on the subject, and remained popular for centuries. His book Tajrid-al-'Aqaid was a major work on al-Kalam (Islamic Scholastic Philosophy) and enjoyed widespread popularity. Several commentaries were written on this book and even a number of super commentaries on the major commentaries, Sharh Qadim and Sharh Jadid.
The list of his known treatises is exhaustive; Brockelmann lists 56 and Sarton 64. About one-fourth of these concern mathematics, another fourth astronomy, another fourth philosophy and religion, and the remainder other subjects. The books, though originally written in Arabic and Persian, were translated into Latin and other European languages in the Middle Ages and several of these have been printed.
Tusi's influence has been significant in the development of science, notably in mathematics and astronomy. His books were widely consulted for centuries and he has been held in high repute for his rich contributions.