Nancy Grace Roman, NASA Chief of Astronomy and "Mother of Hubble"

This post has moved so it can be my 2026 Ada Lovelace Day post. Find it here!

Brains and Buckmoths

A couple more new prints I made for #SciArtSeptember are 'Amygdala' and 'Bogbean Buckmoth' which I made for the almond (shape) and silk prompts respectively. Did you know that amygdala literally means almond-shaped? I did not, but it inspired my print. 

Amygdala, 8" x10" cyanotype print, by Ele Willoughby, 2026

This one of a kind cyanotype on water colour paper has an image of an open source brain MRI with the amygdala highlighted in gold. The amygdala is a paired nuclear complex in the cerebral hemispheres of our brains (and those of other vertebrates). Part of the limbic system, the amygdala has a primary role in the processing of memory, decision-making, and emotional responses (including fear, anxiety, and aggression) but also plays a role in things like social communication and understanding. 

The Bogbean Buckmoth is an endangered giant silk moth, here in Ontario.

Bogbean Buckmoth, 8" x 8" linocut by Ele Willoughby, 2026

This is a hand-printed lino block print of the endangered Bogbean Buckmoth (Hemileuca sp.). It is printed by hand in dark brown, black and rusty-orange in on lovely Japanese washi (or mulberry) paper, 8" x 8".

A day flying silk moth and the only buckmoth (Hemileuca) in eastern Canada, the Bogbean Buckmoth is very distinct with its black and white wings with eyespots and its black body with both white and rusty orange markings on the thorax and abdomen. It is a medium-sized moth with forewing lengths of 26–32 mm for males and 32–36 mm for females. Bogbean Buckmoth populations are known only from eastern Ontario and New York; it is listed as endangered in both jurisdictions. It only lives in open, chalky, low shrub fens containing large amounts of bogbean, an emergent wetland flowering plant which is the primary food of its larvae along with bog cranberry. Though the adults can fly for several kilometres they rarely leave the region around their home in the fens, increasing their isolation.

The Bogbean Buckmoth has a one-year life cycle. These moths spend the winter as eggs and emerge as larvae (black with reddish-orange branched spines along the back) the next spring, becoming adults in mid- to late September.

Here in Ontario they are threatened by habitat loss and changes like water level fluctuations, land development, pesticide use and climate change and its impact on wetlands. Also, its preferred food, the bogbean, is threatened by invasive plants, especially the European Common Reed and Narrow-leaved Cattail.

Pollinators by moonlight and in the garden

Still enjoying playing with cyanotype combined with linocut. Here are a couple of recent ones where I combined a moon cyanotype with varies plants and linocuts of insects.

Moon, moths and lanternfly. 11" x 14" cyanotype and linocut by Ele Willoughby, 2026

Moon, plants, moths and butterfly 11" x 14" cyanotype and linocut by Ele Willoughby, 2026

September is a busy #scicomm month with the Mineral Cup (which you can catch on bluesky or mastodon) and SciArtSeptember. If you've been following along, some of my art that I am sharing daily will be familiar. I also made a brand new linocut for the prompt ruby: a male ruby-throated hummingbird with Canada columbine. 

Ruby-throated hummingbird, 8" x 8" linocut by Ele Willoughby, 2026

Barbara McClintock asking the maize plant to solve specific problems

Barbara McClintock, linocut print, 11" x 14" by Ele Willoughby, 2026

I first read about Barbara McClintock years ago in 'Nobel Prize Women in Science' by Sharon Bertsch McGrayne. McClintock was one of the women portrayed who did actually win the award, rather than the several who should arguably have been included in various wins. Much more recently, I read 'The Exceptions: Nancy Hopkins, MIT and the Fight for Women in Science', by Kate Zernike. When I was an undergraduate and then graduate student in physics at University of Toronto, and served on the Gender Issues Committee, biologist Nancy Hopkins famously showed systemic discrimination against women faculty at MIT with hard data, gathered systematically, if surreptitiously, by literally measuring lab floor space. Her victory was all our victory, because she used the tools of science to convince scientists. Further, she and collaborators showed academics worldwide a strong, convincing, simple and effective strategy for showing discrimination was occurring. For instance, in 2002, the University of Toronto settled a class action suit from retired female faculty, acknowledging gender barriers and pay discrimination. The book is well-written, but I found it a bit hard to read. Barriers and discrimination Hopkins experienced in the 60s onwards, felt all too familiar for my experiences decades later. Further, as a physics student, one of a grand total of 2 women specialists as a undergrad, and as an obvious minority as a grad student, with a grand total of 0 then 1 female faculty, it was pretty undeniable that something was wrong and needed fixing. It took Hopkins, wary of feminism like many of her generation, a very long time to recognize she was facing discrimination and harassment. I found it rather hard to read about naive young Nancy who took so long to question things.

Roaslind Franklin, linocut, 11" x 14", by Ele Willoughby 2020

One of Hopkins' role models, somewhat hidden in the background was Barbara McClintock, who tried resolutely to recruit her. Young Nancy was a bit wary of McClintock whom she viewed as a bit of a square peg, maybe sidelined from the cutting edge of genetics unlike her undergraduate mentor Nobel laureate James Watson. She was both right and quite wrong, as it turned out. Outsider McClintock would go on to win the 1983 Nobel Prize in Physiology or Medicine. It was funny to read about Watson's role as champion and mentor in Nancy's life, knowing him more as a bit of a villain, not so much in Rosalind Franklin's life (as he is often portrayed with imprecision and hindsight), but as a villain in the story of what was and was not remembered about Franklin posthumously until more recently. Also, he has become increasingly notorious for ugly racist and sexist biases about people. Nancy was important to a lot of us women in science in the early 2000s, well beyond biology, for the way she spearheaded the survey of lab space offered women versus men faculty at MIT and gathered hard data of systemic biases. When Nancy was the first person to read Jim Watson's 'Selfish Gene', it did not occur to her that maybe the portrayal of Franklin as uptight harridan might not be the whole story or to wonder why this was the first time she had heard of her. When Watson told Nancy that McClintock was "difficult" she believed him. When McClintock showed Nancy a letter in which she had been described as the best person in the field and that it was a shame that she (McClintock) couldn't be hired because she was a woman, Nancy assumed the problem and McClintock's science both were a thing of the past. But what did come through to me in reading this book was how, all the while, Barbara McClintock was doing her own thing, quietly revolutionary on her own terms. Barbara was there supporting fellow women in science and understood the dynamics of gender in the scientific workplace before Nancy. 

Barbara McClintock (1902-1992) was a cytologist and geneticist who studied maize genetics from graduate school through retirement. She had been named Eleanor when she was born the third of four children to British immigrant in Connecticut, Thomas Henry McClintock, a homeopathic physician, and his upper-middle-class, Mayflower-descendent Boston wife, housewife, artist and poet, Sara Handy McClintock. When she was young, her parents decided that Eleanor was too delicate and feminine and did not suit their solitary, active, independent child, so they renamed her Barbara. To help save money while her father established his medical practice, and relive her mother of caring for both a toddler Barbara and her new infant younger brother, Barbara was sent to live with an aunt and uncle in Brooklyn from the age of three until she began school. She was close with her father but had a difficult relationship with her mother from a young age.

From her uncle she learned to repair machinery and love nature. Her father raised her as a boy, giving her boxing gloves at age four. When a neighbour who disapproved of the athletic child who didn't play like a girl and tried to teach her "womanly" things, her mother told her to mind her own business. She played sports with the boys, but felt they merely tolerated her as a girl. When Barbara found a teacher "emotionally ugly" her parents let her stay home from school. She grew up with a sense of freedom.

Her family moved to Brooklyn in 1908, where Barbara completed high school in 1919, and discovered her love of science. She wanted to continue to Cornell's College of Agriculture but her mother did not want to allow it. She worried Barbara would become unmarriageable, a not uncommon attitude at the time. Mrs. McClintock had convinced Barbara's older sister to reject a scholarship to Vassar. Her father returned from France where he was serving in the army medical corps just in time to intercede on Barbara's behalf, and she managed to register just before the deadline. 

Barbara thrived at college, participating in student government and joining a sorority (though she later broke her sorority pledge). Her friend circle were avant-guard, and most of her women friends were Jewish at a time when there was a large social gap between Jews and Gentiles at Cornell. She studied Yiddish, and when she found her friends were not welcome in sororities she rejected her own bid. She took up jazz music, playing tenor banjo in a group until the late hours began to interfere with her work. A 1921 field course taught by C.B. Hutchinson first peaked her interest in genetics, a brand new field of study. Hutchinson had been impressed and telephoned to invite her take the new graduate course in genetics the next year. She would later say, "Obviously, this telephone call cast the die for my future. I remained with genetics thereafter." She got her undergraduate degree in 1923, her MSc in 1925 and PhD in 1927, all officially in botany, though her graduate work focused on the cytogenetics of maize. Though just a petite younger woman grad student in pants and a man's shirt working with men in the fields and the lab, she was instrumental in assembling a group of plant breeders and cytologists working on maize cytogenetics, including her champion Marcus Rhoades, future Nobel laureate George Beadle and Harriet Creighton, and this group was supported by department head Rollins A. Emerson (who had rediscovered the laws of inheritance established by Mendel). The group remained close friends and allies through their careers. She worked as research assistant to botanists Lowell Fitz Randolph and Lester W. Sharp. She focused on ways to visualize and characterize maize chromosomes (packages of DNA carrying its genetic material). She was the first to show the 10 maize chromosomes using a staining method she developed using carmine looking at cells from the microspore rather than the root tip, effectively scooping her own supervisor who had been working for years on more effective way to image the maize chromosomes. She studied the morphology of chromosomes and was actually able to link chromosome groups to inherited traits.

Every visit home, her mother tried to convince her not to go back, afraid she would become a professor rather than a housewife. Barbara decided she was too independent for emotional relationships, that she was a "dominant person" who would make a man miserable. She broke up with her beau and remained single for the rest of her life. Zernike writes that she "nurtured a vision of herself as gender-free - feeling at home neither as a girl nor a boy - and once complained of her body as 'a nuisance'."*

She was the first to describe the cross-shaped interaction of the set of maternal and paternal chromosomes that pair up (called homologous chromosomes) during meiosis (cell division of germ cells). Together with Harriet Creighton in the 1930s, studying meiosis in corn cells and examining the gene positions on the chromosomes, she discovered that new combinations of nucleotides that make up DNA in offspring were related to the event of crossing. This proved inter-chromosomal genetic recombination, previously only a hypothesis. They published in 1931, only a few months before Curt Stern published the same observation for fruit flies. This landmark paper made her reputation. They went on to observe how the recombination was linked with new offspring traits. McClintock's chromosomal map was consistent with the linkage map published by her supervisor Hutchinson in 1921, and made a basis of her work with Creighton. They also showed that crossing-over occurs in sister chromatids (which occur when chromosomes are copied by DNA and tied together by a centromere). 

Her success and the importance of her publications lead to receiving several National Research Council post-doctoral fellowships and she continued her research at Cornell, the University of Missouri and the California Institute of Technology, driving her model A Ford across the country. She was the first woman postdoc at Caltech, which required the board of trustees' approval. After a visit to the faculty club on her first day, unlike every other visiting scholar, she was never welcomed again. Warren Weaver of the Rockefeller Foundation deemed her "more boy than girl." It was very hard to find a permanent position during the Great Depression. In Missouri in 1931 and 1932, Stadler introduced her using x-rays as a mutagen; greatly increasing the rate of mutation above background levels was a very useful tool in genetic studies. She found ring chromosomes (where the ends of a single radiation-damaged chromosome fuse), which were first reported by Mikhail Sergeevich Navashin, in x-ray-mutagenized maize. She correctly inferred that normally, undamaged chromosomes must have a structure on the chromosome tip to ensure stability, eventually identified as telomeres. She showed that the loss of ring-chromosomes at meiosis caused variegation in subsequent maize generations due to chromosomal deletion. On chromosome 6, she demonstrated the presence of the nucleolus organizer region needed for the assembly of the nucleolus (the largest structure in the cell nucleus). She found that cells can be damaged during non-homologous recombination (the repair of double-strand breaks in DNA) and published this in 1933. 

She earned a Guggenheim Foundation Fellowship which allowed her to work in Germany with Richard B. Goldschmidt director of the Kaiser Wilhelm Institute for six months, but she left due to mounting political tensions there. Emerson hired her as an assistant in his Department of Plant Breeding at Cornell for three years and her work there lead to an offer of an assistant professorship from Lewis Stadler at the Department of Botany at the University of Missouri in 1936. There she continued her work on the effect of x-rays on maize cytogenetics. She found breakage and fusion in irradiated maize chromosomes and found spontaneous breakage in endosperm cells from some plants. She made a key cytogenetic discovery of a breakage-rejoining-bridge cycle. During mitosis (cell splitting) the broken chromatids were rejoined after chromosome replication. In anaphase (when replicated chromosomes are split), the broken chromosomes formed a bridge which was broken when the chromatids moved toward cell poles. These broken ends rejoined in the interphase (just prior to) the next mitosis, causing massive mutations which she could observe as variegation of the endosperm. In 1938 she published a cytogenetic analysis on the centromere, describing its organization, function and ability to divide. While her research was going well, and she was gaining recognition (she was elected vice-president of the Genetics Society of America in 1939) she was not happy at Missouri. She felt her "maverick" ways did not fit with what was expected of a "lady scientist." Whether it was wearing pants, allowing her students to work in the field after hours or simply climbing the fence when she forgot her key, she did not fit. When another woman named Barbara McClintock announced her engagement in the newspaper, she was hauled into her boss' office and told she would be fired if she married. She was excluded from faculty meetings, not told of advertised professorships elsewhere and convinced she would never be get tenure, so she decided to leave. She learned that if Stadler, who had hired her, moved to the University of California, her job would be in jeopardy. She took a leave of absence in 1941 and accepted a visiting professor at Columbia, where Rhoades was now teaching. Rhoades also offered to share his research field at Cold Spring Harbor Laboratory, a research institution funded by the Carnegie Institution of Washington on Long Island. She loved working the lab and said, "I was just so interested in what I was doing I could hardly wait to get up in the morning and get at it." In December, acting director Drosophila expert Milislav Demerec of the Carnegie Institution of Washington's Department of Genetics at Cold Spring Harbor offered her a temporary position there and then, when made Director he offered her a permanent position. She wavered at first but accepted and became a permanent member of staff in 1942. She had found the right fit, somewhere everyone wore jeans, teaching was not required and there were no restrictions on research.

Esther Lederberg, linocut print, 11" x 14" by Ele Willoughby, 2026. Esther Lederberg also worked at Cold Spring Harbor and published on N. crassa in the early 40s.

There she used the breakage-rejoining-bridge cycle to map new genes. In 1944 she was elected to the National Academy of Sciences, only the third woman to be elected. George Beadle invited her to visit Stanford and work on the bread mold Neurospora crassa. He had used N. crassa to demonstrate the one gene one enzyme relationship and within two months McClintock had described its number of chromosomes (or karyotype) and its entire life cycle.  Beadle said, "Barbara, in two months at Stanford, did more to clean up the cytology of Neurospora than all other cytological geneticist had done in all previous time on all forms of mold." In 1945 she was elected president of the Genetics Society of America. All of this she achieved before her Nobel award winning work.

Summer grad students at Cold Spring Harbor would play baseball in the evening, next to Barbara's cornfields. One of them, James Watson, said the ball went all too often into her fields and she would "get pretty mad... like your mother". Little did he know at the time that her cornfields would tell a much more complex story of the operation of genes than could be found in the structure of DNA alone. McClintock could be prickly and Watson also called her "the Katharine Hepburn of science."

She began her systematic study of mosaicism in maize in the summer of 1944 investigating the mechanisms of colour patterns and unstable inheritance. She had noted that colour patterns were too unstable over the generations to be explained by simple mutations. She discovered two dominant genetic loci she called Dissociation (Ds) because it could cause a dissociation (or break) and Activator (Ac) which was like a sort of switch. She found that corn colours, dominant or recessive were turned on or off by Ds. Strikingly, Ds could change position, or transpose, within the chromosomes, disrupting the colour gene. In a few cells it can jump again. The jumping is random, so multicoloured corn is common. She found that Ac terminated the transposition of Ds; the amount of jumping around done by Ds is determined by the numbers of copies of Ac in the cell. Ds had other varying effects on neighbouring genes, like making normally stable mutations unstable, if Ac was present. Then in 1948 she made the unexpected observation that both Ds and Ac could change position, or transpose, on the chromosome. Hence they are now known as transposons. 

By carefully controlling crosses, and observing the colouration patterns in generations of crops and careful microscopic analysis, she was able to describe the relationship between Ds and Ac. She saw that Ac controls how Ds jumps from chromosomes 9, and that when it does the chromosome breaks. Ds which suppresses the aleurone protein colour gene prior to transposition, and releases it when it jumps, resulting in pigment synthesis in cells. The Ds jumps are random, and may happen in some cells and not in others, so colour mosaicism is common in maize. The size of coloured spots depends on the stage of development at dissociation. She called Ds and Ac "controlling units" or "controlling elements" to distinguish them from genes and hypothesized that this gene regulation could explain how multicellular life with a single genome can produce cells of  different functions. Thus the genome was not simply a static set of instructions - dogma at the time. In 1950, she published "The origin and behaviour of mutable loci in maize" in the Proceedings of the National Academy of Sciences and presented a paper of the same name the next year at the annual Cold Spring Harbor symposium. These described this research, the instability due to Ac, or both Ds and Ac in four genes and how those genes can unpredictably revert to the wild phenotype. She also explained there were "families" of transposons which did not interact with each other. She described her colleagues' response to this work as "puzzlement, even hostility," and said, "They thought I was crazy, absolutely mad," but she persisted with her research and published a subsequent paper in Genetics in 1953 about her statistical data and lectured on the work through the 50s. She found another element she called Suppressor-mutator (Spm) for which some versions could transpose on their own and some could not but which, when present, fully rather than partially suppressed mutant genes. McClintock worried she would alienate her colleagues if she continued to publish on controlling elements, so after 1953, she stopped. She felt the need to wait until the field was ready for conceptual change. When she presented her observation that maize did not follow Mendelian distributions where colours would be dictated strictly by copies of dominant or recessive genes, geneticist Sewal Wright suggested she (like other women) simply did not understand the underlying mathematics. During a visit, McClintock threw Joshua Lederberg and colleagues out of her lab for arrogance. He later declared, "By God, that woman is either crazy or a genius." According to McGrayne, a leading molecular biologist described her as "just an old bag who'd been hanging around Cold Spring Harbor for years." McClintock had no patience for arrogance. Barbara did not feel the need to keep defending her work. She said, "If you know you are on the right track, if you have this inner knowledge, then nobody can turn you off... no matter what they say." While McClintock thought her colleagues deemed her mad, she was respected. It might be more accurate to say her colleagues struggled to understand her work. Geneticist Alfred H. Sturtevant said in 1951, "I didn't understand one word she said, but if she says it is so, it must be so!"

She got a grant in 1957 from the National Academy of Sciences to research Central and South American indigenous maize strains so she could investigate the evolution of maize through chromosomal changes. In South America, she could work on a larger scale. In 1959 she was elected a fellow of the American Academy of Arts and Sciences. Through extensive work in the 60s and 70s looking at chromosomal, morphological and evolutionary characteristics of maize strains she and her colleagues published The Chromosomal Constitution of Races of Maize, an influential publication for cytogenetics, paleobotany, ethnobotany and evolutionary biology. She had officially retired in 1967, becoming a Distinguished Service Member of the Carnegie Institution of Washington, which allowed her to continue working with grad students as an emeritus scientist at Cold Spring Harbor. She also received the Kimber Genetics Awards.

In 1961, French geneticists François Jacob and Jacques Monod described genetic regulation of the lac operon and McClintock wrote an article for American Naturalist comparing this to her work on controlling elements in maize. She had effectively discovered genetic regulation though biology was slow to recognize this. When her colleagues finally saw transposons in bacteria, yeast and bacteriophages in the late 60s and early 70s, they had the tools to investigate the molecular basis for transposition, and her discoveries began to receive the credit they deserved. Today, mutant plants are generated using the Ac/Ds mechanism, to characterize gene function. We now know that transposons make up the majority, in fact, 85% of the maize genome and a significant portion of our own. McClintock did not get everything right but she had made a huge leap forward, years before anyone else. 

When the Carnegie Institute of Genetics closed in the early 70s, her corn field was removed to become a library parking lot. McClintock continued working and collaborating with colleagues Ben and Frances Burr at Brookhaven National Laboratory, where she  replanted her seeds and with Nina Federoff at the Carnegie Institute of Embryology in Baltimore. 

In 1970 she received the National Medal of Science. She was the first woman to do so. In 1973 Cold Spring Harbor named a building in her honour. The awards kept coming: the Louis and Bert Freedman Foundation Award (1978), the Lewis S. Rosensteil Award (1978), she received the first MacArthur Foundation Grant, the Albert Lasker Award for Basic Medical Research, the Wolf Prize in Medicine, the Thomas Hunt Morgan Medal from the Genetics Society of America, the Louisa Gross Horwitz Prize from Columbia University, and in 1983 the Nobel Prize for Physiology or Medicine for discovering "mobile genetic elements," 30 years after her discovery. She was the first woman to win the prize solo. When alerted of her win by a 6:00 phone call from the New York Times the morning it was announced, post-doc Grey Freyer found her collecting walnuts and congratulated her. "For what?" she asked. "You won the Nobel Prize!" he told her. "That's nice," she said. The administrative director got her to issue a press release, in which she wrote that it seemed unfair "to reward a person for having so much pleasure, over the years, asking the maize plant to solve specific problems and then watching its responses." When the reporters showed up, they found her again out collecting walnuts in dungarees and shirt. Colleague escorted her to the press conference but she was wearing a Groucho mask as a disguise. She told reporters "I've had a very, very, satisfying and interesting life."

Barbara McClintock in the Groucho mask

That year physicist, feminist and historian of science Evelyn Fox Keller published 'A Feeling for the Organism', a biography which brought McClintock's story to the public. In 1986 she was inducted in the National Women's Hall of Fame. In 1987, The Discovery and Characterization of Transposable Elements: The Collected Papers of Barbara McClintock was published. In 1989 she was elected a Foreign Member of the Royal Society. In 1993 she received the Benjamin Franklin Medal for Distinguished Achievement in the Sciences of the American Philosophical Society. She received 14 honorary doctorates and an Honorary Doctor of Humane Letters. She remained active in the Cold Spring Harbor community, giving talks on mobile genetic elements and the history of genetics for junior scientists for the rest of her life, playing tennis, collecting black walnuts for baking for colleagues. She would place the walnuts in her driveway and roll her Honda Accord over them, to crack them open to make brownies! Known for her lengthy and thorough answers to student questions, she had brownies at the ready when they looked tuckered out. Jim Watson hosted a large party with many of her colleagues for her 90th birthday. She died of natural cause at 90 years of age in 1992. Her colleagues remembered her brilliance, intensity, scientific focus, devoted mentorship, quick wit and sense of fun. Steven Jay Gould wrote, "Her discovery of transposable elements in maize - so-called jumping genes - first presented in the early 1950s before her field had any language to express such a heterodox idea, was, in retrospect, the beginning of modern molecular genetics." Posthumously, in 2005 the USPS issued a Barbara McClintock stamp, the McClintock Prize was named in her honour in 2013, and in 2024 the plant Stellaria mcclintockiae was named in her honour.

References

Chomet, P., and R. Martienssen. Barbara McClintock's Final Years as Nobelist and Mentor: A Memoir. Cell, 170, pp. 1049-1054. September 7, 2017.

Barbara McClintock. NobelPrize.org, Nobel Prize Outreach 2026. January 25, 2026.

Barbara McClintock, Wikipedia, accessed June, 2026.

Barbara McClintock's World, Weed to Wonder, Cold Spring Harbor Laboratory, accessed June, 2026.

Kim, Taeah. The Life of Barbara McClintock and her Jumping Gene. AMI Webinar Online Salon, 2020.

Krueger, Brian. Barbara McClintock discovered a little thing called the transposable element in 1950. omicly.com, May 5, 2024. 

Madrigal, Alexis. What was Barbara McClintock's "mysticism"?  Oakland garden club. September 2, 2023.

McGrayne, Sharon Bertsch. Nobel Prize Women in Science. Birch Lane Press, New York. 1993.

Pearse, Yewande. Meet Barbara McClintock, who used corn to decipher 'jumping genes,' Massive Science, May 11, 2018.

Zernike, Kate. The Exceptions: Nancy Hopkins, MIT and the Fight for Women in Science. Scribner, New York, 2023.

Our Fate is Tied To That of the Insects

Our Fate is Tied To That of The Insects, 16" x 20" linocut print by Ele Willoughby

 

I made this print for Manufactured Ecosystems, and people keep asking me if I could sell them one, so I finally got around to making a small series of them and putting them in my shop. These are quite labour-intensive and involve using 17 different blocks, so I made a slightly variable series rather than a strict edition, but you have a chance to get one now. 

I'm thinking of also having some archival reproductions made which I can offer at a more affordable price point, if people would like them. That way I can maybe reach more people with my pro-pollinator propaganda!

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.

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.

Alicia Boole Stott Envisions the Fourth Dimension

Alicia Boole Stott, linocut print, 9.25" x 12.5" by Ele Willoughby, 2026

 The 9th prompt for #PrinterSolstice2526 is volume, so I thought I would portray a mathematician. Not satisfied with regular old three dimensional volumes, I made a portrait of Anglo-Irish mathematician Alicia Boole Stott (1860-1940), so let's talk about four and more dimensions.

Alicia Boole Stott (1860-1940), the third of five daughters, came to mathematics honestly. Her father George Boole, like her, was an autodidact mathematician, philosopher and logician, who served as the first professor of mathematics at Queen's College, Cork, in Ireland and developed Boolean logic, which would later prove so essential to computer programming. Likewise, her mother Mary Everest Boole was an autodidact mathematician and educator, who was further tutored by George and who edited his book on algebraic language, Laws of Thought. When she was only four years old, her father died, and facing poverty, Mary returned to England with Alicia's sisters, where she found a job as a librarian at Queen's College, London and worked as a mathematics tutor. Mary developed her own novel ideas about fostering imagination in teaching mathematics and science to children. She believed that physical manipulation of objects like sticks and stones, or stitching curves onto cards could help children form an understanding of mathematical concepts. She integrated fables, history, philosophy and literature and a fanciful writing style into teaching mathematics to appeal to children. Her ideas on education were not the only way Mary was unconventional; she organized discussion groups with Queen's College students with John Hinton a promulgator of polygamy, much to the disapproval of the authorities.  She was a believer in parapsychology and the occult and was the first woman to join the Society of Psychical Research. She wrote about topics which were controversial at the time, like the occult, eastern philosophy, evolution and animal rights, as well as the pedagogy of mathematics, so most of her books were published long after they were written. 

Unlike her sisters, Alicia stayed in Cork with her grandmother and great-uncle, until she was 11, when she rejoined her mother and sisters in London. Alicia had felt repressed and unhappy living in Cork, but the lodgings her mother could afford in London were "poor, dark, dirty and uncomfortable." The five girls had to share a room. Her mother sold George's Royal Society Gold Medal, to buy a harmonium so they could have music at home. Alicia went to the school attached to Queen's College London. Mary brought up her daughters doing things like projecting shapes of things such as hanging pendulums onto paper "to acquaint them with the flow of geometry." Alicia learned mathematics from her mother and the first two books of Euclid. She did not attend university. Mary had to leave her job as librarian and become a secretary for John Hinton. When she was 17, Alicia returned briefly to Cork, where she worked in a children's hospital but soon returned to London. She learned about higher-dimensional spaces from her future brother-in-law, mathematician Charles Howard Hinton (son of John Hinton). Charles had mystical beliefs about the fourth dimension and thought we humans inhabit a 4D space we will eventually perceive. He had crafted 4D models with hundreds of small coloured cubes of wood, each labelled with its own Latin name, which he shared with the Boole sisters. He used his cubes to try and get the sisters to visualize a 4D hypercube, for which he coined the word tesseract. His cubes became a popular, but notoriously difficult approach to grappling with 4D geometry; Alicia was the only one who mastered them, becoming more adept than Hinton himself. Among other books, Hinton went on to write The Fourth Dimension. 

There are analogues to 3D shapes in 4D. Imagine the five Platonic solids: the cube, the tetrahedron (a pyramid with a triangular base so it has 4 equilateral triangle sides), the octahedron (like two pyramids glued together at the square base so it has 8 equilateral triangles as faces), the dodecahedron (with 12 pentagonal faces) and the icosahedron (with 20 equilateral triangle faces). These are 3D shapes bound with regular polygons with the same number of edges at each vertex. If you relax the rule that the faces must all be the same, you get the collection of semiregular polyhedra. Each of the Platonic solids, along with  the  the familiar convex regular polygons (equilateral triangle, square, regular pentagon, regular hexagon and so on) has what is called a 4-polytope, which is an analogue in 4D where faces are replaced with 3D cells of identical Platonic solids. Similarly, there are semiregular polytopes you can define from the semiregular polyhedra. 

Alicia Boole's model next to a diagram in Pieter Schoute's diagram
of the same 3D cross-section of a 4D polytope

Alicia discovered that there are exactly 6 regular convex 4-polytopes. Swiss mathematician Ludwig Schläli had beat her to this discovery, in 1850 before she was born, but he had not published his work. He had submitted his manuscript for publication, but it was rejected as it was too lengthy. It was finally published 6 years after he died. He named these shapes polyscheme, but Alicia introduced her term polytope (based on the German term polytop) as she was unaware of Schläli's work (and her term was the one adopted). American mathematician Washington Irving Stringham rediscovered 6 regular convex 4-polytopes and published his results in 1880, but Alicia was unaware of his paper and working in isolation. In 1884, English theologian and schoolmaster Edwin Abbott Abbott published a satirical novella called Flatland: A Romance of Many Dimensions in which lines and 2D polyhedral characters living on a plane encounter a 3D sphere; as it moves through the plane the sphere appears as cross-sections, a sequence of growing and shrinking circles. Analogously, Alicia was able to visualize 4-polytopes as 3D cross-sections, allowing her to unfold a 4D problem into 3D problems. Simply using Euclidean constructions and synthetic methods (the only tools at her disposal, having never learned analytic geometry) she was able to produce 3D central cross-sections of all 6 regular polytypes in 4D, and make coloured drawings and cardboard models of each. Of these 6, 5 are 4D analogues of the Platonic solids (the hypercube or 8-cell, the hyperoctahedron or 16-cell, the hypertetrahedron or 5-cell, the 120-cell and the 600-cell) and 6th, called the 24-cell, has no 3D analogue.

 From left to right, from top to bottom: Mary Stott, G.I. Taylor, Margaret Taylor, P.H. Schoute, A. Boole Stott [Boole Stott, undated(b)]. (Courtesy of the University of Bristol.)

She contributed to Hinton's 1888 book A New Era of Thought, about higher-dimensional reasoning, writing about sections of 3D solids and part of the preface. (By the time the book came out, Hinton and his wife Mary Ellen Boole Hinton had gone to Japan, following his conviction for bigamy for marrying a second wife under an assumed name. This surprising fact is perhaps less so when we recall he was the son of the radical proponent of polygamy, John Hinton). In 1889, she began secretarial work near Liverpool, working for lawyer and amateur mathematician H. John Falk, who was editing Hinton's book. In 1890 she met actuary Walter Stott, who joined Alicia and Falk on editing a new edition of Hinton's book. The pair married  had two children: Mary in 1891 and Leonard in 1892. According to Coxeter, "for some years she led a life of drudgery, rearing her two children on a very small income." In 1895 Walter told her of Dutch mathematician Pieter Schoute's work on central sections of the regular polytopes and she saw that his drawings matched her 3D models, so she mailed him photographs of her work. Schoute replied, asking to meet and collaborate which they did until he died two decades later. They wrote letters back and forth and some summers Schoute would come to stay with the Stott family in England so they could work together. He eventually convinced her to publish, which she did in two papers published in Amsterdam in 1900 and 1910. In her second paper, she was there first person to enumerate all 45 semi-regular polytopes. They also co-authored papers in 1908 and 1910. In 1907, they presented her models at the annual British Association of the Advancement of Science in Leicester. In 1912 Schoute presented his work on semiregular polytopes to the 5th International Congress of Mathematicians in Cambridge, crediting her with the roots of his proof. She made complete sets of models of 120-cell and 600-cell polytopes and left them with Schoute. When he died in 1913, Alicia took a hiatus from mathematics. The University of Groningen granted her an honorary doctorate in 1914, and exhibited her models. She was invited to the ceremony but not able to attend. When the degree arrived in the mail in a cardboard cylinder, she exclaimed, "This will be a good place to keep sticks of macaroni!" 

In 1930, when Alicia was 70, her nephew, physicist Geoffrey Ingram Taylor introduced her to the now famed British-Canadian mathematician Harold Scott MacDonald Coxeter who was 23 and a graduate student at Cambridge at the time. Despite their age difference they two became good friends. Like Taylor, Coxeter called her Aunt Alice. Coxeter wrote, "The strength and simplicity of her character combined with the diversity of her interests made her an inspiring friend." The two met regularly and began working together on topics in 4D geometry. He invited her to one of his supervisor H.F. Baker's celebrated geometry tea parties, where they presented a joint paper and she brought a set of her models, which she then donated to the department of mathematics. They collaborated on the investigation of a special kind of 4D polytope (Gosset's 4D polytope s{3,4,3}) for which she made models of its sections. Alicia made two more important discoveries about constructions for polyhedra related to the golden section. With Coxeter, she presented a joint paper at the University of Cambridge. When Coxeter moved to Toronto in 1936 to take up a professorship at U of T, Alicia gave him an antique stained-glass Archimedean solid shade and wrote to him, "My dear! I don't know how to write to you - words seem so futile besides so great a separation! But indeed one can rejoice, for your sake, that it happened so... While I have been writing my mind has gone back to the lovely world we have visited together, and which you have made so much your own. I wonder where you will get to in it! How I wish I could follow." They managed to continue their collaboration, despite their separation, until her death in 1940. Coxeter when on to work at U of T for 60 years and become regarded as one of the greatest geometers of the 20th century. Much of what we know about Alicia's life is thanks to Coxeter's reminiscing about his dear Aunt Alice.

My portrait contains her 3D unfolding of part of a hypercube, her colour drawings of some of the 3-principle sections of the 600-cell, her expansion of the octahedron - a truncated octahedron, sections of of the 16-cell.

p.s. I have related Alicia's life to some of her family, including mathematician father George Boole, mathematician, educator and activist mother Mary Everest Boole, brother-in-law mathematician (and bigamist) Charles Hinton, nephew physicist Geoffrey Ingram Taylor (who went on to be knighted and win the gold medal of the Royal Society, like his grandfather). But, I recommend reading Moira Chas' article 'The Extraordinary Case of the Boole Family' to also learn about further surprising and fascinating family. Alicia's sister Mary Ellen, first wife of Charles Hinton, was a poet. Charles Hinton also invented a baseball-pitching machine and wrote mathematical romances. Her sister Margaret (mother of Geoffrey Ingram Taylor) was a painter. Her sister Lucy Everest Boole was a Lecturer in chemistry at the London School of Medicine for Women and the first woman elected a Fellow of the Institute of Chemistry. Her sister Ethel was an activist concerned about the plight of the Russian people under Tsarist rule and travelled to Russian where she visited prisons, smuggled propaganda, composed music and wrote wildly successful novels (one of which was made into a film with music by Shostakovich). She married Polish exile and rare book expert Wilfred Voynich, who bought the famed, mysterious, medieval manuscript in an as-of-yet-undeciphered text illustrated with dreamlike images of strange plants and creatures, known as the Voynich manuscript. Alicia's son Leonard was a medical doctor and pioneer in the treatment of tuberculosis who inked a portable x-ray machine, an artificial pneumothorax apparatus and a system of navigation based on spherical geometry. Alicia's nephew Sebastian Hinton invented the jungle gym (inspired by the bamboo structures his father built while in self-imposed exile in Japan to teach his children about 3- and 4-D shapes). Sebastian married Carmelita Chase who founded the progressive Putney School, a boarding school in Vermont (where Coxeter was invited and considered working). Alicia's grandniblings Howard Everest Hinton became a distinguished entomologist, William Hinton a Marxist writer and Joan Hinton a nuclear physicist involved in the Manhattan Project who was so appalled by the consequences of the atomic bombing of Hiroshima she became a pacifist, gave up physics, moved to China and became a Maoist. Alicia's great-grandniblings include award-winning documentarian Carma Hinton and 2018 Turing Award-winning A.I. researcher Geoffrey Everest Hinton. 

References

Alicia Boole Stott, Wikipedia, accessed February, 2026. 

Boole Stott, Alicia. On Certain Series of Sections of the Regular Four Dimensional Hypersolids. Verhnadelingen Natuurkunde, Eerste Sectie, deel 7, nummer 3 (1900), pp. 1-21. 

Chas, Moira. The Extraordinary Case of the Boole Family. Notices of the American Mathematical Society. DOI: https://dx.doi.org/10.1090/noti1996. December, 2019. 

O'Connor, J.J. and E.F. Robertson, Alicia Boole Stott, MacTutor Archive, University of St Andrews. July 2014.

Polo-Blanco, Irene. Alicia Boole Stott, a geometer in higher dimension. Historia Mathematica. Volume 35, Issue 2. pp. 123-139. May, 2008.

Polo-Blanco, Irene. Alicia Boole Stott's models of sections of polytypes. Lettera Mathematica. Volume 2, pp. 149-154. September 9, 204.

Riddle, Larry. Alicia Boole Stott. Biographies of Women Mathematicians. Agnes Scott College. February 19, 2025

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.