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

Eunice Newton Foote and the Greenhouse Effect

Eunice Newton Foote, linocut, 9.25" x 12.5" by Ele Willoughby, 2025

Once again, I am taking part in the Printer Solstice collection of printmaking prompts, starting at the winter solstice (here in the northern hemisphere). The prompts this year are mathematical in scheme, which works well for me, and my on-going series of portraits of women in STEM. The first prompt, "addition" made me think of the greenhouse effect, excess additional atmospheric CO2 and the resulting excess terrestrial temperatures. It made me think of a scientist who has been on my to do list for years: Eunice Newton Foote. The reason I have not tackled her portrait is that there are no known photographs of Eunice Newton Foote. I had hoped, since I knew that climate scientist Katherine Hayhoe and historians of science and others were seeking her portrait, that perhaps I should just wait patiently. As time wore on, we have learned more about Foote's life, but her portrait has not been found. However the waters have been muddied, as more and more people illustrate their posts and even published newspaper articles with images incorrectly labelled as Eunice Newton Foote. So I decided it was my time to add my image of her, to offer another imagined illustration, based on what we do know, rather than misinformation. It's quite easy to get the wrong photograph associated with a little-known historical woman in science, so I can understand how this has happened, but it frustrates me. Eunice Newton Foote deserves to be remembered as a scientist, inventor and activist, and she deserves not to be conflated with her daughters, or worse, random historical women and AI-generated nonsense.

My lino block print portrait shows the amateur pioneering American scientist, inventor and women's rights advocate Eunice Newton Foote (1819-1888) who did the earliest experiments to show the insulating effect of certain gases and correctly concluded that increasing carbon dioxide levels would affect atmospheric temperature and climate, which we now call the Greenhouse Effect. Each print is burnished by hand on lovely cream-coloured Japanese paper, 9.25" x 12.5" in a gradient of cyan, pale blue and bronze.

This is Mary Foote Henderson, again. She is not her mother.
This is specifically a detail of a photo by the Brady Studio. 
Record Unit 7075 - The Henderson Family Papers, 
1868-1923, Smithsonian Institution Archives. 
You can check for yourself.

Eunice Newton was born in Connecticut to Thirza and farmer and entrepreneur Isaac Newton Jr., a distant relative of famed physicist Sir Isaac Newton, who had six sons and five other daughters (though girl died at two years of age). They moved the family to Ontario County in western New York, which was a centre of social activism for abolitionists, dress reform activists, mystics, temperance advocates, and women's rights campaigners. She attended the Troy Female Seminary, a women's preparatory school established by feminist Emma Willard, which offered a much broader curriculum than the typical women's finishing school and where students were actually encouraged to attend science courses at the nearby Rensselaer School, run by a scientist, education innovator and proponent of women's education Amos Eaton. Eaton introduced practical experimentation in the lab alongside teaching theory.

In 1841 Eunice married lawyer Elisha Foote, who trained in Johnstown, New York, under Judge Daniel Cady, the father of women's rights activist Elizabeth Cady Stanton. Elisha bought a house, then deeded it to Cady who gave it to his daughter. Elisha became a judge in Seneca County, but resigned in 1846. Eunice was friends with Elizabeth Cady Stanton and attended the 1848 Seneca Falls Convention, the first women's rights convention. She and Elisha both signed the Declaration of Sentiments, described by Frederick Douglas as the "grand movement for attaining the civil, social, political, and religious rights of women." Eunice was one of the five women who prepared the convention proceedings for publication.

Eunice and Elisha both worked as inventors. Elisha filed a patent in 1842 on a thermostatically controlled cooking stove invented by Eunice presumably because as a married woman, Eunice would have been unable to defend her patent in court. Eunice told Elizabeth Cady Stanton she thought half of all patents filled were in fact inventions by women with the patents taken out by men. In fact, in 1857, Elisha defended the patent and got a substantial settlement for infringement.

Mary Foote Henderson, not her mother.

Elisha went back to working as a lawyer, and Eunice built a lab in their home. The pair had two daughters: writer, developer, suffragette and social activist Mary who became known as "The Empress of Sixteenth Street" and writer and naturalist Augusta, who wrote The Sea-Beach at Ebb-Tide, regarded as a seminal work on the intertidal biology of the United States. The family moved to Saratoga Springs, NY, where Elisha specialized in patent law, then became the Commissioner of Patents, then served on the Board of Examiners-in-Chief for several years.

In her lab Eunice investigated the effect of sunlight on various gases. Using two glass cylinders, each equipped with two mercury-in-glass thermometers, she used an air pump to evacuate the air from one cylinder and compress it in the other cylinder. When their temperatures equalized she placed them both in the sunlight and looked for temperature variances. She contrasted this with when the cylinders were placed in the shade and also tested the temperature results by dehydrating one cylinder and adding water to the other, to measure the effect of dry versus moist air. She noted that the amount of water in the air did affect the temperature. She tried this experiment using air, carbon dioxide (then known as carbonic acid gas) and hydrogen. The cylinder of carbon dioxide in sunlight became hotter than the others. She wrote: "The receiver containing this gas became itself much heated—very sensibly more so than the other—and on being removed [from the Sun], it was many times as long in cooling". Considering the history of Earth, she wrote, "An atmosphere of that gas would give to our earth a high temperature; and if, as some suppose, at one period of its history, the air had mixed with it a larger proportion than at present, an increased temperature from its own action, as well as from increased weight, must have necessarily resulted." She clearly understood and expressed the impact of increased atmospheric carbon dioxide and what we now call the Greenhouse Effect. She submitted these findings as a paper entitled "Circumstances Affecting the Heat of the Sun's Rays", that she submitted for the tenth annual AAAS meeting, held on August 23, 1856, in Albany, New York, where it was presented by physicist Joseph Henry on her behalf. While not published in the proceedings of the AAAS meeting, it was published in the 1856 edition of the American Journal of Science and Arts; it was the first known physics publication in a scientific journal by an American woman. Summaries were also included in several international scientific journals and periodicals. Eunice was praised in the September 13, 1856, issue of Scientific American for backing up her theories with experiments, noting "she was deeply acquainted with almost every branch of physical science"

C'mon people. This one is literally labelled

Mrs. Henderson. It's a photo by Ida

Hindman in 1895, for the Washington

Sketch Book.

Eunice's experiment was not without precedent.  In the 1770s, Horace Bénédict de Saussure found that altitude impacted solar heat in an enclosed cylinder and the 1820s Joseph Fourier theorized that atmospheric gases trapped solar heat. But only Eunice Foote had drawn the conclusion that solar heat would be increased by the presence and proportion of C02 or water vapour in the atmosphere. Three years after Foote's publication, in 1859, physicist John Tyndall performed a more sophisticated experiment which showed several gases both trapped and emitted infrared thermal radiation rather than simply investigating the effect of sunlight. He published "Note on the Transmission of Radiant Heat through Gaseous Bodies" in the Proceedings of the Royal Society, where he cited Claude Pouillet's work on solar radiation through the atmosphere, but did not cite Foote's work. It's unclear if he failed to note her results or did not see their relevance. He did not mention water vapour, carbon dioxide, or climate until several publications later. A very skilled and well-trained (though regrettably quite chauvinistic) physicist, Tyndall is often credited with the earliest evidence of the Greenhouse Effect. Alternatively, the Greenhouse Effect is sometimes credited to physical chemist Svante Arrhenius, who in 1896, used physical chemistry to estimate how much atmospheric CO2 would increase the Earth's surface temperature. There is no denying though that Eunice Newton Foote was the first to specifically argue that our climate would warm with increasing atmospheric CO2.

Foote went on to investigate moisture content and which gases in the air could generate static electricity. She hypothesized that electric charges and fluctuations in atmospheric pressure might explain the Earth's magnetic field and polarity, which we now know is not the case. Her paper "On a New Source of Electrical Excitation" was read by Henry at the 1857 AAAS meeting in Montreal, and published in the Proceedings of the American Association for the Advancement of Science, the first physics publication there by an American woman. 

In 1860 Eunice filed a patent in her own name for a shoe and boot insert made of a single piece of vulcanized rubber to "prevent the squeaking of boots and shoes". In 1864 she developed a new cylinder-type of paper-making machine. In 1868 she invented skates without straps. 

She died in 1888 in Lenox, Massachusetts. She fell into obscurity until historians began researching early women scientists in the 1970s and more recently, climate scientists have revisited and worked to highlight her early contributions to their science.

As her story has been rediscovered people have made a concerted effort to find images of her. Though there are many photographs of her two daughters, especially Mary Foote Henderson, and Augusta Newton Foote Arnold, and her husband Elisha Foote Jr, there are no known photographs, or painted portraits of Eunice. Many stories, including in published newspaper stories, are illustrated with photographs of Mary misidentified as Eunice, or worse, with AI-generated slop images based on completely unrelated women. All we have, so far, is her 21 July 1862 passport application, where she is described as having an oval face, dark brown hair, blue-grey eyes, a small ordinary chin, an ordinary nose, a full forehead and a rather large mouth. Having looked at these photos carefully, I have convinced myself that Mary resembles her father, so I don't even think we can rely on family resemblance and let Mary's image give us an idea of what Eunice looked like. So I chose to illustrate her, without showing her full face, at work in her lab, in Victorian clothing like what other women doing similar work. Her paper describes her experiments with air pump, and two large cylinders with two thermometers each, so I could illustrate these as described.

References

Augusta Foote Arnold, Wikipedia, accessed December, 2025

Elisha Foote, Wikipedia, accessed December, 2025

Eunice Newton Foote, Wikipedia, accessed December, 2025

Foote, Eunice. "Circumstances Affecting the Heat of the Sun's Rays". The American Journal of Science and Arts. 22 (66). New York, New York: G. P. Putnam & Company: 382–383. ISSN 0099-5363. OCLC 1280516952. September, 1856.

Foote, Eunice. "On a New Source of Electrical Excitation". Proceedings of the American Association for the Advancement of Science: Eleventh Meeting. Cambridge, Massachusetts: Joseph Lovering: 123–126. OCLC 923936325.  August, 1857.

Huddleson, Amara. Happy 200th birthday to Eunice Foote, hidden climate science pioneer,  Climate.gov, July 17, 2019.

Josse, Tess. August 1856: Eunice Foote Concludes that Carbon Dioxide Could Warm The Atmosphere, Three Years Before John Tydall Did, APS News, July 12, 2023. 

Kurland, Zoe, Katie Hafner, Elah Feder and The Lost Women of Science Initiative, The Woman Who Demonstrated the Greenhouse Effect, Scientific American,  November 9, 2023.

Mary Foote Henderson, Wikipedia, accessed December, 2025

McNeill, Leila  "This Lady Scientist Defined the Greenhouse Effect But Didn't Get the Credit, Because Sexism". Smithsonian. Washington, D.C.: Smithsonian Institution. ISSN 0037-733December 5, 2016.

Joseph Fourier and the Sinusoids

Joseph Fourier, linocut, 11" x 14", by Ele Willoughby, 2024

Sometimes people ask to commission a scientist portrait of someone I had already considered portraying. I don't think you can study physics for as long as I did and not think about Joseph Fourier. So when asked to make his portrait, I had a plan in mind.

French mathematician and physicist Jean-Baptiste Joseph Fourier (1768-1830) is best remembered for his work Fourier series, Fourier transforms, Fourier’s law of conduction, Fourier analysis and harmonic analysis and their use to solve heat transfer problems. He is also often credited with proposing the greenhouse effect as early as 1824.

Born in Auxerre, a son of a tailor, he was orphaned at age nine. Recommended to the Bishop of Auxerre, he was educated by the Benedictine Order of the Convent of St. Mark. Being a commoner he could not seek a commission in the scientific corps of the army but took a military lectureship in mathematics. He took a prominent part in promoting the French Revolution in his district. Nonetheless he was briefly imprisoned by the Terror. In 1795 he was appointed to the École Normale and later succeeded Lagrange at the École Polytechnique. After accompanying Napoleon as a scientific adviser on his Egyptian expedition in 1798 he was appointed secretary of the Institut d’Egypte, where he organized workshops for the French to make munitions, wrote several papers for the Egyptian Institute (now Cairo Institute). He returned to France in 1801 after the British victories, to resume work at the École Polytechnique but Napoleon appointed him Prefect of the Department of Isère in Grenoble. In Grenoble he began to experiment on the propagation of heat, and contributed to the comprehensive catalogue Description de l’Égype.

In 1820 he published his theorem on polynomial real roots, that a polynomial with real coefficients has a real root between any two consecutive zeros of its derivative. (This is technically a corollary of a theorem published by Budan in 1807 and 1811, also now known as Fourier’s theorem). In 1822 he succeeded Delambre as Permanent Secretary of the French Academy of Sciences, and he published his heat flow research in his Théorie analytique de la chaleur (The Analytical Theory of Heat) which included his important claim that any function of a variable, continuous or discontinuous, can be expanded in a series of sines of multiples of the variable. The idea is true (with some conditions, later discovered by Dirichlet) and a breakthrough. This is the foundation for what we call the Fourier transform, an invaluable tool in math, physics and engineering. During the 1820s he realized that the Earth, at its distance from the Sun should be colder is it is only heated by solar radiation. He wrongly thought Earth has must then receive significant radiation from interstellar space but he did consider the correct answer that the atmosphere acts as an insulator. He referred to experiments by Saussure who measured temperature in a vase with several inset panes of glass, who noted that the inner chambers (under more glass) become hotter. Fourier noted that if the atmosphere makes a layer like the glass in the vase we would get the same effect on Earth (though he noted that Saussure’s experiment did not account for the convection we get in the atmosphere). This is now recognized as the first conception of what we know as the greenhouse effect.

He became a foreign member of the Royal Swedish Academy of Science in 1830. He experienced heart aneurysms in both Egypt and Grenoble and died 16 May 1830. He was buried in Père Lachaise Cemetary in Paris in a tomb with an Egyptian motif and his name is one of 72 inscribed on the Eiffel Tower.

My portrait (inspired by the portrait by Boilly) alludes to Fourier decomposition: the sine waves sum to the violet waveform framing him. With an infinite series of sines, his very outline, as a function of x (the horizontal axis across the page) could be made. Likewise the circles in the background are another visualization of building up an image of Fourier himself from sine waves. If you trace the perimeter of a circle on a continuously advancing sheet of paper you produce a sine wave. (Mathematicians and physicists often use this equivalency to think of a real sinusoid as the real part of a complex function where a vector formed by by its real and imaginary parts traces a circle around the origin). So a simplified function tracing the main lines in Bouilly’s portrait can be produced by the sum of sine waves produced by tracing the series of these epicycle circles. 

There are a lot of great tutorials about this online, but a particular shout out to 3Blue1Brown on YouTube who not only has an excellent series of videos (it's everything you ever wanted to know about Fourier series but were afraid to ask) but he's also specifically made animations of producing a path that approximates Bouilly's portrait with rotating vectors or Fourier epicycles here.

Kathleen Lonsdale, crystallographer, pacifist and prison reformer

 

Kathleen Lonsdale, 11" x 14" linocut print on Japanese kozo by Ele Willoughby, 2023

I chose Kathleen Lonsdale DBE FRS (née Yardley, 1903-1971) for the #printerSolstice prompt shape because she solved a longstanding chemistry conundrum of the shape of benzene & her drawing of electron density for hexachlorobenzene (green) & model of hexamethylbenzene explore shape in different forms. 

Going to Holloway prison was the single most formative experience for Kathleen Lonsdale’s scientific career and it gave her the ability to speak to anyone. Her husband said, “Before prison it might have bothered her to go to Buckingham Palace. Afterwards, Holloway or Buckingham Palace were all the same.” Born the tenth child of a poor family in Ireland, with four brothers who died in infancy, pacifist, prison reformer and physicist Dame Kathleen Lonsdale DBE FRS (née Yardley, 1903-1971) served time, as she was unwilling to compromise her beliefs. She was also a trail blazing crystallographer who solved a conundrum which had plagued chemists for decades: the shape of the benzene ring, proving it was flat using x-ray diffraction on hexamethylbenzene in 1929. She was the first to employ Fourier spectral methods and used them to solve the structure of hexachlorobenzene in 1931. In 1945 she was one of the first two women elected Fellow of the Royal Society and was the first woman in several roles including: tenured professor at University College London, president of the International Union of Crystallography and president of the British Association for the Advancement of Science.

Her father, a soldier and then a postmaster Harry Yardley and her mother, a strict fundamentalist Baptist of Scottish descent Jessie Cameron did not have a happy marriage. Between the unrest in Ireland and her father’s alcoholism, her mother decided to divorce and move the children to Seven Kinds, Essex, England when Kathleen was five. She won a scholarship to the Ilford County High School for Girls but had to go to the boys’ school in her final two years as the girls’ school did not offer mathematics and science. During WWI her home was on the Zeppelin route; she did homework by candlelight during air raids and first developed her opposition to war. Anxious to get to university as soon as possible she went to the Bedford College for Women in London on a county scholarship. After her first year she won a university scholarship and switched from mathematics to physics, against all advice (especially that of her old headmistress who told her she would never distinguish herself in physics). She graduated in physics with the highest score ever for a London University, with a BSc in 1922, which brought her to the attention of physics Nobel laureate William Henry Bragg, one of her examiners.

Bragg offered her a spot on his team at University College (and then the Royal Institution), and a grant of a £180 a year! She lived at home and contributed to family expenses, gaining her MSc from University College London in 1924. She worked with Bragg until she married in 1927 and followed her husband, research chemist Thomas Lonsdale to Leeds, where he had been offered a job at the Silk Research Association. Shortly after her marriage, she applied for an 1851 Exhibition Fellowship which Bragg expected she would win, as several of his other (all male) students had done. Not only did they turn her down for the award, they wrote they “would be breaking the spirit of the regulations in awarding an exhibition to a married woman.” Luckily Bedford College offered her a research grant and she continued to correspond with Bragg. She worked part-time as a physics demonstrator and doing lab work in Leeds. It was here that she was given crystals of hexamethylbenzene, the first important structure she solved. Debate had been raging between organic chemists and crystallographers whether benzene was flat or  had a zigzag shape like cyclohexane, but benzene itself was a challenge to crystallize. Lonsdale had the insight that she could instead look at the benzene within hexamethylbenzene and in the process of solving its form, she proved that the benzene ring (which it contained) was flat. She followed this with solving the structure of hexachlorbenzene; this was important as she was the first to investigate an organic compound with Fourier analysis. She had cleverly found a project she could do with calculations rather than lab work while she focused on starting their family. She also developed popular crystallographic reference tables with W.T. Astbury. She considered giving up science, but Thomas supported her research told her he “had not married to get a free housekeeper.” He encouraged her to continue in research. When they had their first daughter in 1929, Bragg convinced the Royal Institution to grant her £50 to employ some childcare  so she could work on calculations. Then they moved back to London for Thomas’ new job, and had a second daughter in 1931. Bragg, anxious to have her back, was able to find a further £200 to assist her at home so she could  return to work in 1931. They had their son in 1934. She earned her doctorate from the University of London in 1936 while working at the Royal Institution, where she stayed for 15 years. She worked with Bragg until his death in 1942, then with Sir Henry Dale, as a Dewar Fellow from 1944 through 1946.

She was raised a Baptist, but in 1935, she and her husband, both committed pacifists, became Quakers. She became a Sponsor of the UK Peace Pledge Union, which meant she signed the pledge "War is a crime against humanity. I renounce war, and am therefore determined not to support any kind of war. I am also determined to work for the removal of all causes of war.” They turned the top floor of their house into a flat where they welcomed refugees from Germany. When she was required to register for civil defence duties during WWII she refused to do so and refused to pay the small fine for not registering. She believed there should be an exemption for conscientious objection. She was sentenced to serve a month in Holloway prison, where the grim conditions lead to a life-long commitment to prison reform. While she was imprisoned, she found the clothing unclean, medical exam sketchy and she collapsed under her workload, scrubbing and cleaning; only then did they lighten her workload. Sir Henry Dale requested that she be given access to papers and instruments and she was allowed to work in her cell in the evenings.  Her colleagues worried she would be bored; she was in fact absorbed, talking to fellow prisoners about their lives and crimes. Her second fine for refusing to register for civil defence was paid anonymously, much to her chagrin; she would have rather stood on her principles and serve another prison term. She contributed to a pamphlet on Prison for Women about her experiences in Holloway and the need for prison reform.

In 1945 Lonsdale and Marjory Stephenson were the first women elected Fellows of the Royal Society. Then she finally got a permanent position. In 1946 she was appointed Reader in Crystallography and then Professor of Chemistry and Head of the Department of Crystallography at the University College London in 1949, finally beginning to teach and run her own research group, mentoring future crystallographers. She was their first tenured female professor. She researched the use of x-ray imaging at different temperatures and the structure and texture of crystals. She worked on the synthesis of diamonds. She won the Royal Society’s Davy Medal for significant discoveries in chemistry in 1957. Later she worked on solid state reactions, pharmacology and structure of methonium compounds and stones and minerals produced by the human body like kidney stones. She became an emeritus professor after 1968. Nobel laureate Dorothy Hodgkin wrote, "There is a sense in which she appeared to own the whole of crystallography in her time.

In 1953 she delivered the keynote Swathmore Lecture at the Yearly Meeting of British Quakers, “Removing the Causes of War”. She wrote about peaceful dialogue was appointed the first secretary of Churches' Council of Healing by the Archbishop of Canterbury. 

When Thomas retired at 60, they moved to Brexill-on-Sea; this meant 5 hours a day commute for Kathleen, but she felt it worthwhile though she was tired. Thomas helped with her tremendous amount of correspondence about peace and prison reform, and would bring her dinner in bed as soon as she got home. She was someone who never stopped working, even when she became ill and was hospitalized. She died in hospital 1971 from anaplastic cancer, at age 68, the day after Thomas' 70th birthday.

References

Kathleen Lonsdale, Wikipedia, accessed February, 2023

Hodgkin, Dorothy M.C., Kathleen Lonsdale, 28 January 1903 - 1 April 1971, Biographical Memoirs of Fellows of the Royal Society, Volume 21, Issue 21, November 1975

Melinda Baldwin, The Royal Society’s first woman physicist, Physics Today, 25 January, 2018. DOI: 10.1063/PT.6.4.20180125a

One crystal model of hexamethyl benzene, Science Museum Group, Object Number: 1993-421/4/11, Gift of University College London, in memory of Dame Kathleen Lonsdale 

Prints inspired by art history

I am trying to participate in the #PrinterSolstice again this year. They have created a series of prompts for each of 13 weeks starting with the (northern hemisphere) winter solstice. This year the themes are based on 20th century movements in art. It's been challenging to find time; we're once again sheltering at home and schools have gone remote here. Facilitating remote school takes a lot of my time and I cannot print at the same time, though I can plan, draw and carve. 

We started with Abstract Expressionism, which is really outside my wheelhouse, since my prints are representational. But it gave me a chance to work intuitively to create a mono print with scraps of lino.

monoprint by Ele Willoughby, 2022

Next was Art Deco. I looked at a lot of Art Deco artworks. The frequent clamshell motif and the keyhole shape in Art Nouveau works, plus seeing a number of mermaid illustrations reminded me I had long wanted to illustrate the story of Mélusine, the legendary half-fairy ancestor of the House of Lusignan and royals including the Plantagenets, whose lower half became a serpent when she bathed. She marries a nobleman but insists he must never observe her in the bath; of course he does, and she leaves him - so the keyhole shape works just right to tell the story! There are many versions, like most folklore. Sometimes she has two tails, or a fishtail or wings. There are different versions of her name and various stories are found in different regions especially France, Luxembourg and the Low Countries. I first learned of her from Manuel Mujica Láinez’s The Wandering Unicorn, which tells her story through the centuries. Her story also appears in A.S. Byatt’s Possession amongst many other places from operas to video games.

Mélusine linocut, 8" x 10" by Ele Willoughby, 2022

These art history prompts have been a challenge to link to my art practice. I've  been seeking a connection to things like science art. The third prompt was Bauhaus. In looking at Bauhaus paintings I was reminded of nothing so much as Feynman diagrams, and the exuberance action on the quantum scale, so I decided to combine quantum physics with the Bauhaus vocabulary of lines, shapes and colour palette. 

I was thinking more of the paintings of Kandinsky than the regular geometric shapes in Bauhaus design: a welter of black straight, wavy and curly lines, stripes of colour, triangles, circles and concentric rings and washes of pale colour, often on a cream coloured background. 

The Feynman diagrams are a tool of particle and quantum physics to both denote a particle interaction and also can be used to make calculations of probabilities and physical properties. Straight lines denote particles (quarks and leptons like electrons). Wavy lines denote photons. Curly lines are gluons and the dotted line is a Higgs particle. I wanted to include an electron spontaneously giving off a virtual photo and particle-antiparticle pairs, production of a Higgs particle, one diagram of the sort of we see if we smash protons together, and one hilariously named penguin diagram (in this instance producing a gluon).

Feynman Diagram Bauhaus, linocut, variable edition, 8" x 10" by Ele Willoughby, 2022

Looking at all these prints as I try to plan ahead and link them to my art practice and science art I am reminded of Leonard Shlain's book Art and Physics. It should be around here somewhere but I can't find it on my bookshelves. (Aside: this house needs a librarian.) In the book Schlain linked major movements in art with advancements in physics. I am not sure I can agree with his thesis that movements in art presaged new physics (which feels like it violates causality to me) but I greatly enjoyed the book. Others have drawn parallels between art and physics and it's clear that both math and physics were an influence of some of these major modern movements in art. In fact, this has been true for centuries; consider for instance the development of artistic perspective, or the camera obscura. One of the obvious connections is between cubism and the math of the fourth dimension and the physics of relativity. So that is something I'm thinking about for an upcoming print.

Some of the other prompts (colour field, Dadaism, Fauvism, Harlem Renaissance, Minimalism and surrealism) are less obvious for me, but I'm thinking ahead. Op Art is rather clearly related to mathematics. I have a scientific idea for Conceptual art and the seed of an idea for Pop Art. Stay tuned for more!

Mathematician Sophie Germain

 

Linocut 'Sophie Germain' by Ele Willoughby, 2021

French mathematician, physicist and philosopher Marie-Sophie Germain (1776 – 1831), known as Sophie, taught herself mathematics using books in her father's library and by corresponding with leading mathematicians of her day, including Lagrange, Legendre and Gauss, initially using the pseudonym Monsieur LeBlanc since she knew it was unlikely her contemporaries would take a woman in math seriously. She later wrote to Gauss, the leading mathematician of her day that she used the pseudonym "fearing the ridicule attached to a female scientist." Her work on elasticity theory won her the grand prize from the Paris Academy of Sciences. Her trailblazing work on Fermat's Last Theorem set out a strategy and framework for mathematicians pursuing the problem for hundreds of years. She was denied a formal mathematics education or professional standing due to her sex, but Gauss argued she deserved an honourary degree (though it was never granted).

 

She was born to a bourgeois family; her father is usually described as a wealthy silk merchant who was elected to the États-Généraux (later the Constitutional Assembly), as a representative of the bourgeoisie. By the time she was 13, the Bastille fell, and she remained indoors for safety during those tumultuous times, her father's library her only source of entertainment. She was fascinated reading about Archimedes' death at Roman soldiers' hands during the siege of Siracusa, unable to tear himself away from mathematics. It piqued her interest and she devoured the mathematics books she found, even teaching herself Latin and Greek in order to read Sir Isaac Newton and Leonard Euler's works. Her parents disapproved this sudden interest in a subject deemed inappropriate for a woman and they denied her warm clothes or a fire to study at night. She simply wrapped herself in quilts and studied by candlelight, when it was so cold her ink froze, eventually winning over her mother's support. Sophie was lucky in that she was not forced to marry and her family was wealthy enough to support her throughout her life, and though mostly excluded from formal education and the society of mathematicians, she was able to pursue her self-study.

 

The École Polytechnique opened - to men only - in 1794, but lecture notes were made available on request. Students were requested to send solutions to faculty and Sophie began submitting notes to Joseph Louis Lagrange under the name of a former student who had died young, Monsieur Antoine-Auguste Le Blanc. Lagrange recognized "Le Blanc's" ability and requested a meeting, so her rouse was up. Luckily, Lagrange was not opposed to a woman studying mathematics and agreed to mentor her. In 1798, Adrien-Marie Legendre published Essai sur la théorie des nombres and Sophie became interested in number theory and began corresponding with Legendre. Impressed, he included some of her work in the supplement to the second edition of his book, praising it as très ingénieuse ("very ingenious"). Then Gauss published his magnum opus Disquisitiones Arithmeticae. She worked through it for three years before writing him, again as M. Le Blanc, to discuss his book and tell him about her work on Fermat's Last Theorem, a famous grand problem of number theory. Unfortunately, she had made a weak assumption in one of her proofs, and Gauss did not reply to this first letter.

 

Mathematician Pierre de Fermat famously scrawled his eponymous last theorem in the margin of a book around 1637, without supplying any proof, noting simply that the proof was too long to fit. After 354 years of effort by countless mathematicians, Andrew Wiles was finally able to prove the theorem correct in 1995. The theorem states that no three positive integers x, y, and z satisfy the equation x^p + y^p = z^p for any integer value of p greater than 2. Sophie was working on this problem and making real in-roads.

 

During the Napoleonic wars, France occupied the German town of Braunschweig, where Gauss lived, and Sophie feared he might suffer the same fate as Archimedes. She wrote family friend General Pernety pleading for him to ensure Gauss' safety. Soldiers were dispatched and found the confused Gauss perfectly safe. Gauss, of course, did not know that Sophie Germain was none other than M. Le Blanc. She decided to reveal her identity and he replied,

 

How can I describe my astonishment and admiration on seeing my esteemed correspondent M. Le Blanc metamorphosed into this celebrated person ... when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarising herself with [number theory's] knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the noblest courage, extraordinary talent, and superior genius.

 

They became friends and Gauss truly respected her ability, though he was not a reliable correspondent and generally did not review her work (and she would have really benefited from such feedback, lacking mentorship in number theory, and having gaps in her knowledge since she was self-taught). 

 

She became interested in other problems. German physicist and musician Ernst Chladni had published his experiments on vibrating plates (following the trailblazing work of Robert Hooke). He used a violin bow to vibrate a metal plate covered in sand, so that the sand would concentrate on nodal lines marking divisions between regions that moved in opposing directions. His drawings of the patterns produced are known as Chladni figures (like those shown in lavender in my print). Germain was able to attend his demonstration in Paris. The Paris Academy of Sciences launched a contest to develop the mathematics explaining the vibration of an elastic surface and comparing this to experimental data like Chladni's, with a reward of 3,000 francs. Lagrange pointed out that a new branch of analysis would be required and scared off all would-be contestants with the exception of Sophie and Denis Poisson. But Poisson was elected to the Academy, thus became a judge, leaving only Sophie. She began, mentored by Legendre, but her submission was deemed insufficient, though she provided some ingenious results, which allowed Lagrange to derive an equation, correct under certain conditions. Lagrange died within two years, and Sophie lost a mentor. The Academy decided to extend the contest and Sophie persisted. After initially helping, Legendre withdrew his support. Sophie submitted another attempt anonymously, but it had several errors (of the sort she would have been taught to avoid had she been allowed to study math at a university). She consulted Poisson, and he had access to all her notes as a judge. He then published his own work on elasticity without acknowledging any of her work or their conversations on the subject. At that point in 1816, she published under her own name, "Recherches sur la théorie des surfaces élastiques" partially so what Poisson had done would be clear, and to point out the errors in his work. They extended the contest again partially in response to the breach of confidentiality by Poisson and she persisted with her efforts. She won the gold medal and became the first woman to win a prize from the Paris Academy of Sciences but did not attend the prize ceremony. The Academy was not entirely satisfied; she had the correct differential equation, but having used an incorrect equation by Euler she had incorrect boundary conditions. Even as a prize winner, she was still denied entry to academy meetings as a woman for several years until she made friends with Joseph Fourier, a secretary of the Academy, who got tickets on her behalf. She published her prize-winning essay in 1821, at her own expense as the Academy had neglected to do so, complete with her notes on errors she had made. In 1826, she submitted a revised version of her work; the Academy considered it trivial but they did not want to reject her as they would a man and professional colleague. They both denied her access and were patronizing in their misguided attempt at kindness. She published this essay on the advise of mathematician Augustin-Louis Cauchy. Her nephew later made sure she had a final publication on elasticity, publishing "Mémoire sur la courbure des surfaces" posthumously on her behalf in 1831.

 

In 1815, the Academy offered an award for a solution to Fermat's Last Theorem, rekindling her first love of number theory. She wrote Gauss with her strategy for a general proof and the significant in-roads towards a proof she had made, but Gauss never replied. She produced what is now known as Sophie Germain's Theorem. To show that Fermat's Last Theorem holds, you can divide the powers p into numbers which are not divisors of x, y or z, or powers p which are a divisor of at least one of x, y or z. She proposed her theorem:

 

Let p be an odd prime. If there exists an auxiliary prime P = 2Np + 1 (N is any positive integer not divisible by 3) such that:

1. if x^p + y^p + z^p ≡ 0 (mod P), then P divides xyz, and
2. p is not a p-th power residue (mod P).

and she used this result to show that Fermat's Last Theorem holds true for all odd primes p < 100. Her method was later used to show it holds true for all p < 1700. Her theorem is known from a footnote in Legendre's treatise on number theory, where he used it to prove Fermat's Last Theorem for p = 5. The text in my print is from one of her on unpublished manuscripts:

Remarque sur l'impossibilité de satisfaire en nombres entiers a l'équation x^p + y^p = z^p. L'impossibilité de cette équation serait hors de doute si on pouvais démontrer la théorème suivant: Pour toute autre valeur de p que p = 2, il y a toujours un infinité de nombres premiers de la forme Np + 1 pour lequels on ne peut trouver deux residus 1^ièmes puissances  dont la différence soit l'unité.

 

(My gloss: "Remarks on the impossibility of any whole numbers satisfying x^p + y^p = z^p . The impossibility of this equation can be shown to be without doubt if we can demonstrate the following theorem: For all p > 2, there are an infinite series of primes of the form Np + 1 for which we cannot find two residues of the first power separated by 1"). She goes on to note that if there's any numbers which do satisfy Fermat's equation for p > 5 it must be numbers "whose size frightens the imagination", around 40 digits long.  

 

She also pursued philosophy and psychology on her own. Her nephew had two of her works published posthumously: Pensées diverses, a history of science and math with her commentary and Considérations générales sur l'état des sciences et des lettres, aux différentes époques de leur culture in which she argued there no difference between the sciences and the humanities and gained the praise of philosopher August Comte. 

 

She continued working despite pain after her diagnosis of breast cancer in 1829. She died in 1831, listed only as a property owner, not a mathematician on her death certificate. She is now recognized for her brilliance and originality, but her progress was often sadly hampered by the lack of instruction and the way her peers treated her as a novelty, and avoided proper constructive criticism. She wrote, “These facts are my domain and it is to me alone that they remain hidden. That’s the privilege of the ladies: they get compliments and no real benefits.” Several scholars argue that a contemporary man with similar skills and interest would have had his abilities embraced and talents nurtured. Sophie Germain was able to achieve what she did through both her tremendous talent and extraordinary persistence. Along with her theorem, subsequent discoveries in number theory have been named in her honour, as well as a street in Paris and the Sophie Germain Prize in mathematics offered by the same Academy which had snubbed her.

 

References

Sophie Germain, Wikipedia, accessed March 2021

Sophie Germain’s Theorem, Wikipedia, accessed March 2021

Ernst Chladni, Wikipedia, accessed March 2021

Ernst Chladni, Entdeckungen über die Theorie des Klanges, 1787, via Chladni Figures (1787) on Public Domain Review

Cristina P. Tanzi, Sophie Germain's Early Contribution to the Elasticity Theory, MRS Bulletin , Volume 24 , Issue 11 , November 1999 , pp. 70 - 71 DOI: https://doi.org/10.1557/S0883769400053549

Alexanderson, G.. “About the cover: Sophie Germain and a problem in number theory.” Bulletin of the American Mathematical Society 49 (2012): 327-331.

Richard Baguley, Sophie Germain: The Mathematics Of Elasticity, Hackaday.com, March 20, 2018

Evelyn Lamb, Thank You, Sophie, and I'm Sorry, Scientific American Blog, April 1, 2017.

Maria Popova, How the French Mathematician Sophie Germain Paved the Way for Women in Science and Endeavored to Save Gauss’s Life, Brainpickings, org, February, 2017.

Reinhard Laubenbacher and David Pengelley,  “Voici ce que j’ai trouvé:” Sophie Germain’s grand plan to prove Fermat’s Last Theorem, Historia Mathematica Volume 37, Issue 4, November 2010, Pages 641-692