Wang Zhenyi astronomer

Wang Zhenyi, linocut, 11" x14" by Ele Willoughby, 2026

For the 12th and final #PrinterSolstice2526 prompt multiplication, I have chose Qing era polymath - astronomer, mathematician, meteorologist and poet - Wang Zhenyi (王贞仪), who amongst her accomplishments in her brief life, was a book on mathematics for young readers with simplified rules for multiplication and division, to help children learn even those she lived when formal education for girls was rare. In the absence of any known portraits, I made my print after researching Qing Dynasty pavilions, lanterns, tables and mirrors, along with women's fashions and available astronomical instruments in China in the 1790s.

Astronomer, mathematician, meteorologist and poet Wang Zhenyi (1768-1797) left her impact on Qing era China during her short life. Raised by her father and grandparents, her ancestral home was in Anhui province. Her grandfather, Wang Zhefu, an avid reader and collector of books, was governor of Fengcheng County and the Xuanhua District. When her father, Wang Xichen failed the imperial examination to enter the civil service, he decided instead to study medicine, and wrote a 4-volume Collection of Medical Prescriptions. While many Qing women were denied literacy and education, Zhenyi absorbed it all: astronomy from her grandfather, poetry from her grandmother Dong, medicine, geography and mathematics from her father. When she was 9, her grandfather died and the family travelled to Jilin near the Great Wall to mourn and attend his ornate funeral. They remained there for five years. While there, Zhenyi and three other upper-class girls studied under the Lady of Bu Qianyao, and she was able to read her grandfather's library with its full 75 bookcases. She also learned to ride, do archery on horseback and martial arts from the wife of the Mongolian General Aa. She became an expert mounted markswoman. On her own, she began further exploring mathematics and astronomy, reading Chinese texts, and Western classics like Euclid's Elements.

Zhenyi then travelled with her grandmother and father, visiting Beijing, Shaanxi, Hubei, Guangdong and Anhui. This unusual experience exposed her to more history and more breadth of society than was common for most young women. She and her father travelled south of the Yangtze river, before moving back to the capital and settling in Nanjing when she was 16. At 18, her poetry united her with female scholars in Jangling, and she began to focus on mathematics and astronomy. At 25, deemed late to marry at the time, she married Zhan Mei from Xuancheng in her home province. Their marriage was happy but they had no offspring. She gained fame from her poetry, mathematics and astronomy knowledge. She advanced meteorology to work on weather forecasts for farmers. She even took on some male students, an extraordinarily uncommon thing for a young woman scholar at the time. 

Flemish Jesuit missionary and polymath Ferdinand Verbiest (1623-1688), known as Nan Huairen in Chinese, became Director of the Imperial Astronomical Bureau, introduced updated armillary spheres, sextants and celestial globes to China and had them adorned with Chinese motifs. He reformed the inaccurate Chinese calendar and diplomatically fostered Sino-European scientific exchange.

 
The Qing Dynasty closed door policy meant that astronomy in China was isolated from advancements that were being made in the West. Jesuit missionaries had shared the works of Copernicus, Galileo and Brahe. Copernicus' model was shared as a useful tool rather than a doctrine, so they could both avoid Church ire and respect local traditions. However, Newton's Principia, including his universal law of gravitation, was not available in a Chinese edition until 1850. When Wang Zhenyi took pains to explain how we could live on a globe without falling off, she was doing so without benefit of an explanation of gravity.

She wrote Dispute of the Procession of the Equinoxes using her observations of celestial phenomena, explaining how equinoxes, the two days each year in the spring and fall when days are nights are equal length, move and how to calculate their movements. Using both her observations and astronomical texts, she wrote about the number of stars, the direction of the revolution of the sun, moon, Venus, Jupiter, Mars, Mercury and Saturn, as well as describing lunar and solar eclipses. Only a small fraction of her works survive. Later articles included Dispute of Longitude and Stars, Explanation of Lunar Eclipses, and Explanation of the Starry Sky. Zhenyi was interested in the causes of lunar eclipses and published her correct understanding in Explanation of Lunar Eclipses. She summarized astronomical theories, from Yu Xi (307-345) who discovered the precession of the equinoxes, to Gui Shoujing (1231-1316) who is credited with inventing the gnomon and a water powered armillary sphere, and managed to calculate the length of a year as 365.2425 days (mere seconds short of the modern value). She connected these scholars' work with Islamic, Western and modern calendars. At a time when many of her contemporaries would attribute an eclipse to the anger of the gods, she bluntly wrote, "In fact, it's definitely because of the moon." She made a demonstration in an outdoor pavilion to show that how these phenomena could be simply explained by the relative motion of Earth (represented by a round table), moon (represented by a mirror) and sun (represented by a suspended round crystal lamp). Moving these three, as celestial bodies would move she could explain lunar eclipses. She could show how the Earth's shadow could pass over the Moon. She explained that a lunar eclipse can only happen during a full moon, and a solar eclipse can only happen during a new moon, but only when the alignment is right. Her work also cleared up misunderstandings about celestial mechanics and addressed the gradual shift in stellar positions. She affirmed the Earth is a sphere, writing the Theory of the Earth's Roundness, refuting ideas of a flat Earth. In The Geocentric Theory of the Annual Cycle, she made the case for a heliocentric system. She was a proponent of the Western sun-based, heliocentric calendar over the lunar calendar, for its precision and advocated for its adoption. She argued people needed to be open to new scientific and mathematical ideas, regardless of their origin. 

To improve weather-forecasting she worked on calculating atmospheric humidity. She investigated making better predictions of floods and droughts, understanding that Chinese farmers suffered in extreme weather conditions. 

She mastered the book Principles of Calculation by famed early Qing dynasty mathematician Mei Wending (1633-1721). Knowing the challenge of trying to teach oneself mathematics, she rewrote it in simpler, more accessible language as The Musts of Calculation. To further make mathematics easier for beginners, she developed simplified means of performing multiplication and division. By the time she was 24, this work culminated in her writing The Simple Principles of Calculation. Another math text which she wrote and survives today, is the Explanation of the Pythagorean Theorem and Trigonometry.

She complained that anyone with access to medical books could believe themselves experts and dispense risky medical advice. Though widely read, and taught by her father, she refrained from treating her own ailments. On the other hand, she advised being wary of quacks, and speaking up on if necessary. When her female cousin was given a prescription, she checked her pulse and consulted books on female health. She condemned the physician's prescription as unsuitable for a woman. She emphasized the use of preventative medicine and clearly had practical medical knowledge.

She wrote 13 volumes of poetry which were well-received, praised for their strength and clarity. Her style was not feminine and flowery, as was more common amongst female poets. She wrote about the classics, the history she learned travelling with her father, ordinary working people, the plight of women and the contrast between rich and poor. Her poems showed her compassion for people she encountered. She wrote about the wealthy hoarding rice until it rotted, while the poor faced starvation and how the increasing tax burden impacted rural regions. She faced criticism when she published her poems for pursuing fame and literary writing. She wrote that she "dare not defend herself" since she should adhere to Confucian ethics and its prescriptions for the roles of women, but she also wrote that the classics were intended for both men and women. Thus, it was stubborn and careless to insist that women should not read. She wrote, 

    It's made to believe,

    Women are the same as Men;

    Are you not convinced?

    Daughters can also be heroic?

She pointed out that both women and men, "are all people, who have the same reasons for studying."

She died when she was only 29, likely after a relapse of malaria. Before she died, she entrusted her manuscripts to her friend Qian Yuling, who in 1803 passed them on to her nephew Qian Yiji. He compiled her mathematics texts and wrote a preface praising her achievements. Most of her works have since been lost and are known only through references from other writers. Her work helped bridge the gap between Western and Chinese astronomy and modernize Chinese astronomical understanding. Two hundred years later, her impact is being acknowledged. In 1994 the International Astronomical Union's Working Group for Planetary System Nomenclature approved a small crater on Venus has being named in her honour. We can only wonder what such a prolific and insightful scholar as she might have achieved had she lived a longer life.

References

Astronomy Week 2025: Honouring the Life and Legacy of Wang Zhenyi, School of Mathematics, University of Edinburgh. Accessed March, 2026.

Bernardi, Gabriela. Wang Zhenyi (1768-1797). In: The Forgotten Sisters. Springer Praxis Books(). Springer, Cham. https://doi.org/10.1007/978-3-319-26127-0_23

DeBakcszy, Dale. Champion of Chinese Heliocentrism: The Stellar Mathematics of Wang Zhenyi. The Women in Science Archive. April 25, 2023.

Lutz, R.C. Wang Zhenyi, EBSCO Knowledge Advantage. Accessed March, 2026.

Mehta, Devang. The prolific life of Wang Zhenyi, autodidact, astronomer and poet. Massive Science. November 3, 2017.

Wang Zhenyi (astronomer), Wikipedia, accessed March, 2026

Wang Zhenyi (王贞仪) – Mirror, Wellesley University blog, accessed March, 2026.

Wing-Chung Ho, Clara. The Cultivation of Female Talent: Views on Women's Education in China During the Early and High Qing Periods. Journal of the Economic and Social History of the Orient. Vol. 38, No. 2, Women's History (1995), pp. 191-223 (33 pages)

Yang, Binbin. Guardians of Family Health in Qing China: From the Exemplary Wife to the Reformer. Modern China. Vol. 41, No. 5 (September 2015), pp. 506-538 (33 pages). Published By: SAGE Publications, Inc.

Also, hat's off to this tumblr which carefully presents a full history of Qing Dynasty women's fashions and hairstyles:

https://audreydoeskaren.tumblr.com/post/697018790909820928/abridged-history-of-qing-dynasty-han-womens

Elisabeth Koopmann-Hevelius Set Her Sight on Being an Astronomer

Elisabeth Koopmann-Hevelius, linocut print 11" x 14" by Ele Willoughby, 2026

For the 11th #PrinterSolstice2526 prompt angle, I've made a portrait of astronomer Elisabeth Koopman Hevelius using (sextant or ) an octant, literally measuring angles to astronomical bodies. 

One of the earliest recorded women astronomers, Elisabeth Catherina Koopmann-Hevelius (Elżbieta Heweliusz, 1647-1693) was born to a wealthy, land-holding, Dutch Lutheran, merchant Nicolas Koopman (1601-1672) and his wife Joanna Mennings (or Mennix; 1602-1676) in the largely German-speaking city of Danzig, then part of the Pomeranian Vovoidship of Royal Prussia in the Polish-Lithuanian Commonwealth, part of the Hanseatic League, now known as Gdańsk, Poland.  Her parents had been married in Amsterdam in 1633, then moved to Hamburg and again to Danzig by 1636. Her education included languages (including at some point Latin, the international language of science of the day) and natural sciences. Elisabeth was fascinated with astronomy from the time she was a child. The year she was born, local politician, brewer and astronomer Johannes Hevelius (1611-1687) published his beautifully and elaborately illustrated Selanographia, about the moon, the first geographical book about a body other than the Earth. By 1650 he already had an international reputation, a complex of three houses and 200 square metre observatory equipped with several large telescopes, the largest observatory in Europe. The young Elisabeth approached him and he promised he would show her the splendour of the night sky when she was older. In 1662, his first wife Katharina Rebeschke died. Elisabeth had become ever more fascinated by astronomy and had realized that Johannes was in fact a renown astronomer, and her admiration of him grew. She reminded the elder astronomer of his promise. Despite their age difference, based largely on their mutual love of astronomy, the two decided they could be happy together and wed when Elisabeth was 16 and he was 52, in 1663. Such an age gap would not have shocked their contemporaries, and for a young woman like Elisabeth, barred from university education, marriage would have been the only means for her to pursue astronomy. Elisabeth had to run the complicated Hevelius household and she both assisted Johannes and pursued her own astronomical interests. They had four children; a son, who died in infancy and three surviving daughters. 

Detail of Johannes and Elisabeth Hevelius observing the sky with a brass octant (1673).

While awaiting the arrival a new assistant, Elisabeth aided her husband in his observations; she excelled at the job and loved observing. In 1663, France awarded him a pension for his astronomical work, and Johannes began corresponding with Henry Oldenburg, secretary of the Royal Society in London. Elisabeth became his partner in observation from 1664 onwards. That year, Johannes was inducted as the first foreign member of the Royal Society of London. Also that year their son John Adeodatus was born but he died a year later. Their daughters Catherine Elisabeth, Julia Renata and Flora Constance were born in 1666, 1668 and 1672, respectively.  In 1668, Johannes published their work in Cometographia, listing comets and sunspots. Showing herself to be competent in the use of the large sextants and quadrants, when Johannes published his Machina coelestis in 1673 he included two engravings showing Elisabeth using the octant and sextant with him respectively. These are the first printed images of a woman astronomer at work. They employed advanced astronomical instruments such as brass quadrants, sextants and octants (named for the amount of a circle they encompassed) and their observatory was a hub of innovation. The large sextants and octants required two people to operate. Each were equipped with an alidade, a sort of ruler to fix on the distant object being observed, and then its position could be read off. Johannes had invented his own precise alidade with cylinder to fix an objects position. With her knowledge of language, Elisabeth corresponded and struck up friendships with other astronomers. The French physicist and astronomer François Arago recounted that that she was both making useful observations and preforming calculations. In 1677 they were visited by King Jan III Sobieski, who gave them a stipend. Despite owning telescopes with which he had for instance, carefully observed the surface of the moon, Johannes was a hold-out where it came to making observations of stellar positions with telescopes, first employed for astronomy by Galileo Galilei (1564-1642) in 1609.  Johannes feared that telescopic observations might introduce distortions in locations. He is considered the last great astronomer to make observations with the unaided eye. 

This unusual attitude towards telescopes lead Johannes into controversy. In England, at the Royal Society, Robert Hooke accused him of making inaccurate observations and sent fellow astronomer Edmond Halley to visit Danzig, from May 26, to July 18, 1679. While Hooke was right about the utility of using telescopes, Halley was very impressed with the precision of Johannes and Elisabeth's naked-eye observations. Though privately he doubted naked-eye observations were the way to go, he confessed that in his controlled test, he could not determine which observations were more accurate. Six separate observers, including Johannes, Elisabeth and Halley with his with a 2-foot quadrant with telescopic sights made the same observations and Halley compared the data. Hooke was quite rude about the entire debacle, and Hevelius responded in kind. Other astronomers, like John Wallis, defended Hevelius because they were annoyed with Hooke. None of the members of the Royal Society involved in the bitter dispute came away with their reputations unbesmirched, with the exception of Halley, who had more diplomatic sense than the rest of them. That summer, they published Machina coelestis par posterior 'Astronomical instruments, second part' including a biography of Johannes, description of their instruments and 1,564-star catalogue of stars based on their observations.  

Then September 26, 1679 they suffered a devastating fire which destroyed their home, their observatory, their instruments, their library and printing press. Luckily, as Johannes wrote, before the fire he was feeling uneasy and "To lift my spirits, I persuaded my young wife, the faithful assistant for my nightly observations, to spend the night in our country retreat outside the walls of the city..." so they were unharmed. People present, including their 13 year old daughter Catherine Elisabeth managed to save several books including Kepler's works (purchased from his son), his new and improved celestial globe, thirteen volumes of his correspondence with scientists and royalty and the most importantly, the star catalogue by breaking into the burning house and throwing them out the windows! Luckily, dozens of copies of Machina coelestis which had already been sent out were not destroyed, but they lost everything else. Elisabeth had asked Halley to buy her a silk dress in London, in exchange for three of Johannes' books, and he wrote how when choosing the fabric he was uncertain if she would be in mourning because, having heard about the fire, astronomers in England feared Johannes had perished. Both King Jan III Sobieski and King Louis XIV of France sent them thousands of thalers to help them rebuild, and Sobieski granted him a yearly stipend of 1,000 Danzig gulden for the remainder of his life,  but it was nowhere near the estimated value of what they lost, which was over thirty thousand thalers. Undetered, they rebuilt their observatory by August 1781 and resumed work on their star catalogue, incorporating 341 stars only visible in the southern hemisphere, reported to them by their friend Edmond Halley. Elisabeth did much of the mathematical calculations and editing of the text. 

Johannes and Elisabeth Hevelius observing the sky with a brass octant (1673), Engraving from Johannes Hevelius' Machine Colestis: Pars Prior fig. O, facing p. 254. 

In 1685, Johannes published Annus climacterius 'Climactic Year' documenting their most recent observations and retelling the tale of the 1679 fire. Swiss mathematician and astronomer, Johann III Bernouilli wrote that Elisabeth contracted smallpox and was badly marked by it. Though Johannes had never contracted the disease he nursed her and never left her sick-bed. They began working on what would be Johannes' final publication. He died on his 76th birthday in 1687. After his death, she secured funding, took over the completion and publication of the Prodomus Astronomicae, 'The Elements of Astronomy". In 1690 she published the Prodomus Astronomicae, documenting two decades of observations, in three parts: the Prodomus was a preface with unpublished observations, which Elisabeth completed as well as writing and signing the dedication to the king as "Elisabeth, widow of Hevelius";  Catalogus Stellar Fixarum 'Catalogue of the Fixed Stars' (dated 1687) was a star catalogue including the positions and relevant data for 1,888 stars; and Firmamentum Sobiescianum sive Uranographia 'Sobieksi's Heavens, or a Map of the Heavens' (dated 1687) was a 56 sheet atlas of constellations for both northern and southern hemispheres from the catalogue complete with seven new constellations he delineated which are still in use (Canes Venatici, Lecerta, Leo Minor, Lynx, Scutum, Sextans, and Vulpecula) plus three which are now obsolete (Cerebus, Mons Maenads, and Triangulum Minus). Hevelius named one of these constellations for the king (Scutum Sobiescianum, or 'Shield of Sobieski' shortened now to Scutum) and one for his precious sextant, as well as several animals. It represented a significant advancement in astronomical observations and knowledge, containing both more stars and more accurate positions than Johan Bayer's Uranometria (based on Tycho Brahe's measurements). Elisabeth had not only ushered the book through publication, she participated in observations and calculations in a meticulous and systematic way. She died three years later, December 22, 1693 at 46 and was buried in the same tomb as her late husband. Arago wrote, "A complimentary remark was always made about Madame Hevelius, who was the first woman, to my knowledge, who was not frighted to face the fatigue of making astronomical observations and calculations." Arago was unaware of how Sophia Brahe (1556 or 1559-1643) had aided her brother Tycho, or of their near-contemporary Maria Cunitz (1610-1664), who was rather isolated from the astronomical community, so we should say that Elisabeth was amongst the first but not the earliest woman bravely facing late night observing and astronomical calculations. But her correspondence and friendships with fellow astronomers, as well as her collaboration with her husband, appearance in his books and her publication of the Prodomus, means that she and her accomplishments were recognized and remembered. A minor planet discovered at the Palomar Observatory in 1960 was named 12625 Koopman and a crater on Venus is named Corpman, a variant on the spelling of her maiden name, were named in her honour.

References

Ashworth, William B. Scientist of the Day - Elisabeth Hevelius. Linda Hall Library, University of Missouri-Kansas City. December 22, 2017.

Elisabeth Hevelius, Wikipedia, accessed February, 2026.

Jardine, Lisa. The Curious Life of Robert Hooke - The Man Who Measured London. Harper Collins. New York. 2003.

Masters, Karen. The Astronomers' Library. Ivy Press. London. 2024. 

Lutz, R.C. Elisabeth Hevelius, EBSCO Knowledge Advantage, 2022.

O'Connor, J.J. and E.F. Robertson. Elisabetha Koopman (1647-1493) - Biography. MacTutor. School of Mathematics and Statistics, St Andrews University. December, 2008.

O'Connor, J.J. and E.F. Robertson. Johannes Hevelius (1611-1687) - Biography. MacTutor. School of Mathematics and Statistics, St Andrews University. December, 2008.

Popova, Maria. Ordering the Heavens: Hevelius's Revolutionary 17th-Century Star-Catalog and the First Moon Map. The Marginalian. 2014.