Al-Tusi was one of the greatest scientist, mathematician, astronomer, philosopher, theologian and physician of his time. He was a prolific writer. He wrote many treatises on such varied subjects as Algebra, Arithmetic, Trigonometry, Geometry, Logic, Metaphysics, Medicine, Ethics, and Theology.
Abu Jafar Muhammad ibn Muhammad Ibn al-Hasan Nasir al-Din al-Tusi was born in Tus, Khurasan (present Iran) in 1201 C.E. He studied sciences and philosophy under the tutelage of Kamal al-Din Ibn Yunus. Al-Tusi was kidnaped by the Isma'ili Hasan Bin Sabah's agents and sent to Alamut where he remained until its capture by the Mongol Halagu Khan in 1256 C.E. Impressed by Al-Tusi's exceptional abilities and astrological competency, Ilkhanid Halagu Khan appointed him as one of his ministers. Later, he served as an administrator of Auqaf.
In 1262, he built an observatory at Meragha and directed its activity. It was equipped with the best instruments from Baghdad and other Islamic centers of learning. It contained a twelve-feet wall quadrant made from copper and an azimuth quadrant and 'turquet' invented by Al-Tusi. Other instruments included Astrolabes, representations of constellation, epicycles, and shapes of spheres. Al-Tusi designed several other instruments for the Observatory.
Al-Tusi produced a very accurate table of planetary movements and a star catalogue, and he published it under the title "Al-Zij-Ilkhani" which was dedicated to Ilkhan, Halagu Khan. The tables were developed from observations over a twelve-year period and were primarily based on original observations.
Al-Tusi calculated the value of 51o for the precession of the equinoxes. Al-Tusi was among the first of several Muslim astronomers who pointed out several serious shortcomings in Ptolemy's models based on mechanical principles and modified it. His critique on the Ptolemy's theories convinced future astronomers of the need to develop an alternative model ending in Copernicus famous work. The Al-Zij Ilkhani was the most popular book among astronomers until fifteenth century.
His memoir on astronomy entitled "Tadhkira Fi Ilm Al-Haya", includes his ingenious device for generating rectilinear motion along the diameter of the outer circle from two circular motions. At the end of his long outstanding career, he moved to Baghdad and died within a year in 1274 in Kadhimain (near Baghdad, present Iraq).
Al-Tusi pioneered spherical trigonometry which includes six fundamental formulas for the solution of spherical right-angled triangles. One of his most important mathematical contributions was the treatment of trigonometry as a new mathematical discipline. He wrote on binomial coefficients which Pascal later introduced.
Al-Tusi revived the philosophy of Ibn Sina. His book "Akhlaq-i-Nasri" (Nasirean Ethics) was regarded as the most important book on ethics and was popular for centuries. The Tajrid-al-Aqaid was an excellent work on Islamic scholastic philosophy. He also composed a few verses of poetry.
Al-Tusi was a prolific writer. He wrote his works in Arabic and Persian. According to George Sarton, sixty four treatises are known to have survived. These were translated into Latin and other European languages in the Middle Ages. Al-Tusi's book "Shaq al-Qatta" was translated into Latin by the title "Figura Cata". Among Al-Tusi's well-known students are Nizam al-Araj, who wrote a commentary on the Almagest, and Qutb ad-Din ash-Shirazi, who gave the first satisfactory mathematical explanation of the rainbow.
Al-Tusi's contributions were highly valued for several centuries.