Shen Kuo genius

Shen Kuo (1031-1095)

Shen Kuo  (1031-1095)

Work & Publications
Genius Quotes
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Age of Death
Birth Place
Qiantang, Song Empire
Death Place
Runzhou, Song Empire
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Meet Shen Kuo, a remarkable polymath and statesman from the Song Dynasty in China (960-1279). With a courtesy name of Cunzhong and a pseudonym of Mengqi Weng, Shen was renowned for his exceptional skills in mathematics, optics, and horology. Throughout his career as a civil servant, Shen held various high-ranking positions including finance minister, state inspector, head official for the Bureau of Astronomy, Assistant Minister of Imperial Hospitality, and academic chancellor. As a dedicated member of the Reformist faction known as the New Policies Group, led by Chancellor Wang Anshi, Shen's political allegiance added to his influence in the court.

Shen Kuo's Breakthrough in Navigation: The Magnetic Compass

Shen Kuo's Dream Pool Essays of 1088 revolutionized navigation with his discovery of the magnetic needle compass. He was the first to describe its use, preceding European description by Alexander Neckam in 1187. Shen's experiments with suspended magnetic needles led to the concept of true north, determined by magnetic declination towards the North Pole. This groundbreaking discovery improved the use of compasses for navigation and may have gone unknown in Europe for another four hundred years. Evidence of German sundials from 1450 even show markings similar to Chinese geomancers' compasses in terms of magnetic declination.

Shen's confidant, Emperor Shenzong of Song (r. 1067–1085), a Song era portrait painting.

Shen Kuo's Contributions to Science and Technology

Along with Wei Pu, Shen aimed to map the orbital paths of the Moon and planets in a five-year project but it was thwarted by political opponents. To support his work in astronomy, he improved designs of the armillary sphere, gnomon, sighting tube, and invented a new type of inflow water clock. In geology, Shen presented a hypothesis for land formation based on findings of inland marine fossils, knowledge of soil erosion, and the deposition of silt. He also suggested a theory of gradual climate change, observing petrified bamboos preserved underground in dry northern habitats. Shen was one of the first to mention the use of drydocks for repairing boats and wrote of the effectiveness of the canal pound lock. Although not the first to document camera obscura, he noted the relation between the focal point of a concave mirror and a pinhole. He wrote extensively about Bi Sheng's invention of movable type printing, preserving the legacy of this invention and understanding of early movable type for later generations. During a border inspection, Shen created a raised-relief map following an old Chinese tradition. As an amateur archaeologist, his description of an ancient crossbow mechanism proved to be a Jacob's staff, a surveying tool unknown in Europe until Levi ben Gerson described it in 1321.

Shen Kuo was a multi-talented individual who wrote on various subjects beyond the Dream Pool Essays. Sadly, much of his writing in other works is no longer available. Some of his poetry can still be found in later compiled works. In addition to his focus on science and technology, Shen also explored divination and the paranormal, including recounting accounts of mysterious flying objects. He also offered insights on ancient Daoist and Confucian texts.

Portrait painting of Wang Anshi.


Birth and youth

Shen Kuo was born in Hangzhou, China in 1031. His father, Shen Zhou, was a lower-class gentry who held provincial-level posts and his mother was from a similarly-ranked family in Suzhou. Shen received his early education from his mother, who was well-educated and taught him and his brother military doctrines. With no prominent family background like many of his peers, Shen relied on his wit and determination to excel in his studies, eventually passing the imperial exams and becoming a state bureaucrat.

Shen's family moved around Sichuan province and finally to the port of Xiamen, where his father held minor provincial posts. Shen observed the topography of the land and the challenges of governance as he traveled with his family. His early illness sparked an interest in medicine and pharmaceutics.

Shen's father died in 1051/52 and Shen observed a period of mourning for three years before serving in minor government posts. He was skilled in planning, organizing, and design, such as when he oversaw the drainage of swampland into farmland. Shen noted the success of the project relied on the effective use of sluice gates.

Official career

Shen Kuo was a prominent scholar-official in China's central government in the 11th century. He was a top scorer in the imperial examinations, the test required to enter the government, and caught the attention of Zhang Chu, the governor of Yangzhou. Shen was appointed to several important positions including ambassador to Western Xia and Liao dynasties, military commander, head of hydraulic works, and leading chancellor of the Hanlin Academy. He was appointed head of the Bureau of Astronomy in 1072 and was responsible for projects to improve calendrical science, alongside his colleague Wei Pu. As a finance commissioner, Shen was highly regarded for his skills in economy and finance.

Shen was also a mentor to Li Zhiyi, who was married to Hu Wenrou, a famous female mathematician. When Shen needed clarification for his mathematical work, he would sometimes ask Li to relay questions to Hu. Shen was known to have said, 

"If only she were a man, Wenrou would be my friend."

Painting of a Buddhist luohan, by Liu Songnian, painted in 1207; Shen Kuo not only listed literati painting as one of his cherished pastimes, but also Buddhist meditation.

Shen was sent out to inspect the granary system of the empire, investigating issues such as illegal tax collection, negligence, ineffective disaster relief, and inadequate water conservancy projects. When he was appointed regional inspector of Zhejiang in 1073, the Emperor requested he visit poet Su Shi, and Shen took advantage of the opportunity to copy some of Su's poetry, which he later presented to the Emperor, claiming it contained "abusive and hateful" speech against the Song court. This led to the Crow Terrace Poetry Trial in 1079. For his loyalty and abilities, Shen was awarded the title of State Foundation Viscount and became a companion to the heir apparent.

Shen was a political favorite of the Chancellor Wang Anshi, leader of the Reformers or New Policies Group. Shen had a history with Wang, as he had composed the funerary epitaph for Shen's father. Shen impressed Wang with his skills and abilities, and was sent to supervise the dredging of the Bian Canal in 1072. He demonstrated his value as an envoy when he went to the Khitan Liao dynasty in 1075 and successfully refuted the emperor's bluffs, reestablishing the rightful border line. In his Dream Pool Essays, Shen showed knowledge of the players involved in the prelude to the Sino-Vietnamese War of 1075–1077. He was a trusted member of Wang Anshi's inner circle of political loyalists.

Wang Anshi's New Policies included state finance, land tax reform, and the imperial examinations, but also had a military focus. The policies aimed to raise militias, establish government monopolies on saltpetre and sulphur production, and adopt an aggressive military policy.

Impeachment and later life

The new Chancellor, Cai Que, held Shen Kuo responsible for a disaster that resulted in loss of life and abandoned the territory fought for by Shen. As a result, Cai ousted Shen from his seat of office and placed him under probation in a fixed residence for 6 years. During his time in isolation, Shen dedicated himself to scholarly studies, producing two geographical atlases that were rewarded with a lifted sentence and pardon from the court.

In his leisure time, Shen Kuo enjoyed the cultural pastimes of the Chinese gentry and literati, as described in his "Dream Pool Essays." He was known for enjoying the "nine guests," which included playing the zither, meditation, calligraphy and painting, tea drinking, alchemy, poetry, conversation, and wine.

Five bracket arm bases and two cantilever arms, from the Yingzao Fashi of 1103.

Shen Kuo was married twice, with his second wife being the daughter of Zhang Chu from Huainan. Lady Zhang was known for her abusive behavior towards Shen and even attempted to pull off his beard. Despite this, Shen fell into a deep depression after Lady Zhang died and attempted to drown himself in the Yangtze River. He eventually passed away a year later.

Shen Kuo purchased a garden estate in the 1070s, naming it "Dream Brook," where he spent the last years of his life. It was there that he completed his book "Dream Pool Essays," and passed away in 1095.

Scholarly achievements

Shen Kuo was a prolific writer, covering a diverse array of topics in his works. From creating two geographical atlases to writing on mathematical harmonics in music, government administration, astronomical instruments, defensive tactics and fortifications, painting, tea, medicine, and poetry, Shen's works showcase his vast knowledge and expertise in various fields.


Shen Kuo was an accomplished mathematician who excelled in practical mathematical problems. He mastered complex formulas for geometry, circle packing, and chords and arcs problems using trigonometry. He even tackled the challenge of writing out very large numbers, such as (104)43. His "technique of small increments" established a foundation in Chinese mathematics for solving equal difference series in packing problems. According to Sal Restivo, Shen utilized the summation of higher series to determine the maximum number of kegs that could be stacked in layers in a space shaped like the frustum of a rectangular pyramid. He also devised the "technique of intersecting circles" to approximate the arc of a circle given the diameter, sagitta, and chord length. This work formed the basis for spherical trigonometry developed in the 13th century by Guo Shoujing. Shen also streamlined the counting rods method by presenting shortcuts in algorithm procedures used on the counting board, an idea expanded upon by Yang Hui. Victor J. Katz believes that Shen's "dividing by 9, increase by 1; dividing by 8, increase by 2" method was a precursor to the rhyme scheme method of repeated addition "9, 1, bottom add 1; 9, 2, bottom add 2".

Yang Hui triangle (Pascal's triangle) using rod numerals, from a book by mathematician Zhu Shijie, 1303
Yang Hui triangle (Pascal's triangle) using rod numerals, from a book by mathematician Zhu Shijie, 1303

Shen wrote extensively about his experiences working for the state treasury, which included mathematical problems related to computing land tax, estimating requirements, currency issues, and metrology. He calculated the terrain space required for battle formations and the longest possible military campaign, taking into account the limits of human carriers and their food supplies. He also wrote about the Buddhist monk Yi Xing, who applied an early escapement mechanism to a water-powered celestial globe. Using mathematical permutations, Shen described Yi Xing's calculation of possible positions on a go board game, resulting in a total of 847,288,609,443.

An 18th-century diagram of camera obscura

Magnetic needle compass

The Chinese have used the south-pointing chariot, a non-magnetic compass, since the time of engineer and inventor Ma Jun (c. 200–265). In 1044, the "Collection of the Most Important Military Techniques" recorded that fish-shaped iron sheets, magnetized through thermoremanence, were used for direction finding in a water-filled bowl enclosed by a box. This was used in addition to the south-pointing chariot.

The Han dynasty (202 BC–220 AD) used a lodestone south-pointing compass for geomancy, but not for navigation. It wasn't until the time of Shen Kuo that magnetic compasses were used for navigation. Shen Kuo made the first recorded reference to the magnetic compass needle and the concept of true north. He wrote about steel needles being magnetized by rubbing them with lodestone and floating them or mounting them. He stated that the suspended compass was the best form to use and that the needle pointed either north or south, but with a slight deviation towards the east.

Shen Kuo preferred the use of a twenty-four-point rose compass over the old eight compass cardinal points. This preference may have arisen from his more accurate measurement of the astronomical meridian between the pole star and true north. Alternatively, it could have been influenced by geomantic beliefs and practices. The first recorded use of a compass for seafaring navigation was in Zhu Yu's "Pingzhou Table Talks" published in 1119. Zhu Yu's book covers events from 1086, which was during the time Shen Kuo was writing the "Dream Pool Essays." This suggests that the compass might have already been in use for navigation during Shen Kuo's time. Regardless, Shen Kuo's writings on magnetic compasses have provided valuable insight into China's earliest use of the compass for navigation.

Beliefs and philosophy

Shen Kuo was a strong supporter of philosophical Daoist ideas, which challenged the authority of empirical science in his time. While much information could be obtained through observation and study, Daoism claimed that the secrets of the universe were boundless and that scientific investigation could only provide limited understanding. Shen used the ancient Daoist text I Ching to explain spiritual processes and knowledge beyond what can be obtained through physical evidence. Nathan Sivin argues that Shen was the first to distinguish between experiences and the underlying cause we assume to explain them. He believed in fate, divination, and strange events, but also warned against believing that everything in life was predetermined. He wrote about a lightning strike on a house, where wooden walls turned black but didn't burn, lacquerware was unaffected, but metal objects melted, and described it rationally.

Most people can only judge of things by the experiences of ordinary life, but phenomena outside the scope of this are really quite numerous. How insecure it is to investigate natural principles using only the light of common knowledge, and subjective ideas.

Shen Kuo was a firm believer in the teachings of Mencius and the idea of following one's inner truth. He emphasized the limitations of sensory experience in achieving full knowledge and instead stressed the importance of an autonomous inner authority in guiding moral choices. Drawing from his own life experiences of self-reliance and success, Shen's writing reflects his views on the power of individual choice. In addition to his commentary on classic Chinese texts, Shen also explored the topics of supernatural divination and Buddhist meditation, further showcasing his diverse interests and beliefs.

Burial and posthumous honors

Shen Kuo was buried in a tomb in Hangzhou's Yuhang District at the foot of Taiping Hill. The tomb was destroyed but its location was found in 1983 and protected by the government in 1986. The brick structure remnants and Song dynasty artifacts (glassware and coins) were discovered. In 2001, the Hangzhou Municipal Committee restored Shen's tomb.

Bamboo and rocks by Li Kan (1244–1320); using evidence of fossilized bamboo within China's dry northwestern climate zone, Shen Kuo hypothesized that climates naturally shifted geographically over time.

The Mengxi Garden estate in Zhenjiang, Shen's former 2-acre property, was restored by the government in 1985. Only part of the original garden remains, but the renovated garden has a Memorial Hall displaying a painting of the original garden, a statue of Shen, copies of his Dream Pool Essays, marble banners, and a model of an armillary sphere. There is also a small museum showcasing Shen's achievements.

In 1964, the Purple Mountain Observatory in Nanjing discovered an asteroid and named it 2027 Shen Guo after Shen Kuo.

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