Guo Shoujing

Guo Shoujing (; 1231–1316), courtesy name Ruosi , was a Chinese astronomer, hydraulic engineer, mathematician, and politician of the Mongol Empire and Yuan dynasty. The later Johann Adam Schall von Bell (1591–1666) was so impressed with the preserved astronomical instruments of Guo that he called him "the Tycho Brahe of China." Jamal ad-Din cooperated with him. He was raised primarily by his paternal grandfather, Guo Yong, who was famous throughout China for his expertise in a wide variety of topics, ranging from the study of the Five Classics to astronomy, mathematics, and hydraulics. Guo Shoujing was a child prodigy, showing exceptional intellectual promise. By his teens, he obtained a blueprint for a water clock which his grandfather was working on, and realized its principles of operation. He improved the design of a type of water clock called a lotus clepsydra, a water clock with a bowl shaped like a lotus flower on the top into which the water dripped. After he had mastered the construction of such water clocks, he began to study mathematics at the age of 16. From mathematics, he began to understand hydraulics, as well as astronomy. After the success of this project, Kublai Khan sent Guo off to manage similar projects in other parts of the empire. He became the chief advisor of hydraulics, mathematics, and astronomy for Kublai Khan.

Guo began to construct astronomical observation devices. He has been credited with inventing the gnomon, the square table, the abridged or simplified armilla, and a water powered armillary sphere called the Ling Long Yi. The gnomon is used to measure the angle of the sun, determine the seasons, and is the basis of the sundial, but Guo Shoujing revised this device to become much more accurate and improved the ability to tell time more precisely. The square table was used to measure the azimuth of celestial bodies by the equal altitude method and could also be used as protractor. The abridged or simplified armilla was used to measure the angle of the sun, as well as the position of any celestial body. The Ling Long Yi is similar to an abridged armilla except larger, more complex, and more accurate. Kublai Khan, after observing Guo's mastery of astronomy, ordered that he, Zhang, and Wang Xun make a more accurate calendar. They built 27 observatories throughout China in order to gain thorough observations for their calculations. In 1280, Guo completed the calendar, calculating a year to be 365.2425 days, just 26 seconds off the year's current measurement. In 1283, Guo was promoted to director of the Observatory in Beijing and, in 1292, he became the head of the Water Works Bureau. Throughout his life he also did extensive work with spherical trigonometry. After Kublai Khan's death, Guo continued to be an advisor to Kublai's successors, working on hydraulics and astronomy. However, he never left China which would have made it more difficult for him to access others' ideas. Otherwise, Guo was highly regarded throughout history, by many cultures, as a precursor of the Gregorian calendar as well as the man who perfected irrigation techniques in the new millennium. Many historians regard him as the most prominent Chinese astronomer, engineer, and mathematician of all time.

His calendar would be used for the next 363 years, the longest period during which a calendar would be used in Chinese history. He also used mathematical functions in his work relating to spherical trigonometry, building upon the knowledge of Shen Kuo's (1031–1095) earlier work in trigonometry. It is debated amongst scholars whether or not his work in trigonometry was based entirely on the work of Shen, or whether it was partially influenced by Islamic mathematics which was largely accepted at Kublai's court. An important work in trigonometry in China would not be printed again until the collaborative efforts of Xu Guangqi and his Italian Jesuit associate Matteo Ricci in 1607, during the late Ming Dynasty. as an example of solid practical scholarship, anticipating the rise of the Changzhou School of Thought and spread of the "evidential learning".

Asteroid 2012 Guo Shou-Jing is named after him, as is the Large Sky Area Multi-Object Fibre Spectroscopic Telescope near Beijing.