Polymath Claude Shannon and Theseus the Electromechanical Mouse in a Maze

 

Claude Shannon, linocut print, 11" x 14" by Ele Willoughby, 2026

I was recently commissioned to make a portrait of Claude Shannon. It seemed clear that it would need some binary to represent his work, and the math and computer science in particular. I opted to also include Theseus in his maze, which hits on the electrical engineering, and the humour in what he did.

This is my linocut portrait of Claude Elwood Shannon (1916-2001), mathematician, electrical engineer, computer scientist and cryptographer credited with laying the foundations for the Information Age. Each hand-printed linocut on 11" x 14" Japanese kozo (or mulberry paper) shows Shannon in front of binary numbers and with his electromechanical mouse Theseus with its maze. Though partially behind him, the binary numbers represent the standard ASCII code for "CLAUDESHANNON". 

At the University of Michigan, he took two degrees: one in electrical engineering and the second in mathematics, graduating in 1936. His MIT masters thesis is arguably one of the most impactful ever completed. In it, "A Symbolic Analysis of Relay and Switching Circuits", he showed that we can construct any logical numerical relationship through the electrical applications of Boolean algebra. This is now the underlying theoretical basis for   digital computing and digital circuits. He completed his doctorate at MIT in 1940 on mathematical genetics.

During WWII he worked in the field of cryptanalysis for US national defence, doing fundamental work on codebreaking and secure telecommunications, and writing a paper which is considered one of the foundational pieces of modern symmetric-key cryptography.

His 1948 paper "A Mathematical Theory of Communication" laid the foundations for the field of information theory. This paper was important to the invention of the compact disc, the internet, mobile phones and even our understanding of blackholes. He introduced the term "bit," invented the signal-flow graph and co-invented pulse-code modulation and the first wearable computer. 

In 1950, he designed and built a learning machine, with the help of his wife mathematician and research collaborator Betty Shannon. They built an adjustable maze with sensors (an electromechanical relay circuit) which followed the path of an electromechanical mouse whimsically named Theseus. Theseus could search corridors until it found a target (the penny in my portrait). Then, the mouse could be moved to anywhere in the maze. If the location was known, it would go immediately to the target. If the location was unknown, the mouse would search until it found a known position, adding this knowledge to its memory, and proceed from the known position. This way it could eventually find the most direct route. This is the first known artificial learning device.

In 1951 he joined the CIA's  Special Cryptologic Advisory Group. He was a professor at MIT from 1956 to 1978. His work was also foundational for artificial intelligence. He was a co-organizer of the 1956 Dartmouth workshop, considered to be the discipline's founding event. He published papers on the programming of chess computers. His Theseus machine was the first electrical device to learn by trial and error, being one of the first examples of artificial intelligence.

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.

Rosalyn Sussman Yalow

Rosalyn Sussman Yalow, linocut print, 9.25" 12.5" by Ele Willoughby, 2026

For the 10th #PrinterSolstice2526 prompt 'fraction' I made the portrait of the woman who taught us how to measure the fraction, or concentration of many things, like antigens like hormones to drugs to within our blood, and to diagnose and monitor related diseases, medical physicist and Nobel laureate Rosalyn Sussman Yalow. 

Rosalyn Yalow (née Sussman, 1921-2011) was born to a Jewish family in the Bronx during the Great Depression and attended Walton High School. Her parents had not had the opportunity to attend high school, but valued education and encouraged their children, Rosalyn and Alexander, to read books from the local library. Like Esther Lederberg, she got the opportunity for higher education at the all-female Hunter College, tuition-free. Her mother hoped she would become a teacher but Rosalyn opted to study physics.  She read Eve Curie's biography of her mother, double-Nobel laureate Marie Skłodowska-Curie, and Rosalyn got excited about nuclear physics. A lecture by Enrico Fermi in 1939, on nuclear fission, newly discovered by Lise Meitner, Otto Hahn and Fritz Strassman, captured her imagination. So, she became Hunter College's first physics major and even graduated early with honours. Money was tight, and opportunities for graduate school for a young Jewish woman were few, so she got herself a secretary to a biochemist at Columbia University, Dr. Rudolf Schoenheimer (who developed a technique of isotope labelling of biomolecules). She thought eventually she might go to graduate school at Columbia. She graduated Hunter College in 1941 She did not think that as a woman, she could get financial support for graduate school as she found a second secretary job. Columbia immunologist Dr. Michael Heidelberger hired her on condition that she study stenography. When the US joined WWII, suddenly there was more opportunity for women. Many male physics grad students were drafted or being sent to do secret wartime research and universities decided was better to admit women students, as men were otherwise occupied, than to have to close their doors. She was offered a teaching assistant position in the college of engineering at the University of Illinois Urbana-Champaign, where she was the first woman since 1917 and the only woman among 400 members. There were no women's washrooms, a real inconvenience when working late in the lab. She took extra undergraduate courses in physics to fill in gaps in her education. She was ambitious, and assertive and felt disapproval, particularly from other women, for not taking up teaching, the socially acceptable role for a woman at the time. She married fellow physics student, Aaron Yalow, the son of a rabbi in 1943. She learned how to build her own equipment and measure and work with radioactive substances.  She earned her PhD in 1945, then took further tuition-free physics back home in New York, under government auspices at New York University. 

Aaron knew he was not marrying a housewife, and supported her pursuing her career in physics, but he did not, on the other hand, help around the house. She valued the traditional roles of wife and mother. Her parents had not kept a kosher home, but she did for Aaron and later, their two children, Benjamin and Alanna. If Rosalyn had to travel, she would prepare his meals in advance, for him to warm up. Rather than the more modern ideas of work-life balance, Rosalyn's solution was simply to stint on sleep. Like many in her generation she was a bit wary of feminism and feminist organizations, placing a high priority on the role of wife and mother. She worried feminism lead women to eschew traditional duties. Conversely she advocated for more women in science and served as a loyal and dedicated role-model and mentor to younger women. She wrote, "The world cannot afford the loss of the talents of half its people if we are to solve the many problems which beset us." But, she did not want women in science to be treated differently from men so she disapproved of organizations for women in science. She recognized that WWII had created opportunities for women, but suggested that if the numbers of women decreased post-war, perhaps they were simply not interested. Nonetheless, she devoted her retirement years to advocating for better-quality child care and science education, aware that these could both make a significant positive impact on women's participation in science.

After grad school, Rosalyn got a job as an assistant electrical engineer at the Federal Telecomminations Laboratory, where she was the only woman. In 1946 she returned to Hunter College, where she taught physics. In 1947, Aaron introduced her to Columbia University medical physics Edith Quimby, who used radioactive isotopes. She asked to volunteer in Quimby's lab, anxious to get back into research; Quimby instead introduced her to influential medical physicist Gioacchino Failla. Failla immediately called the VA Hospital in the Bronx and got her a part-time job as a researcher there, to set up their Radioisotope Services. She set up a lab in an old janitor's closet, often building her own equipment, as the field was so new. She split her time between working in the lab and as a physics lecturer until 1950, because she wanted to keep mentoring students. One especially promising student had caught her attention: Mildred Spiewak (later the "Queen of Carbon Science" Dresselhaus), whom she persuaded to apply to graduate school for physics, rather than teacher's college. Rosalyn remained an active mentor to Millie through her career. 

Rosalyn Yalow with her research partner Solomon Berson, when she won the 1961 Ely Lilly Award of the American Diabetes Association. (via here)

The Veterans Association wanted to institute a research program on the medical uses of radioactivity, and by 1950, Yalow had equipped a radioisotope lab at the Bronx VA Hospital and she left teaching for research. There she met her longtime collaborator, physician Solomon Berson. He had already accepted a job with the VA Hospital in Bedford, Massachusetts, but after interviewing Rosalyn, they hit it off famously, and he changed his plans. Each happily married to someone else, they became "work spouses," an inseparable, complementary pair, in the lab for 22 years, using radioactive isotopes to study the human body. Sol taught Rosalyn immunology and Rosalyn taught Sol about radioactivity.

She wrote, "The only difference between men and women in science is that women have the babies. This makes it more difficult for women in science but, ... it is merely another challenge to overcome." The VA policy was that once women employees reached their fifth month of pregnancy, they had to leave, so, when expecting her children, she ignored the policy and deliberately neglected to inform the VA.

Rosalyn and Sol were interested in what happens to the insulin diabetics injected to allow them metabolize sugars. Rosalyn had a personal reason for her interest in addition to their scientific reasons; Aaron was diabetic. So they labelled insulin by adding a radioactive isotope of iodine, so they could follow the insulin in patients' bodies by the location of the radiation. Was the insulin being broken down by the body and passed through urine? To their surprise, diabetics who had been injecting insulin for some time, were retaining the insulin longer than health patients (themselves included amongst their healthy subjects). The insulin was being produced by cattle, and it was quite similar, but not identical to human insulin. They realized that the diabetics' bodies were detecting a foreign substance and producing an immune response to the cattle insulin, which was why it was processed more slowly and remaining in their bodies, but it also meant it was becoming less effective. These patients needed human insulin, and thus we now produce insulin which is identical to that naturally produced in healthy humans. 

They realized they could flip their method around to measure the insulin in blood. If they mixed a patient's blood with a mixture of radioactively tagged insulin and natural antibodies the antibodies would then pair with the tagged or patient insulin. Since the antibodies prefer the nonradioactive version of the insulin (or any other hormone they wanted to measure in this way), gradually, they separate from their radioactive partners and pair with the natural hormone. Then, they could separate all the hormone-antibody pairs (whether radioactive or not) and measure the radioactivity of the mixture. The difference between the radioactivity of the mixture from the original sample of tagged samples is a measure, or assay, of the amount of hormone in the blood sample naturally. Suddenly, rather than 100 cubic centimetres of blood, a diabetic patient's insulin level could be measured with a tiny blood sample. They proved that type 2 diabetes was caused by the body's inefficient use of insulin, rather than lack of insulin. Better yet, this method could be used with virtually anything which produced an immune response and did not require the patient to be exposed to any radioactivity. Yalow and Berson had developed the radioimmunoassay by 1960. Their methodology can be applied to measure minute quantities of hundred of substance, like hormones, vitamins, viruses, drugs and enzymes, and diagnostic hormone-related conditions and diseases, revolutionizing diabetes treatment. Their published many papers and trained many young scientists in their tight-knit "Mom and Pop" lab, by then grown much larger than the old janitor's closet.

Recognizing both its huge commercial potential and potential for improving or saving lives, Yalow and Berson refused to patent the method. Yalow was appointed a research professor in the department of medicine at Mount Sinai Hospital. Yalow won a Fullbright fellowship to go to Portugal, and the 1961 Ely Lilly Award of the American Diabetes Association.  In 1921, she won the Gairdner Foundation International Award for biomedical scientists advancing humanity and the American College of Physicians award. In 1972, she won the annual William S. Middleton Award for Excellence in Research, the highest honour of the Biomedical Laboratory Research and Development Service for outstanding biomedical science pertaining to the healthcare of veterans. She also won the Koch Award of the Endocrine Society. Tragically, also that year, Sol died at 54. Yalow named her lab for him and became the Solomon Berson Distinguished Professor at Large and became known at the "Mother of Endocrinology." Rosalyn knew that the Nobel Committee did not grant posthumous awards and would not generally award surviving researchers of joint research if one of the researchers had died. She knew she would have to prove herself on her own, and not simply as the "Mom" or their "Mom and Pop Lab." 

In 1975, Yalow and Berson (posthumously) were awarded the American Medical Association Scientific Achievement Award. In 1976 she became the first woman or nuclear physicist to receive the Albert Lasker Award for Basic Medical Research. In 1977, Rosalyn Yalow received the Nobel Prize in Physiology or Medicine for her role in developing the radioimmunoassay technique (along with Roger Guillemin and Andrew V. Schally, for their work on hormone production in the brain). She won the 1977 Golden Plate Award of the American Academy of Achievement. In 1978 she was elected Fellow of the American Academy of Arts and Sciences. She won the A. Cressy Morrison Award of the New York Academy of Sciences in 1986 and the National Medal of Science in 1988. She continued conducting research at her VA lab until she retired in 1991. She was inducted into the National Women's Hall of Fame in 1993. She died in the Bronx in 2011 at 89.

 

References

Berson, Solomon A., Rosalyn S. Yalow, Arthur Bauman, Marcus A. Rothschild, and Katharina Newly, Insulin-I'13 Metabolism in Human Subjects: Demonstration of Insulin Binding Globulin in the Circulation of Insulin Treated Subjects, The Journal of Clinical Investigation, February 1, 1956. 

Harrod, Jordan. Meet Nobel Prize winner Rosalyn Sussman Yalow, who let doctors see into your blood. Massive Science. May 12, 2019.

Rosalyn Sussman Yalow, Wikipedia, accessed February, 2026

Gellene, Denise. Rosalyn S. Yalow, Nobel Medical Physicist, Dies at 89. New York Times. June 1, 2011

Rosalyn Yalow. NobelPrize.org. Nobel Prize Outreach 2026. accessed February 2026.

Rosalyn Yalow and Solomon Berson, Science History Institute Museum & Library, accessed February, 2026.

The Nobel Prize in Physiology or Medicine 1977. NobelPrize.org. Nobel Prize Outreach 2026. accessed February 2026.

https://department.va.gov/history/featured-stories/dr-rosalyn-yalow/

https://www.acs.org/education/whatischemistry/women-scientists/rosalyn-sussman-yalow.html

Microbiologist Esther Lederberg, Printmaking to Replica Plating, the Lambda Phage and Bacterial Fertility Factor F

Esther Lederberg, linocut print, 11" x 14" by Ele Willoughby, 2026

The 8th #PrinterSolstice2526 prompt is two, so I thought of duplicates. This reminded me of trailblazing microbiologist Esther Miriam Zimmer Lederberg (1922-2006) whose pioneering contributions to bacterial genetics include such fundamentals as the first successful implementation of replica plating (with her first husband, Nobel laureate Joshua Lederberg) which allows microbiologists to reproduce a pattern of microbes on different Petri dishes and, for instance, compare their response to various things put in each plate. Reading about how they would press a velveteen-covered disk onto the primary plate with microorganisms and then imprinting the secondary plate (or plates) with the same distribution of microbes, I recognized this as printmaking, so I was delighted to read that her biographer believes she was inspired by having worked in her father's print shop as an adolescent. She also discovered the lambda phage and the bacterial fertility factor F. While she and Joshua both were awarded the Pasteur Medal from the Society of Illinois Bacteriologists, Esther's contributions, including work she did on her own, were often misattributed to Joshua, and she was not included in his Nobel win, nor was she even ever offered a tenured position. In life, she cared more about the science than her reputation, but today microbiologists are working to make sure she gets more of the recognition she always deserved.

Microbiologist Esther Lederberg (née Zimmer, 1922-2007) made discoveries fundamental to modern understanding of bacterial gene regulation, recombination and exchange, but her work was both overshadowed by, and sometimes misattributed to her male collaborators. 

Esther and her younger brother Benjamin were children of Orthodox Jewish Romanian immigrant, David and Pauline Geller Zimmer, herself the daughter of Romanian immigrants, who ran a print shop in the Bronx. Money was tight. The Zimmer children grew up helping in the shop during the Great Depression. David's siblings worked in the garment industry.  Esther had a talent for language. Esther pleased her maternal grandfather by learning Hebrew, unlike her cousins, and won awards for French and Spanish at school. She graduated from Evander Childs High School when she was only 15, and won a scholarship to attend Hunter College, where she planned to study French or literature. Once there, she chose to switch to biochemistry, though teachers warned she would have trouble finding a job, as a woman. Nonetheless she found work as a research assistant working on Neurospora crassa, a red bread mold,  with plant pathologist Bernard Oglivie Dodge. By the time she was 19 in 1942 she had graduated cum laude with a BSc in genetics. 

She got a position with Alexander Hollander at the Carnegie Institution of Washington (later the Cold Spring Harbor Laboratory), continuing her work on N. crassa and making her first scientific publication. She won a fellowship for Standford in 1944 to work with George Wells Beadle and Edward Tatum (who together would later go on to win the 1958 Nobel in Physiology or Medicine with her future husband Joshua Lederberg). Tatum told her would only teach her genetics if she could work out why one of the Drosophila fruit flies in a bottle had different coloured eyes; she did this so well, he made her his Teaching Assistant. After summer school at Stanford's Hopkins Marine Station with microbiologist Cornelius Van Niel, she entered the master's program, and completed her M.A. in genetics with her thesis "Mutant Strains of Neurospora Deficient in Para-Aminobenzoic Acid" in 1946. She married one of Tatum's students at Yale, Joshua Lederberg, and moved to Yale's Botanical Laboratory. Joshua completed his doctorate in 1947 and was offered an assistant professorship at the University of Wisconsin, so the couple moved to Madison, Wisconsin. Esther enrolled in the doctoral program and was awarded a fellowship by the National Cancer Institute. Joshua developed a reputation as a brilliant thinker while Esther developed a reputation as a skilled expert experimentalist and they worked well as a team. Her 1950 doctoral thesis under supervision of plant geneticist R.A. Brink was titled "Genetic control of mutability in the bacterium Escherichia coli". She had already made some foundational discoveries of the fertility factor, but Joshua insisted she focus on completing her PhD, rather than follow up with further experimentation. 

She spent most of the 50s at the University of Wisconsin, and in 1951 she discovered the lambda bacteriophage, a virus which infects and replicates within bacteria, and she published a detailed description in Genetics in 1953 with Joshua as the second author. He had asked her to wait before publishing because he felt it was not the top priority for the lab at that time. When Joshua won the 1953 Eli Lilly Award he told a reporter that Esther should have be recognized too. The lambda phage became a foundational discovery in molecular genetics, invaluable for understanding gene regulation and recombination. She incubated a mix of a parent E. coli K12 strain and a mutant E. coli K12 strain made with UV light and saw plaques, which indicated the presence of a bacteriophage. This type of virus would have been killed by UV light, so it must have come from the parent strain. She called this the lambda phage and found it had two lifestyles: either the typical, well-known phage lifestyle, the lytic cycle, where it rapidly made copies of itself inside the E.coli before bursting out (called lysis) or alternatively existing quietly as just another genetic marker within E. coli, without killing the cell.  With her husband, she found that the quiescent form genetically mapped near the genes in the E. coli which metabolize lactose sugar (gal). The Lederbergs proposed that the lambda's genetic material integrates into the E. coli chromosome next to the gal genes, which let it replicate as a prophage along with the host bacteria's own DNA (a process called lysogeny). This was the first time this 2-part cycle had ever  been described and today, the lambda phage is a key model for understanding other viruses (such as herpes simplex virus) which exhibit these split lytic-lysogenic lifecycles. To leave the host, the prophage needs to excise itself from the bacterial DNA and sometimes when this occurs the phage DNA is accompanied by some adjacent host DNA which the phage can then introduce into a new host; this is called specialized transduction.  Esther presented her lambda studies, including  λ lysogeny and specialized transduction in Canberra, at the Symposium of Bacterial and Viral Genetics in 1957, and her results on where it integrates, the fine-structure mapping of the gal locus in Montreal in 1958 at the 10th International Congress of Genetics.

While studying where the lambda prophage, she crossed bacteria with the prophage with strains without the prophage but will known genetic markers. She found that some crosses failed to form recombinants. She suspected something, a fertility factor, must be missing, writing that during her studies, "one day, ZERO recombinants were recovered... I explored the notion that there was some sort of 'fertility factor' which if absent, resulted in no recombinants. For short, I names this F." She published with Luigi Cavalli-Sforza and Joshua. She was right and others' later research showed that F was a DNA sequence with genes which allow a bacterium to donate DNA to a recipient bacterium by direct contact or conjugation. This DNA sequence can be either an independent plasmid or integrated into the cell's chromosome. Likely because of the delay between her discovery of the fertility factor F and her follow-up experiments and publications, this work is often unfairly primarily attributed to Joshua in textbooks. 

Microbiologists had been struggling to make identical geometrical configurations of microbes on multiple plates and tried using everything from toothpicks, paper, wire brushes and multi-pronged inoculators, until Esther and Joshua successfully implemented their simple solution to replica plating. Their process, pressing a plate of bacterial colonies onto sterile velvet and stamping them onto secondary plates of media with different ingredients to suit the traits needed for study (for instance, containing various antibiotics), mimics how a press works, like in Esther's father's shop! The first time she tried out the idea, she was inspired by her own powder puff, the velveteen pad in her makeup compact. It was, after all, designed to transfer powdered makeup to a person's face; maybe it could transfer configurations of microbes from plate to plate, so she tried it. Esther, whose family were garment workers, was the one familiar with textiles and she used this knowledge to source the best fabric for the job. Nonetheless, this method has also often been inaccurately credited to Joshua only. Since they could reliably replicate their plates, they were able to show, as previously demonstrated by Luria and Delbrück, that bacteriophage- and and antibiotic-resistant mutants spontaneously arose even in the absence of phages or antibiotics. These mutations were not occurring in response to their environment, as held by Lamarckism. Luria and Delbrück's work relied on mathematical arguments and had not gained traction but the simplicity of the Lederbergs' methods finally convinced their colleagues. Their method for replica plating remains a staple of microbiological laboratory work today.

In 1956, both Lederbergs jointly won the Pasteur Award for their contributions to science.  In 1958, Joshua Lederberg shared the Nobel Prize for Physiology or Medicine for discovering bacterial conjugation, with Edward Tatum and George Beadle for their work with genetics. Joshua had discovered that bacteria do not only make identical copies of themselves; they sometimes reproduce by mixing genetic material, as occurs in sexual reproduction, to make something new. Esther, whose work, like discovering the fertility factor with allows this genetic mixing to occur, was essential to, or made in collaboration with Joshua's research, was not included in his win. Attending the formal ceremony in Stockholm, by his side, in her gown, only playing the role of scientist's spouse, must have been bittersweet. Esther became perceived as merely his research assistant. Joshua thanked her simply for her "companionship" in his acceptance speech. Castelli-Sforza wrote, "Dr. Esther Lederberg has enjoyed the privilege of working with a very famous husband. This has been at times also a setback, because inevitably she has not been credited with as much of the credit as she really deserved. I know that very few people, if any, have had the benefit of as valuable a co-worker as Joshua has had."

In 1959 Esther and Joshua returned to Stanford, where Joshua became the head of the Genetics department. Esther could not be employed in the Genetics department because of anti-nepotism rules. Esther and two other women petitioned the dean of the medical school over the lack of female faculty. Eventually she got an untenured faculty position as a research associate professor in the Department of Microbiology and Immunology, where Esther worked for the rest of her career. This meant that her job was not secure and her short-term appointment was renewed on a rolling basis, dependent on her ability to secure grants. After their divorce in 1968, Esther had to fight to retain her position. She founded and directed the Plasmid Reference Center (PRC) from 1976 to 1986, where she organized, maintained, named, and distributed plasmids of various types including those coding for antibiotic-resistances, heavy-metal-resistance, virulence, conjugation, colicins, transposons and insertion sequences. Her sequential numbering system continued until her retirement. In 1974 she was effectively demoted and forced to transition to an adjunct professor of medical microbiology. She retired from the Department of Microbiology and Immunology in 1985 but continued as a volunteer at the PRC.

While not working as a scientist, Esther was a devoted amateur musician focusing on early music, playing medieval, Renaissance and baroque music on original instruments including several different sizes of recorder. She founded the Mid-Peninsula Recorder Orchestra, which plays music dating back to the 13th century, in 1962.  A lover of the works of Charles Dickens and Jane Austen, she belonged to the Dickens Society of Palo Alto and the Jane Austen Society. Through her pursuit of early music, she met fellow enthusiast, engineer Matthew Simon newly arrived at Stanford in 1989, and they married in 1993. She died in 2006 of pneumonia and congestive heart failure at age 83. Esther always thought the science itself was more important than her reputation, but her second husband understood that her work was under-appreciated because she was a woman. Simon has worked tirelessly to make an extensive memorial website for Esther, so her story and role in the development of microbial genetics is not forgotten. The wealth of biographical information and documents there from her career has helped her biographers and microbiologists working to tell a more complete and accurate story of the development of their field.

References

Esther Lederberg, Wikipedia, accessed February, 2026.

Barron, Madeline. Esther Lederberg and the Rise of Microbial Genetics. American Society for Microbiology. October 4, 2023. 

Joshua Lederberg, Wikipedia, accessed February, 2026.

Lederberg, J and E.M. Lederberg. Replica plating and indirect selection of bacterial mutants. J Bacteriol. 1952 Mar;63(3):399-406. doi: 10.1128/jb.63.3.399-406.1952. PMID: 14927572; PMCID: PMC169282.

Simon, Matthew. Esther M. Zimmer Lederberg Memorial Website. Accessed February, 2026

Steinmetz, Katy. Esther Lederberg and Her Husband Were Both Trailblazing Scientists. Why Have More People Heard of Him? Time Magazine. April 11, 2019.

"Women in Microbiology -Esther Lederberg" Live session from ASM Microbe 2017 hosted by Hazel Barton with guest Mark O. Martin interviewed by Rebecca V. Ferrell.

Zeldovich, Linda, Esther Lederberg changed our understanding of how bacteria breed. Popular Science, May 23, 2022.

Agnes Pockels Find Wonder While Washing Dishes and Invents Surface Science

Agnes Pockels, linocut, 11" x 14" on Japanese paper, by Ele Willoughby, 2026

The seventh prompt for #PrinterSolstice2026 is division, and I have decided to focus on the dividing line or interface, and the self-taught scientist who pioneered surface science. 

When Agnes Pockels (1862-1935) was 18, she did not get the chance to go to university and study physics like her brother Friedrich, who became a professor of theoretical physics and discovered the Pockels effect studying optics and electromagnetism. She took her "passionate interest for natural science" to those household chores she was allowed to pursue, and applied her analytic mind and careful observation to what she saw even in greasy dishwater. She became fascinated with how soap behaves on the surface of the water, and especially in the effect of impurities. She began performing experiments as an amateur chemist. In so doing, she pioneered the entire field of surface science describing physical properties of liquids and solids at interfaces, gained international recognition, published a series of peer-reviewed papers and earned an honorary doctoral degree from Braunschweig University, Germany. Performing kitchen-table research, she developed a surface film balance technique to study soap and surfactants at the air-liquid interfaces and defined the Pockels point, the minimum area a single molecule can occupy in a monomolecular film.

Agnes Pockels' first paper 'Surface Tension'
published in Nature in 1891, complete
with Lord Rayleigh's introduction.

Born in Venice in 1862, when it was part of the Kingdom of Lombardy-Venetia, Agnes' father Theodor served in the Austrian army. Malaria was an ever-present risk in the region and struck the family. When Theodor fell ill in 1871, he retired and moved the family, his wife Alwine, daughter Agnes and son Friedrich, to Brunswick, in the newly formed German Empire. Agnes was interested in science, and attended the Municipal High School for Girls. Though she would have loved to pursue higher education in science, and especially in physics, women were not admitted to German universities (with a very few notable exceptions). So, she studied science at home, while caring for her parents for three decades, as expected for an unmarried daughter. When her younger brother Friedrich went to study physics at the University of Göttingen, he would share his textbooks with her. Later, he would supply her with research in the academic literature to help her pursue her own self-taught studies. When the universities finally began admitting women, Agnes followed her father's wishes and refrained from attending so she could continue keep house and to care for her sick parents.

She began experiments when she was 18, and by age 20 in 1882, she had devised a slide through for making quantitative measurements of soapy water and other materials. Her water-filled through was 70 cm long, 5 cm wide and 2 cm deep and she laid a metal strip (about 1.5 cm wide) on the water, across the width of the through, so she could divide the surface into two parts. A lengthwise ruler along the through allowed her to precisely measure the surface area of both sides as the strip was moved along the length of the through. Building on the plate method of Ludwig Wilhelmy, she devised a simple but clever means of measuring surface tension in either area with a ceramic button (6 mm in diameter) placed on the surface. She would raise the button with an apothecary's balance or weighing scale to measure the force required to lift it from the water. She could then compare the force required to lift her button from pure water, or water with various added substances and impurities. Using her through, she investigated surface forces of monomolecular films, emulsions, solutions and the effect of impurities on physical properties and she came to understand surfactancy, the property of a chemical compound to decrease surface tension at an interface between different materials (at least one of which is a fluid).  She found that small amounts of impurities could have a large impact on surface tension. 

Agnes Pockels in 1885

Her through influenced future experimentalists in colloidal and surface science who employ the modern Langmuir-Blodgett through, an improved apparatus based on her work, still in use today. When Irving Langmuir won the 1932 Nobel Prize in Chemistry for his work in the surface chemistry of oil films, he was building on the 18 year old autodidact Agnes Pockels' experiments with a button and thin tray, performed in her kitchen (not that he bothered to mention this in his Nobel lecture). Her sister-in law, Elisabeth Pockels wrote, "every day, millions of housewives were unhappy to see greasy dish water and just wanted to get rid of it, but it inspired this very person to make observations and finally also work on scientific treatises." She made her meticulous investigations for a full decade without any communication or collaboration with the world of academic science. She had tried writing to physicists at the University of Göttingen about her work but received no reply. Then in 1890, her brother sent her a paper on surface phenomena by renown physicist Lord Rayleigh.  With her brother's encouragement, she wrote Rayleigh a modest, 12 page letter, including all her results. She explained that she had been unable to publish her results in any scientific journal and she gave him her permission to use her results if they were at all useful. Rayleigh did not speak German, but luckily, his wife Evelyn could translate the letter for him. He instantly recognized the importance of Agnes' work and to his credit he sent them to Nature, putting the weight of his reputation behind supporting the work of an unknown amateur, writing, "I shall be obliged if you can find space for the accompanying translation of an interesting letter which I have received from a German lady, who with very homely appliances has arrived at valuable results regarding the behaviour of contaminated water surfaces. The earlier part of Miss Pickles' letter covers nearly the same ground as some of my own recent work, and the main harmonises with it. The later sections seem to me very suggestive, raising if they do not fully answer, many important questions. I hope soon to find opportunity for repeating some of Miss Pockels' experiments." Nature published Ages' letter with Rayleigh's cover letter. This paper, 'Surface Tension' is considered a landmark in the history of surface chemistry.

Seeing her research published encouraged her to continue her experiments, and her correspondence with Rayleigh. She wrote to him about the paramount importance of cleanliness in these experiments and her recognition of how contamination had hampered her previous efforts. Even dust could hinder reproducibility. To study monolayer films, she developed a procedure for the deposition of the compound of interest as a solution in benzene on the surface of the water in her trough and she was able to measure layer thickness at 13Å (an Angstrom is a billionth of a metre, roughly the size of a single atom). She published her second paper, with Rayleigh's help, in Nature in 1892. She went on to study forces on monomolecular films, the calming effect various oils can have on water, various liquids and their adhesion on glass and the surface tension of emulsions and solutions, other surface phenomena like capillary and contact angles, publishing her results in scientific journals including Nature, Wissenschaftliche Rundschau, Annalen der Physik, and Science.  She was invited to give public lectures by German universities.  She published subjects beyond surface science, including her translation of Georg Howard Darwin's 'The Tides and Kindred Phenomena in the Solar System' and a philosophy paper in Annalen der Naturaphilosophie. 

German scientists finally took notice. At the Physikalische Institut of Techniche Hochschile Brauschweig (the Physical Institute of the Technical University Brauschweig), crystal physicist Woldemar Voigt (1850-1919) offered her lab facilities, so over the next decade, she squeezed in further research there around her responsibilities at home. 

Soaps are surfactants made of molecules which have a "water loving" hydrophilic head and a water-repelling hydrophobic tail which is insoluble in water and tends to sit on its surface. Using her sliding through, Agnes found the tiny addition of surfactants had a small impact on surface tension until the slider passed a certain point, where tension would suddenly increase. She plotted surface tension versus slider position, showing the compression isotherm. She realized that the point the compression isotherm abruptly changed was when the continuous film of surfactant was a single molecule thick. With further experimentation she found that the threshold point is the same for a variety of surfactants. Knowing the volume of surfactant soap and the surface area covered by the film, she was able to calculate the surface area of the water occupied by a single molecule to be 20 square Angstroms, now known as the Pockels Point.

Early in the new century, in 1902, her parents' worsening health interrupted her work at the university and she became their full-time carer. Her father died in 1906, her brother died in 1913 and her mother died in 1914. She herself was in quite poor health and she needed to have a stay in a sanitarium. Then during the first world war, she lost contact with the scientific community. Germany was isolated and she was unable to access the foreign scientific literature. Her health and eyesight deteriorated. She had invested wisely and was more financially insulated than other Germans from the post-war financial chaos. She felt the responsibility to protect those around her from the threat of hunger and homelessness and she stopped carrying out her experiments. She published the last of her 14 papers, reviewing her classic work, in 1926. She spent her later years travelling in Europe and as the devoted Auntie Agnes to her brother's children. She finally received public recognition for her work, winning the Laura R. Leonard Prize of the Colloid Society in 1931. In 1932, Techniche Hochschile Brauschweig granted her an honorary doctorate in engineering. She was the first woman to receive such an award. Legendary German colloid chemist Wolfgang Ostwald published her biography on her 70th birthday in 1832. Her sister-in-law Elisabeth Pockels also wrote a biography of Agnes, focusing on her personal life. Since 1993 the university has granted the Agnes Pockels Medal to people who have made outstanding contributions to the development of the university, promoting research and teaching, particularly by women. In 2002 Techniche Hochschile Brauschweig established the Agnes Pockels Laboratory to foster chemical education and aid chemistry teachers, focusing on children under 10, especially girls.

Despite her limited access to education Agnes Pockels found wonder in a mundane tub of dishwater, and launched an entirely new field of science.

References

Agnes Pockels, Wikipedia, accessed January, 2026

DeBakcsy, Dale. How a Kitchen Experiment Spawned a New Science: The Surface Physics of Agnes Pockels. The Women in Science Archive. October 16, 2023.

Derrick, M. Elizabeth. Agnes Pockels, 1862-1935, Journal of Chemical Education, vol. 59, no, 12, pp. 1030-1031, December 1982

Gratzer, Walter (ed.). A Beside Nature - Genius and Eccentricity in Science 1869-1953. W.H. Freeman and Company, New York. pp. 88. 1999.

Kruse, Andrea and Sonja M. Schwarzl. "Zum Beispiel Agnes Pockels," Nachrichten aus der Chemie, 06, 2002, translated as "Who was Agnes Pockels - Agnes Pockels - Housewife and Chemist", Braunschweig Technical University, accessed January, 2026.

RAYLEIGH Surface Tension. Nature 43, 437–439 (1891). https://doi.org/10.1038/043437c0

Mathematician Olga Ladyzhenskaya, Turbulent History, Fluid Dynamics and Partial Differential Equations

Olga Ladyzhenskaya, linocut print, 11" x 14" by Ele Willoughby, 2026

For the 6th #PrinterSolstice prompt 'expression' I chose Olga Ladyzhenskaya, a mathematician who overcame personal tragedy, faced Soviet totalitarianism and the catastrophic political upheaval of the 20th century to make a huge impact on the math, making important contributions to study of partial differential equations and left a legacy of influence on a school of students and collaborators in this field. She changed the very way partial differential equations are examined and was one of the leading figures to popularize the notion of weak solutions (which satisfy the equations but may not be differentiable) for partial differential equations. Expressions included in my portrait are for the Navier-Stokes equation, quoted directly from her 1958 paper on the subject*. She was known for her courage, kindness and integrity as well as her indelible mark on mathematics.

Born in the wild woods in Kologriv, a small, remote town on northwest of Moscow, Olga Ladyzhenskaya (1922-2004) and her older sisters were taught mathematics by their math teacher father Aleksandr Ivanovich Ladýzhenski. He would formulate a theorem and ask his daughters to prove it, a technique which fostered Olga's mathematical intuition. Olga showed the most promise amongst her sisters and soon she and her father were working on calculus together. His family had descended from nobility, and it was not a good time to be either an intellectual, or descendent from nobility, in the USSR. His uncle, who also lived with the family in Kologriv, was a famous watercolour painter, Gennardy Ladýzhenski. Olga was close with her great-uncle, whom she called "Dedushka" or grandfather, and she carefully preserved his landscape paintings of the River Ounja. Her mother Anna Mikhailovna was originally from a small town in Estonia and was the homemaker. Their home was full of books and the girls were exposed to culture, though they grew up in what felt like the hinterland. Olga had a lifelong love of art and literature. Aleksandr stood up for his students after their parents were arrested by the NKVD (the predecessor of the KGB secret police). In his epic The Gulag Archipelago Solzhenitsyn recounted that a peasant warned Aleksandr Ladýzhenski that he was on a list of enemies of the state, but he refused to hide. Shortly thereafter in 1937 he was arrested and executed, likely in a NKVD torture chamber like many other great teachers, declared an "enemy of the people." It was a great shock to his family. Olga's mother and eldest sister managed to support the family through this terrible time. Her mother made dresses, soap and other craft work to earn an income and survive. Olga's older sisters were expelled from school as daughters of Aleksandr. Her father's status, and the resulting impacts on his family, was not rehabilitated until 1956, when Khrushchev delivered the "Secret Speech" at the 20th Party Congress of the Communist Party which denounced the Stalin's purges and exonerated the teachers who had been killed. This was a speech which also finally allowed a resumption of communication between mathematicians, across the Iron Curtain. Prior to the speech the two groups were working in isolation of each other. Olga had been tackling the some of the most difficult equations of mathematical physics without the benefit of knowing about progress made in the West.

Despite her excellent grades, when Olga graduated from high school two years later, she was not admitted to Leningrad State University, as the daughter of an "enemy of the people." She was allowed to attend Pokrovski Teachers' Training College in Leningrad. Then during the war years, she was forced to leave Leningrad and she taught at an orphanage at Godorets before returning home to teach at the high school in Kologriv, like her father, as well as in her home. She welcomed all students, regardless of their ability to pay. In thanks for her kindness, a student's mother interceded on her behalf and Olga got an opportunity to study mathematics at Moscow State University. She was awarded a Stalin stipend (despite her family history) and ration card so she could survive as a student, but she was often hungry. Sometimes she had to sleep on the auditorium benches, joking that she was learning through osmosis by using her books as a pillow. 

She wrote a thesis supervised by renown mathematician Ivan Georgievich Petrovskiǐ.  She started studying algebra and number theory and her interest in partial differential equations (PDEs) grew. This is the calculus of multivariable functions, a way to determine the rate of change of a function with respect to one of its variables. This is a branch of mathematics which is invaluable to physics, engineering and other fields which use applied mathematics. It is often impossible to find explicit formulas for solutions for partial differential equations so a lot of modern math and science research goes into finding approximate numerical solutions for PDEs. In pure mathematics, there is research into what we can know qualitatively about the nature of solutions of certain important, but impossible to explicitly solve, PDEs: things like whether solutions exist at all, if so, whether are they unique, whether they are differentiable or smooth, whether solutions are regular or stable. 

After she graduated in 1947, she got married to Alekseevich Kiselev, a specialist in number theory and the history of mathematics who lived in Leningrad. Thus she moved to Leningrad for graduate school, where she taught in the physics department. Though they had a loving marriage, it was brief. She and her husband separated because he wanted children whereas she wanted to devote her life to mathematics and felt that children would be an obstacle. She remained single thereafter. 

Her official supervisor for her thesis on linear and quasilinear hyperbolic systems of partial differential equations was Sergei Sobolev, but unofficially she was guided by Vladimir Smirnov and they became friends. Smirnov was in charge of several branches of mathematics, seismology, hydrodynamics and aerodynamics and she was strongly influenced to study mathematical physics. She defended her PhD in 1951. Two years later, 1953 was an important year for Ladyzhenskya; She published her first book, she also defended her "habilitation" dissertation (the highest university degree awarded in some European nations typically 5 to 15 years after a PhD) and Stalin died, thus things slowly began to change in Russia. She went on to publish six monographs (some as long as 700 pages) and more than 250 papers! 

Ladyzhenskaya and Smirnov started the weekly mathematical physics "Smirnov Seminar," in 1947 and she took over the seminar after his death in 1974. She is remembered for asking just the right questions in seminars, which were revealing for teaching. She organized sporadic very popular conferences of differential equations and their applications.  She was known for her work on partial differential equations and especially her work on whether the solutions to regular problems in the calculus of variations are analytic, which is the 19th of famed mathematician David Hilbert's list of 23 (at the time) unsolved problems. In 1954 she joined the Stekov Institute mathematical physics laboratory and would go on to become its head in 1961. 

By the mid-50s she was working on problems in fluid dynamics, a particularly mathematically-challenging field of physics, and the Navier-Stokes equations for the motion of viscous fluids, in particular. These equations would interest her for the rest of her career. These partial differential equations are vital to modelling everything from the weather, to turbulence, to ocean currents, to flow in a pipe, or in blood vessels or around an airplane wing. Despite having been developed in the 19th century and their importance to such a wide array of science and engineering, to this day, there is much we still do not know about these equations. Turbulence may be common in everyday life but the physics and underlying mathematics remain some of the least understood. Physicists are interested in how the smooth laminar flow say in a river, breaks down when it hits an obstacle causing eddies upon eddies in the flow until we are left with turbulence - and whether we can correctly model that turbulence thereafter. In my portrait I show precisely this: laminar flow lines hitting an obstacle, the ensuing eddies and devolution into turbulence. Mathematicians however still have not even been able to show whether smooth solutions even always exist in three dimensions. We do not even know if the equations will allow us to model fluids with any given initial conditions, indefinitely into the future. This is called the Navier-Stokes existence and smoothness problem, deemed one of the seven most important unsolved math problems. The Clay Mathematics Institute is offering a 1 million US dollar Millennium Prize award for a proof or counter-example to the problem. 

In the 1930s, Jean Leray had demonstrated the existence of weak solutions of the Navier-Stokes equations, but it had proved more difficult to show whether solutions were unique, until Olga was able to show both existence and uniqueness. She did this at a time when, as a Soviet mathematician, she was not able to read Leray's work. She was the first to prove the convergence of finite difference methods to solve the Navier-Stokes equations. That means she showed that we can reliably find a solution to the equations of how viscous fluids move by using the very useful trick of approximating derivatives with finite differences. She also analyzed the regularity of solutions under certain conditions for two-dimensional flows. Her resulting monograph of the Navier-Stokes equations ranks amongst the most influential mathematical books ever published. She believed that when flow becomes highly turbulent in 3D systems that the Navier-Stokes equations are insufficient so she present her own modification to the equations at the International Congress of Mathematicians in Moscow in 1966. 

She also analyzed the regularity of other types of partial differential equations, including parabolic equations (Vsevolod A. Solonnikov and her student Nina Ural'tseva) and quasilinear elliptical equations. These two types of equations are invaluable to the physics and engineering of time-dependent and steady-state phenomena, respectively. In the 1960s, these three published a veritable encyclopedia on the subject of the regularity of the solutions of PDEs that remains authoritative today. She published her influential text The Mathematical Theory of Viscous Incompressible Flow in 1961. She dedicated the book to the three people she most respected: her father, Vladimir Ivanovich Smirnov and Jean Leray.  At a time when exchanges between Western and Soviet scientists and mathematicians were virtually non-existent, she extended the results of Ennio De Giorgi, Jurgen Moser and John Nash ( the 1994 Nobel Laureate in Economics). 

Olga Ladyzhenskaya

She taught mathematics throughout her career and was recognized as one of the most significant and influential 20th century mathematicians. She nominated for the 1958 Fields Medal. She was president of the St Petersburg Mathematical Society. She was awarded the 1969 State Prize of the USSR and the Chebyshev Prize of the USSR Academy of Science. She was elected a corresponding member of the USSR Academy of Science in 1981, a foreign member of The German Academy of Scientists Leopoldina in 1985, a foreign member of the Academia die Lincei in 1989, a full member of the Russian Academy of Sciences in 1990 and a foreign member of the American Academy of Arts and Science in 2001. In 1989 Communist rule in the USSR ended, and Olga could travel more freely. She won the Great Gold Lomonosov Medal in 2002. Her name is inscribed in marble on a table at the Science Museum of Boston alongside the other most influential 20th century mathematicians. 

She counted amongst her friends dissent writer Aleksandr Solzhenitsyn, famous for raising awareness of repression and the Gulag prison system in Soviet Russia, and poet Anna Akhmatova, who wrote about the Stalinist terror, was twice nominated for the Nobel Prize for literature and dedicated a poem to her. She loved nature and travelling and was a skilled storyteller. She was once on the city council, and was engaged in her community, often risking her own safety and career to aid people opposed to the Soviet regime. She helped many mathematicians in Leningrad obtain apartments, free of charge, for themselves and their families. She cared deeply, was beloved and known to be full of energy and as a person of integrity, courage, faith, and unafraid to express her viewpoint despite a dangerous political climate. Nonetheless she remained a patriotic Russian and encouraged fellow Russian mathematicians to remain in Russia. She was plagued by eye problems and relied on special pencils to work in later years. She loved the sun and with her vision loss found the dark St Petersburg winters a challenge in later life. She was about to make a trip to Florida, and complete a paper on computational hydrodynamics when she died in her sleep in 2004 at the age of 81.

*The text reads "систему уравнений Навье — Стокса" which means 'a system of Navier-Stokes equations' and also "для функций" which means 'for functions' and "при граничных и начальных

условиях" which means 'under boundary and initial conditions'.

References

Dumbaugh, Della, Panagiota Daskalopoulos, Anatoly Vershik, Lev Kapitanski, Nicolai Reshetikhin, Darya Apushkinskaya, and Alecander Nazarov, The Ties That Bind - Olga Ladyzhenskaya and the 2022 ICM in St. Petersburgh. Notices of the American Mathematical Society. DOI: https://dx.doi.org/10.1090/noti2047. March, 20220.

Friedlander, Susan, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural'tseva, and Mark Vishik. Olga Alexandrovna Ladyzhenskaya (1922-2004). Notices of the AMS, Volume 51, Number 11, pp. 1321-1331, December, 2004. 

Goudon, Thierry and Irina Sophia Antipolis. Olga Alexandrovna Ladyzhenskaya. Brèves de Maths - Mathématiques de la planète Terre. April 23, 2013.

O'Connor, J.J. and E.F. Robertson, Olga Alexandrovna Ladyzhenskaya. MacTutor. University of St. Andrews, August, 2005.

Olga Ladyzhenskaya. Wikipedia, accessed January, 2026.