Jamshid al-Kashi

Jamshid ibn Masud al-Kashi was one of the greatest mathematicians and astronomers of the medieval Islamic world, born around 1380 CE in the ancient city of Kashan in present-day Iran. He grew up in difficult circumstances, living through years of poverty and hardship before eventually finding patronage and recognition for his extraordinary talents.

Al-Kashi's early career was marked by self-directed study and astronomical observation, during which he produced works of remarkable precision despite having few resources. His mathematical genius drew the attention of the great Timurid prince Ulugh Beg, who was himself a passionate astronomer and scholar. Around 1420 CE, al-Kashi was invited to Samarkand to join the celebrated academy and observatory that Ulugh Beg was building, an institution that would become one of the finest scientific centers of the era.

At the Samarkand observatory, al-Kashi flourished. His most celebrated achievement was the computation of pi to sixteen decimal places — an accuracy that would not be surpassed in the Islamic world for centuries and was not matched in Europe for nearly two hundred years. He accomplished this using a polygon of three times two to the twenty-eighth power sides, demonstrating extraordinary computational endurance and ingenuity. He also developed the decimal fraction system and the formula now known as the Law of Cosines, which he called the theorem of the chord.

His major works include the Miftah al-Hisab (Key of Arithmetic) and the Risala al-Muhitiyya (Treatise on the Circumference). He died in Samarkand in 1429 CE, leaving behind a legacy that would influence mathematicians for generations. Ulugh Beg praised him as a singular scholar whose equal could not be found from east to west.