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

Bibha Chowdhuri, from the heights of the Himalayas down into the mines, studying cosmic rays and discovering mesons

Bibha Chowdhuri, linocut, 11" x 14" by Ele Willoughby, 2025

The second Printer Solstice prompt is 'even', so I made a portrait about the discovery of mesons. When students are introduced to quarks, the fundamental particles, usually they learn how nucleons, that is, protons and neutrons are each made of trios of quarks. Quarks are weird because they have fractional charge (like +/- a third or two thirds of and electron's charge), and we only ever observe integer charge (say, things have, for instance -1e, 0 or +1e charge). They come in perfectly ridiculously named flavours: up, down, top, bottom, charm and strange (and of course, anti-up, anti-down, anti-top, anti-bottom, anti-charm and anti-strange). Little groups of three quarks can be stable and long-lived, and in fact, a significant proportion of the mass of regular, every day matter, what we call baryonic matter, can be explained by trios of quarks in neutrons and protons. So you can make a proton (+1e) with two up quarks (+2/3 e each) and one down quark (-1/3 e) and the math works out. But it's also possible to make matter with even numbers of quarks. These unstable particles are called mesons. Usually they are made with quark-antiquark pairs, but there are also some exotic mesons with four quarks. Long before we had developed the Standard Model and before quarks themselves were proposed (by Gell-Mann and Zweig, in 1964) as an explanation for baryonic matter, mesons were proposed as an explanation for nuclear forces (what held the neutron and the proton within the nucleus - a real mystery as this force must overcome electromagnetic repulsion) by theorist Hideki Yukawa in 1934 and they were first observed by Bibha Chowdhuri (1913-1991) and her supervisor Debendra Mohan Bose in 1940. In the early days of particle physics, before physicists were accelerating and smashing particles together at incredible speed and energies, the easiest way to observe these particles was in naturally occurring cosmic rays or high-energy ionizing radiation from space which rains down on our atmosphere. Physicists literally climbed mountains and used hot air balloons to get as much altitude as possible to measure these particles. At the time, Chowdhuri, Bose and others called these particles they observed in cosmic rays "mesotron showers" but we now know them as mesons. Seven years after Chowdhuri and Bose published their discovery another physicist, Cecil Powell performed similar experiments. He was granted the 1950 Nobel Prize for working on photographic methods of studying nuclear processes and his subsequent "discovery" of the pi-meson. He had access to higher quality of photo emulsion than his Indian colleagues did during WWII, but his measured mass for the particle was very similar to their results. He did acknowledge their work during his Nobel acceptance (well, he called her "Chaudhuri") but essentially, he repeated their discovery with somewhat higher precision, as well as observing muons decay into electrons. The photographic emulsion method itself, in turn, was pioneered by another under-appreciated woman, Marietta Blau (and her student Hertha Wambacher). Blau was also nominated for, but did not win, the 1950 Nobel Prize. Blau discovered what she called "disintegration stars" which were particle tracks of high-energy cosmic rays nuclear reactions recorded in photographic plates; as a Jewish Austrian scientist, her research was interrupted in 1938; mercifully, she was able to secure a position in Oslo and leave Austria, but having to flee for her safety negatively impacted her career and delayed recognition of her research. One could easily argue that Chowdhuri, Bose, and Blau were at least as qualified to win the 1950 Nobel as Powell.

Bibha was born in Kolkata, to a family of the landlord Zamindar class. Her father Banku Behari Chowdhuri was a doctor. Her mother, Urmila Devi's family were followers of Brahmoism, a reformist religion which branched off of Hinduism, rejecting polytheism, rituals and the caste system.  To marry her mother, Banku had to convert and was outcast from Hindu society. He even lost the right to his parent's property. Education of women in India at that time was quite rare, but Brahmo Samaj, the societal aspect of the Brahmoist religion, promoted education, especially of women and girls. Several of the Chowdhuri children (Bibha had four sisters and one brother) were highly and equally educated, while in pre-independence India, the education of girls was so extremely rare as to be virtually non-existent; their expected role was to marry and serve their husbands. None of the Chowdhuri siblings married, which was a rare privilege at the time for the girls.

Detail of my screen print "Cloud Chamber" showing particle trails in yellow
as recorded in a Wilson Cloud Chamber against a cloudy blue sky.

She studied physics at the Rajabazar Science College of Calcutta University, where she was the only woman in a class of 24 to graduate with an M.Sc. in 1936. She joined the Bose Institute in 1939 to study cosmic rays with the legendary Debendra Mohan Bose, who had worked with C.T.R. Wilson to build the Wilson Cloud Chamber (a tool for recording the tracks of high energy particles in a supersaturated cloud-like vapour or water or alcohol).  He has been reluctant to take her on as a student, and told her he did not have any projects suitable for a woman, but she persisted. He had built a cloud chamber on his return to India, and was building his reputation as India's first cosmic ray physicist. She published her paper in the Transactions of the Bose Institute based on photographic plates exposed to cosmic rays for four months at an altitude of 12,000 feet (3600 m) atop Sandakphu, a mountain peak in Nepal, shown in my portrait. She set up the instrumentation at each site and gathered the exposed plates afterwards for analysis, travelling on horseback - a potentially scandalous action for an unmarried Indian woman in the 1930's. Her research showed the superiority of using photographic plates to employing cloud chambers, and the Bose Institute thenceforth adopted photographic plates.

Next, she proceeded to expose Ilford R2 and the new halftone photographic plates at three different altitudes at Darjeeling at 7000 feet (2000m), Sandakphu at 12,000 feet (3600 m) and Pharijong at 14,000 feet (4300 m), to study what they called "mesotron showers." Yukawa had proposed the particles we now call mesons, to explain the strong nuclear forces which confine protons and neutrons within the nucleus, just a few years previous, and the race was on to confirm their existence. She exposed plates directly to air, and some under paraffin wax or water. Plates were exposed for 150 to 202 days. Using a high-power microscope, she and Bose examined the lengths, spacing and scattering of the recorded tracks to determine the mass, energy and momentum of the particles they recorded. Scattering angle could be linked to mean energy, and the mean grain spacings along tracks could be used to calculate velocities. They found that most tracks were from particles of higher velocities and lower kinetic energies than protons, suggesting, importantly that they were lower mass than protons, as expected fro Yukawa's theoretically proposed particle. She published four papers in Nature from 1940-1942 with her results. Bibha Chowdhuri was the first person to measure the mass of a meson and she quickly published even more precise results. She realized they would need improved photographic plates to continue the research, but these were unavailable due to imposed WWII restrictions. Cosmic ray research at the Bose Institute stopped. 

Chowdhuri went to England to pursue her doctorate and join the cosmic ray research laboratory of Patrick Blackett in 1945, with thesis advisor J.G. Wilson, when extensive air showers in cosmic rays was the hot topic in particle physics. She recorded the spectrum of penetrating extensive air showers taking photographic plates within a cloud chamber surrounded by Geiger counters. She defended her thesis, "Extensive Air Showers associated with Penetrating Particles," in 1949. Extensive Air Showers refers to the cascade of subatomic and ionized nuclei particles that we get when cosmic rays enter our atmosphere from space and collide with the nuclei of various air molecules (discovered by Bruno Rossi in 1934); it then extends itself through several more generations of collisions as shown in my portrait. Interviewed by the Manchester Herald, Bibha said, "Women are terrified of physics - that is the trouble. It is a tragedy that we have so few women physicists today. In this age when science, and physics particularly, is more important than ever, women should study atomic power; if they don't understand how it works, how can they decide how it should be used? I can count the women physicists I know, both in India and England, on the fingers of one hand." The same year, Blackett had won the Nobel for "his development of the Wilson cloud chamber method, and his discoveries therewith in the fields of nuclear physics and cosmic radiation." 

Chowdhuri applied to do post-doctoral work in Paris at École Polytechnic with Louis Leprince-Ringuet on photo emulsions, seeking financial support from the government of India. She had a letter of recommendation from J.G. Wilson who was one of her thesis examiners. Her application was sent to Homi Babha for comment and he wrote Wilson to inquire whether it would really be worth the investment for her to study photo emulsions for 6 months when her doctorate was on extensive air showers. Both men seem to have forgotten her prior world-class research on photographic methods with Bose, and Wilson backed off his prior recommendation and replied that, "Miss Chowdhuri cannot be regarded as a first-class physicist but she can make good progress under fairly done guidance" and as she had done good work on air showers, she should "not be encouraged to go into a new field of work." Yet, it was photo emulsion work which led to Powell's Nobel.

After her brief stay in Paris she returned to India to work at the Tata Institute of Fundamental Research (TIFR), with a glowing recommendation from Blackett (in complete contrast with Wilson's lukewarm support). She worked as a Research Fellow with the Experimental Physics Group for 5 years, the first woman at TIFR. This was the lowest rank at which they could hire her; all the contracts were written with the presumed pronoun for a physicist of "he." She was in charge of the Cloud Chamber Group investigating penetrating particles in extensive air showers.

She decided to apply for a Senior Research Fellow position in the cosmic-ray project at Bengal Engineering College, Shibpur in 1954. The post had a lower salary and the college was not known for basic research. Her reasons for this decision are unclear, as are Bhabha's for writing her a letter or recommendation but not trying to persuade her to stay. Perhaps she wished to be closer to home, but within a year she left for Paris where she worked with Leprince-Ringuet and studied many new K mesons in cloud chambers in the Alps. While in Paris, her American colleague, a Visiting Fullbright Scholar Wayne Hazen invited her to teach at the University of Michigan. She spent two years working with him and as a Visting Lecturer in physics at the University of Michigan, then worked briefly in Bruno Rossi's MIT lab working on Plastic Scintillators for detecting large air shows and collaborating on planning a new extensive shower array in New Mexico. 

In 1961 she joined the Physical Research Laboratory (PRL) in Ahmedabad. Despite her two decades of experience she was only offered a temporary position as a Senior Research Fellow but she was interested and took the job. After beginning her career studying extensive air showers high in the Himalayas, at PRL she investigated  high energy muons in cosmic rays at a depth of 700 feet (2000 m) in the Kolar Gold Field with simultaneous measurements at ground level at TIFR in collaboration with Vikram Sarabhai, director of PRL. She and her students and technicians donned miner's hats to descend daily in the elevator cage down to their instruments, sometimes carrying their own oxygen if conditions were unsafe. Sarabhai's untimely death interrupted her future research plans. Once again she saw her research interrupted by factors beyond her control.

After retiring from PRL she returned to Kolkata and continued her research, collaborating with colleagues at Calcutta University, the Saha Institute of Nuclear Physics, the Variable energy Cyclotron Centre and the Indian Association for the Cultivation of Science looking at nucleus-nucleus interactions at relativistic energies to learn about  astrophysics and cosmic rays.

She was publishing research until the end of her life, though after returning to India, she chose to publish only in Indian journals. She was never made a fellow of any of the Indian scientific societies. She was woefully under-appreciated during her lifetime; it seems likely she faced gender discrimination and was underestimated by her male peers. She became less and less remembered internationally, and when she died in 1991 no obituary appeared in any scientific journal, but her story and accomplishments have begun to be recognized posthumously. In 2019, the International Astronomical Union named a star "Bibha," Bengali for "ray of light," in her honour. In 2020, when then Indian government decided to establish 11 named research chairs after famous women scientists, the physics chair was named after Bibha Chowdhuri.

References 

Bibha Chowdhuri, Wikipedia, accessed December, 2025

Bibha Chowdhuri, Mirror Wellesley Blog, accessed December, 2025

Bhattacharya, Amitabha. The woman who could have won a Nobel. The Telegraph, November 28, 2018. 

Jacob, Julie. Bibha Chowdhuri: A Missed Nobel Prize and an Unfulfilled Prophecy. The Lovepost. January 14, 2021.

Mondal, Naba K. Bibha Chowdhuri and Her Remarkable Scientific Endeavours. Resonance. Vol. 28, no. 10, DOI: https://doi.org/10.1007/s12045-023-1686-1. October, 2023

Nagarajan, Archana. Bibha Chowdhuri. Sci-Illustrate. August 8, 2019.

Sinha, Atreyee and Ritam Sinha, Bibha Chowdhuri: A Ray of Light. Building from Diversity, CTAO News. November 30, 2022.

Roy, S.C. and Rajinder Singh. Bibha Chowdhuri - Her Cosmic Ray Studies in Manchester. Indian Journal of History of Science. 53.3 (2018) 356-373. DOI: 10.16943/ijhs/2018/v53i3/49466

Roy, Suprakesh and Rajinder Singh. Bibha Chowdhuri - The First Woman Scientist at the TIFR. Physics News Tata Institute of Fundamental Research, Vol 51 (1-2), Jan-June, 2005

The Nobel Prize in Physics 1948, NobelPrize.org, accessed December, 2025

Maria Goeppert Mayer: Nuclear Physics, Magic Numbers and the Onion Madonna

Maria Goeppert Mayer, linocut, 11" x 14", by Ele Willoughby, 2025

The first thing that came to mind when I thought about lead for the next #PrinterSolstice2425 prompt is how it is the end of many chains of nuclear transmutations. Lead is particularly stable. The woman who figured out why was the second woman to win the Nobel Prize for physics: German-American theoretical physicist Maria Goeppert Mayer (1906-1972, née Göppert). Another woman would not win the physics prize until Canadian Donna Strickland in 2018.

Maria Göppert was born in Kattowicz, a Silesian city then part of Prussia, now part of Poland, the only child of father, pediatrician and sixth generation professor Frederich Göppert and mother Maria (née Wolfe). Maria would grow up, proud to be a seventh generation academic. The family moved to Göttingen when she was four when her father got a position at the university. She was closer to her father, reasoning, he was more interesting, "He was after all a scientist." He encouraged her to aim for more than a life as a housewife. She went to schools for girls intending to pursue higher eduction. When her suffragette-run private prep school closed before she completed the three year program, she took and passed the university entrance examination at 17, a year early. She entered the University of Göttingen, where Emmy Noether was a professor, to study mathematics, in 1924, spending a term in Cambridge before completing her degree. The prestigious university was known for its world class math and physics departments. Renown mathematician David Hilbert was a neighbour and like famed physicists Max Born and James Franck, a family friend of the Göpperts. There were other female students but the others were studying to become mathematics teachers for girls. Göppert on the other hand became interested in physics and decided to pursue her doctorate with Max Born, himself later a Nobel laureate. In her 1930 thesis, she studied two-photon absorption by atoms - something which was virtually impossible to verify until 1961 with the invention of the laser. Year later, her fellow Nobel laureate Eugene Wigner called her thesis, "a masterpiece of clarity and concreteness" and today the two-photon absorption cross-section is named the Goeppert-Mayer (GM) unit.

She met American physical chemist Joseph Edward Mayer, a Rockefeller Fellow who was working for Göttingen physicist (and later Nobel laureate) James Franck, who boarded with the Göppert family. The two fell in love and married in 1930 after she completed her PhD. They moved to the United States, where he got a faculty job at John Hopkins, at the height of the Depression. They had two children: Maria Ann and Peter Conrad. Like many women scientists married to scientists, she found anti-nepotism rules prevented her from getting a professorship at John Hopkins, but she was hired as an assistant dealing with German correspondence. The job had a small salary, but allowed her access to the facilities and she was able to teach courses. She collaborated with her husband and with Karl Herzfeld, a fellow German theoretical physicist at John Hopkins, on applying quantum mechanics to the chemistry of organic molecules. She also made several visits back to Göttingen to collaborate with Max Born in 1931, 1932 and 1933, before the nazis came to power and Born and Franck lost their jobs. She and Herzfeld became involved with refugee efforts, horrified to see academics of Jewish descent driven out of university jobs. She became an American citizen in 1933. She published a landmark paper on double beta decay in 1935. In 1935 Edward Teller got a position at the nearby George Washington University and they would discuss developing theoretical physics. In 1937, her husband was fired; he believed this was because of Maria's presence in the lab and the dean of science's hatred of women. Herzfeld agreed, but also noted the anti-German sentiment that greeted him, Maria and Franck who were all now at John Hopkins. Mayer got a job at Columbia n 1937, where Maria took an unpaid position. Harold Urey and Enrico Fermi arrived at Columbia in 1939 and the three became good friends. In 1940, Joe and Maria published their textbook Statistical Mechanics. Fermi asked her to work on the valence-shell of transuranic elements, which she correctly predicted would form a new series similar to rare earth elements. In 1941 she was elected a fellow of the American Physical Society; the letter from APS was address, "Dear Sir," as if they had not considered an other possible greeting might be appropriate for fellows. She still had no salary, until later that year when she was hired by Sarah Lawrence College, initially part-time, to teach mathematics, physics, physical chemistry and general science courses. 

In 1942, she was recruited to work for the Manhattan Project. First she worked part-time for Urey at Columbia's Substitute Alloy Materials Laboratories trying to separate the fissile uranium-235 which could be used for weapons from natural uranium. She looked at uranium hexafluoride and investigated whether photochemical reactions could be used; while unfeasible in the 1940s, now lasers can be used to separate isotopes. Joe was working on conventional weapons at the Aberdeen Proving Grounds in Maryland five days a week. It was a challenging time for the family. The children had a nanny while their parents were occupied with war work. She was vehemently anti-nazi but found feared the consequences of producing a weapon which would harm friends and family in German if it were deployed there. She had taught her students at Sarah Lawrence that, "Man's scientific discoveries and inventions might very likely destroy him." She was stretched pretty thin and suffered several illnesses and on top of her full time teaching duties and childcare so negotiated reduced hours working for Urey. Teller recruited her to work on  the Opacity Project on the properties of matter and radiation at extremely high temperature; Teller was working on his "Super" bomb, which would become the basis of the H-bomb. Her husband Joe was sent to fight in the Pacific; Maria decided to leave the children in New York and join Teller's team at Los Alamos. When Joe came back early they returned together to New York in 1945. 

After the war her husband got a job at the University of Chicago; as did she, but it was as a voluntary professor of physics. When Teller joined the university she continued working on the Opacity Project and on the origin of elements. She was offered a part-time senior theoretical physicist job at the nearby Argonne National Laboratory. She responded that she didn't "know anything about nuclear physics" when offered the job. It was a shift in focus which laid the ground for her most impactful discoveries. She programmed the Aberdeen Proving Grounds ENIAC early computer to solve criticality problems of their liquid metal cooled reactor using Monte Carlo methods (that is, with statistical models you might use if trying to calculate gambling odds at the casinos in Monte Carlo). With Jacob Bigeleisen she derived the Bigeleisen-Mayer equation, also known as the Urey model (who independently arrived at the idea), of approximate isotope fractionation in isotope exchange reactions used in quantum chemistry and geochemistry. 

She began working on her mathematical model of the nucleus to explain why nuclei with certain numbers of nucleons (protons and neutrons) are more stable. As you grow nuclei from hydrogen (one proton) to the hundreds in transuranic elements by adding nucleons there are points where the binding energy of the next nucleon is a lot lower than the last and the nuclei are more stable and common in nature. The numbers of nucleons producing very stable nuclei: 2, 8, 20, 28, 50, 82 and 126 were dubbed "magic numbers" by Wigner. For protons these nuclei are helium, oxygen, nickel, tin, lead and the theoretical unbihexium. From her work on the origin of elements she recognized that these were all more common than their periodic table neighbours. You can also get nuclei with magic numbers of neutrons or "doubly magic" nuclei with magic numbers of protons and of neutrons. In 1932 Ivanenko and Gapon were the first to propose that perhaps nucleons were distributed in shells. But in 1937, Niels Bohr and  Kalcar proposed the useful "liquid drop" model of the nucleus. The liquid drop model helped physicist comprehend binding energies, and was for instance, how Lise Meitner and her nephew Otto Frisch explained nuclear fission. But the model did not explain the relative stability of different nuclei or the nature of magic numbers. Because Goeppert Mayer had not come from a nuclear physics background she was less biased in favour of the liquid drop model.

In 1948 she published her first paper summarizing the support for a shell model, but she did not yet have an explanation for the distribution of magic numbers. Fermi suggested she look at spin coupling, and she had a flash of insight. She realized that magic numbers could be explained by a nested sequence of closed nuclear shells where pairs of protons and neutrons would couple together.  In 1949, Maria Goeppert Mayer build her nuclear shell model (green diagram) where the magic of these numbers is explained by a nested sequence energy levels (determined by spin and angular momentum & like with electrons beyond the nuclei, the Pauli exclusion principe) of filled shells. Pauli himself called her “The Onion Madonna” for her model’s onion-like layers. 

In quantum mechanics nucleons have two possible spins: up or down. If you combine spin with their orbital motion you get total angular momentum. She’d found that if orbital and spin motions align to produce a maximum total angular momentum, nucleon energy level shifts down but when they go opposite directions nucleon energy level shifts up. The largest gaps between these shifted energy levels explain the “magic numbers” and these points mark the shells boundaries. Further, her model explained the ground state spins and magnetic moment of nuclei, for which there had been no previous explanation.

Very shortly thereafter, other physicists (Haxel,  Jensen & Suess) independently developed the same idea and & she started collaborating with them & co-authored a book: Elementary Theory of Nuclear Shell Structure with Jensen in ‘50.  In ’63, she & Jensen shared half the Nobel "for their discoveries concerning nuclear shell structure" with Wigner awarded other half.  In a letter, she addressed Jensen as "My Nobel Shell Brother."

She was finally appointed a full professor of physics at a major university in 1960, at UCSD, where her husband was also offered a position. She suffered a stroke but continued teaching and working despite health problems. In 1971 she suffered a heart attack that left her comatose and she died in February 20, 1972. 

The American Physical Society now awards the Maria Goeppert Mayer award to women in physics at the beginning of their careers. In 2018 they named Argonne National labs an APS Historic Site in recognition of her work. A crater on Venus has been named in her honour. In 1996 she was inducted in the National Women's Hall of Fame. The UCSD physics department is named Mayer Hall after her and Joe.

References

August, 1948: Maria Goeppert Mayer and the Nuclear Shell Model, APS News, August 1, 2008

Buntar, Simran, Maria Mayer - The First Woman to Win the Nobel Prize for Nuclear Physics, Secrets of the Universe blog,  accessed January, 2025

Maria Goeppert  Mayer, Wikipedia, accessed January, 2025

Maria Goeppert Mayer: Revisiting Science at Sarah Lawrence College, Sarah Lawrence College Archives Exhibit, accessed January, 2025

Landau, Elizabeth. The Last Woman to Win a Physics Nobel, Scientific American, September 26, 2017.

Magic number (physics), Wikipedia, accessed January, 2025

Nuclear shell model, Wikipedia, accessed January, 2025

Sachs, Robert G. Maria Goeppert Mayer, 1906-1972, National Academy of Sciences, 1979.

Hertha Ayrton, Mathematician, Physicst, Engineer and Inventor

 

Hertha Ayrton, linocut, 9.25" x 12.5" by Ele Willoughby, 2021.

This is my linocut portrait of British engineer, mathematician, physicist & inventor Hertha Ayrton (1854-1923). She is remembered for her research on the electric arc lamp, on ripple marks in sand & water, and her inventions including of mathematical line dividers which allowed artists, architects & engineers to enlarge or diminish drawings. I’ve shown her with a diagram of the dividers from her 1st of 26 patents, one of her diagrams about the origin & growth of ripple marks & one of her diagrams of an electric arc lamp (a subject on which she literally wrote the textbook).⁠
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Born Phoebe Sarah Marks in Portsea, Hampshire, she was the third of eight children of a Polish Jewish immigrant watchmaker father & seamstress mother. After her father’s death when she was 7 in 1851, the family was left penniless and her mother returned to work as a seamstress. Sarah, as she was then known, had to care for her younger siblings. When she was 9, her maternal aunt Marion Hartog, who ran a school in north-west London with her husband Alphonse Hartog, invited her to join their household and attend their school. Though a hardship to her family, her mother recognized her potential and supported the move to London and the opportunities for her daughter. Her cousins introduced her to math and science. In her family, she was known as a fiery and occassionally crude character. By 16, she was living independantly, employed as a governess.

Her friend Ottilie Blind nicknamed her Hertha after the poem by Algernon Swinburne. They coached each other to prepare for the Cambridge entrance exam. Blind introduced Hertha to her mentor feminist, suffragette and founder of Girton College (the first residential college for women in England), Barbara Bodichon, after who she would later name her daughter. Her extended family and the suffrage community helped her get a higher education; author George Eliot* (a friend whom she met through Bodichon) wrote in support her application to Girton College, at Cambridge. She did not win a scholarship and would not have been able to afford tuition but she was supported with loans and donations from the suffrage community. While there studying math, she founded the fire brigade, led the choral society, and with fellow student and mathematician Charlotte Scott, formed a mathematics club. She also developed her first patented invention, the line divider and developed and built a sphygmomanometer (for measuring a person's pulse) while still an undergraduate. She passed the famous Mathematical Tripos in 1880, but Cambridge wouldn’t grant women degrees. She was able to take and pass a University of London equivalency exam, and they granted her a BSc in 1881.⁠
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She earned an income teaching embroidery and math. She ran a club for working girls and looked after her invalid sister. By 1884 she had her first patent for a line divider; she also sought a US patent for it in 1885. Lady Goldsmid and Barbara Bodichon provided the funding she needed to seek these patents. The invention was well-received and got good reviews in the scientific press. She presented a paper on her invention to the Physical Society in 1885 and the device was manufactured in six sizes by a scientific instrument maker. Supporters encouraged her to become an entreprenneur and inventor but she wanted to pursue a scientific career.

She began evening classes on electricity with Professor Will Ayrton, trailblazer in engineering education at Finsbury Technical College. She was one of 3 women among 121 students. He was a widower with a young daughter, and a supporter of women's education and fight for voting rights. They married in 1885 and began collaborating on physics experiments and she was able to work from the lab in their home. A year later, they had a daughter, Barbara Bidochon Ayrton. From 1888 she taught practical and domestic electricity to women. Between this, domestic chores and raising her young daughter she had little time for research.

When her mentor Bodichon died in 1891, she left Ayrton enough money to support her mother and hire a housekeeper. Will supported her research but was also careful to not always collaborate with her, so that her work would be recognized as independant from his. He once told a friend “you and I are able people, but Hertha is a genius.” She began her own studies of the electric arc, solving the pressing problem of why they would flicker and hiss. She showed this was a result of oxygen coming into contact with carbon rods used to create the arcs. She patented a number of improvements to arc lights and published 12 articles on her advances. She was the first woman to deliver a paper to the Institution of Electrical Engineers (IEE), which was more progressive than other institutions and always allowed women to attend meetings. She was also able to present three papers to the British Association for the Advancement of Science (BAAS, now the British Science Association) in 1895, 1896 and 1898. She was elected a member of the IEE, recognized a professional qualification, in 1899; she was the sole female full member of the institution until 1958. Her cousin Marcus Hartog used her 1900 lecture at the International Electrical Congress in Paris to argue that the British Association for the Advancement of Science shouls allow women on their committees. Denied the right to present her paper to the Royal Society due to her sex, renown engineer John Perry (and Will's former colleague) presented it on her behalf in 1901. After she published her textbook The Electric Arc, Perry proposed her as Fellow of the Royal Society but they rejected this (as she was married, and hence had no independant legal standing). But in 1904, she became the first woman to present her own paper ‘The Motion of Ripples in Sand and Wave’ to the Royal Society. By 1906 she was the first woman to win the Hughes Medal, for her work on ripples and the electric arc.⁠
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In Paris in 1903 she met Marie Curie and they became close friends, both physicists who collaborated with their physicist husbands and dedicated to social causes, and concerned about the role of women in society. They visited whenever Ayrton was in France. Ayrton vocally defended Marie, when Pierre died and the British press identified him (rather than Marie) as the discovered of radium, writing ‘Errors are notoriously hard to kill, but an error that ascribes to a man what was actually the work of a woman has more lives than a cat.’ Then in 1911, Marie won the Nobel for chemistry but endured a scandal in when her affair with married physicist Paul Langevin. Ayrton defended her again, and Marie and her daughters took refuge with the Ayrtons in England for two months. She was deeply involved in the women’s suffrage movement, marched in many marches (and recruited her friend Marie Curie to the cause).⁠
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After poisoned gas was used as a weapon during WWI, she put her expertise in fluid dynamics to work trying to develop a means of removing gas from the trenches. She also invented a fan and despite initial resistance from the War Office was able to demonstrate its effectiveness in protecting soldiers from poison gas and she herself organized production of her first manually operated fans in 1916. By 1917 she had developed a new, mechanically operated fan, more resistant to high winds, and she again fought War Office bureaucracy and organized the production of 104,000 sent to the Western Front.⁠ Her research on fans was later used to improve ventilation in mines and sewers. She continued to study vortices until she died. She left much of her estate to the IEE.

*Apparently, the character Mirah, in George Eliot's novel Daniel Deronda, is based on Hertha. You might recall that George Eliot was also friends with another mathematician I've portrayed, Sofia Kovalevski. The sentence "In short, woman was a problem which, since Mr. Brooke's mind felt blank before it, could hardly be less complicated than the revolutions of an irregular solid," from Eliot's Middlemarch, is undoubtedly due to her friendship with Kovalevski. I like to imagine George Eliot was quietly a math groupie. 

 References 

Elizabeth Bruton, The life and material culture of Hertha Marks Ayrton (1854–1923): suffragette, physicist, mathematician and inventor, Science Museum Group Journal, Autumn 2018, Issue 10 Article DOI: http://dx.doi.org/10.15180/181002

Ayrton, Hertha. “The origin and growth of ripple-mark.” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 84, no. 571 (1910): 285-310.

Kim Martini, The origin of ripples and other fantastic fluid experiments by Hertha Marks Ayrton, Deep Sea News, April 28, 2016.

Hertha Ayrton, Wikipedia, accessed February, 2021.

Joan Meiners, Meet Hertha Ayrton, the mathematician who cleared WW1 trenches of poisonous gas, Massive Sci, June 5, 2020.

Archives Biographies: Hertha Ayrton, The Institute of Engineering Technology, accessed February, 2021

Émilie du Châtelet and the Foundations of Physics

Émilie du Châtelet linocut, 11" x 14", by Ele Willoughby, 2019

This is a hand-printed portrait of Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (1706-1749), a natural philosopher, mathematician and physicist, inspired by contemporary portraits, and shows her along with her diagrams. Each 11" x14" (27.9 cm x 35.6 cm) linocut print is printed on lovely, delicate, Japanese paper. The diagrams are from Principes Mathématiques de la Philosophie Naturelle, a two-volume translation and commentary of Newton’s Principia, published in 1759 in French in Paris.

While historically she was merely remembered as Voltaire's lover, she in fact was not only responsible for all his ideas about physics but was the first to postulate the conservation of total energy (which includes kinetic and other forms of energy combined). Further, she found the relationship between kinetic energy, mass and velocity of an object. Before translating Newton, she published her magnum opus Institutions de Physique (or Foundations of Physics) in 1740 and within a mere two years it had been translated into many languages and republished. Debate raged at the time about how the measure the force of an object and how to formulate conservation principles. She was an active participant in this dispute known as the vis viva debate. There was a schism between the Newtonians in England and the continental philosophers who followed Leibniz, particularly in German-speaking regions; she wanted the best of both while contemporaries viewed Newton and Leibniz' work as fundamentally opposed interpretations of the world. Institutions de Physique covered philosophy, space, time, matter, laws of nature and gravity including Galileo's results and Newton's more general work. In Principes Mathématiques de la Philosophie Naturelle, she combined Newton's text with Leibniz' more elegant formulation of calculus, pushing physics forward. She was recognized during her lifetime by the greatest thinkers of the day including renowned mathematicians such as Johann II Bernoulli and Leonhard Euler, her works were translated into other languages and discussed in scholarly journals and represented in (or even plagerized by) the Encyclopédie of Denis Diderot and Jean le Rond D'Alembert. She made a large impact on contemporary physics and philosophy.

Fronstispiece from Algorotti's
Il Newtonianismo Per Le Dame, 1737 Venice

After much goading and many years, Newton finally published the bulk of his understanding of mechanics and his famous three laws in Philosophiæ Naturalis Principia Mathematica, known simply as the Principia, in 1687 with two further corrected editions in in 1713 and 1726. As the title implies, the text is written in Latin. Though he had to derive the concepts of calculus to complete the work, it's largely absent from the text in favour of the geometrical approaches to infinitessimal calculus. So Émilie du Châtelet's work does not simply represent a translation - she reorganized the work using Leibniz' calculus, wrote commentaries and explanations and most importantly, added her own discoveries about kinetic energy. To this day, du Châtelet's version is the standard French translation of the Principia and modern translators still rely on Émilie's translation.

She taught herself mathematics, and then was tutored in algebra and calculus by Moreau de Maupertuis, a member of the Academy of Sciences (who had been trained by mathematician Johann Bernoulli, who also taught Leonhard Euler).  Then she turned to his protégé mathematician Alexis Clairaut, author of Clairaut's equation and Clairaut's theorem, who became a life-long friend, and other top French mathematicians. On one occassion she was ejected from Café Gradot, where men held intellectual discussions, for being a woman. So, she had some men's clothing made and boldly returned. She became a world authority on Newtonian mechanics, at a time when few imagined a woman capable or even interested in such a thing. Émilie's impact on continental physics, and bringing Newton's Principia to Europe (and to those in England more able to read French than Latin) cannot be overstated.

She was aristocrat who not only dedicated herself to knowledge, writing about physics and experimentation, she enjoyed clothing and could be extravagant. She loved fashion, gambling and jewellery.  She used her mathematics ability to devise successful gambling techniques, when she needed money for books as a teen. Voltaire was known to call her Madame Newton-Pompom-du Châtelet for the pompoms she wore. His own writings on physics were written in collaboration with her and often quoted her word for word. It wasn't long before her skills and interest far exceeded his own. She had some insight into the relationship between light, colour and heat, long before a modern understanding of energy. At the time, scholars debated whether kinetic energy or momentum was the pertinent thing - we now know that both are important, yet distinct. She leaned towards Leibniz' ideas on the subject, which shows how she was at the cutting edge of contemporary physics knowledge and debate.

She translated Mandeville's The Fable of the Bees into French and used the preface to denounce the prejudice that prevented women from access to a proper education. Nonetheless, a product of her time, she focused more on her daughter's marriage prospects and her son's education. She had to fight to be taken seriously and deal with sexism from even the well-meaning; she and contemporary part-time Bolognese physics professor Laura Bassi were not impressed when their friend Algarotti wrote a rather patronizing popularization of Newton's physics called (I wish I were kiding) Newtonianism for the Ladies. Worse, the frontispiece of his book shows a man speaking to a lady who suspiciously ressembles du Châtelet, implying he had explained Newtonianism to her. Her short-term mathematics tutor Samuel König, a student fo Mauterpuis, also tried to undermine her by claiming responsibility for Institutions de Physique. This lead to her estrangement from Mauterpuis. Ironically König later fell out with Euler and accused Mauterpuis of having plagerized him.


The story of her long-lasting relationship with Voltaire is quite fascinating, a relationship she pursued with the knowledge and blessing of her husband, Marquis Florent-Claude du Chastellet-Lomont (Châtelet is the modernized spelling of Chastellet). She first met Voltaire as a child at one of her father's salons. They became close when she re-entered society after the birth of her children. She invited Voltaire to live at their country house, a refuge for him when he was in disfavour, and there they worked together on their publications and set up a lab. They both submitted essays to the 1738 Paris Academy prize contest on the nature of fire; neither won (they lost to Euler) but they both earned honourable mention and their essays were published by the Academy. Hence, du Châtelet because the first woman to have a scientific paper published by the Academy. Eventually their relationship became a comfortable, platonic collaboration. At age 42, she began a new affair with the poet Jean François de Saint-Lambert. She feared she could not survive her subsequent unplanned pregnancy. Six days after the birth of a daughter, on 10 September 1749, at Lunéville, she suffered a fatal pulmonary embolism. Voltaire, her husband and final lover Saint-Lambert were all at her bedside with she died.

References
Project Vox, Duke University, accessed August, 2019
Émilie du Châtelet, Wikipedia, accessed August, 2019
Philosophiæ Naturalis Principia Mathematica, Wikipedia, accessed August, 2019
Robyn Arianrhod, Seduced by Logic: Émilie du Châtelet, Mary Sommerville and the Newtonian Revolution, Oxford University Press, 2012

Émilie du Châtelet, Principes mathématiques del la philosophie naturelle, vol. 1.,  Paris, Desaint & Saillant etc., 1759

Cynthia J. Huffman, Mathematical Treasure: Émilie du Châtelet’s Principes Mathématiques, Convergence (January 2017)

Interstital Intro - My portraits of Canadian Women in STEM

Featuring artwork by me, Cheryl Hamilton and Paige Blumer, Curiosity Collider's artshow Interstitial: Science Innovations by Canadian Women is on exhibit until June 22. Since I was unable to attend the Opening in Vancouver, they asked me to share a short video introduction to me and my artwork. So now, I'm sharing the video with you. Comes complete with a peek inside my studio and some of the artwork you could find there. I think I was so focused on pronouncing "electrophoresis" that I slipped up on the more common "geneticist", but it tells about the work.

The exhibit is open from 11 am to 6 pm from Tuesday to Saturday until June 22 at The Beaumont Studios gallery spaces, located at 316/326 West 5th Street, Vancouver, BC, V5Y 1J0.

Mathematician Emmy Noether, Symmetries and Conservation Laws

Emmy Noether, linocut, 11" x 14", Ele Willoughby, 2018

Emmy Noether (1882-1935, pronounced NER-ter) has long been on my "to do" list of scientist portraits. Noether's Theorem is one of the most fundamental and profound theories in physics and I think it's impossible to overstate its importance. In some ways it's astonishing that Noether's Theorem wasn't discovered until one century ago in 1918 and in some ways its true import wasn't clear until much later. The theorem is so powerful that I struggled with how I could depict it visually. It can be written in many different ways. I could have reproduced her actual equations as her paper is widely available in the original German and in English translation. But, my goal with my art is to communicate science, and even writing a single equation cuts the potential audience. I hope that expressing ideas visually through geometry is more accessible to more people. So, in my portrait, I chose to depict a young Emmy in front of a blackboard with a more simple formulation of her theorem and three specific applications of it, shown schematically, using pictures and geometry. In simple terms, Noether's theorem shows us that any symmetry of a system (say, a given problem in physics, like a ball rolling or a molecule or a solar system or the universe itself) implies a conservation law.

The three examples I give are probably the best known, but just give a hint of the power of this theorem. If you do an experiment and then move three steps to the right and repeat it, you usually expect the same results. In general, a lot of things will have this translational symmetry. Noether's Theorem shows that if you get the same result in two reference frames which are shifted from one another, your system conserves momentum (p with an arrow, as a vector quantity). Thus, we have conservation of momentum in any inertial frame of reference. That means that any place where we don't have to worry about any significant differences from acceleration or gravity, we can solve physics problems by simply knowing that the total momentum never changes. In my print I show a set of x, y, z axes moved (translated) to get a new set of axes x', y' and z' and then the quantity p. Similarly, if your system doesn't care if you rotate it or how it's oriented in space, the conserved quantity is angular momentum (L with an arrow, as a vector quantity); hence in my print, I show a set of x, y, z axes rotated x', y' and z' along with conserved quantity L. Your system itself doesn't need to be symmetric. A lumpy asteroid conserves angular momentum every bit as much as a planetary system made of perfect spheres. If it's irrelevant to results whether you do your experiment at 3:00 or 6:25 then your system has a time symmetry and conserves energy (E). This method of using observed symmetries of something and then finding things which are invariant allows us to easily solve all sorts of problems in physics. Further, using observed symmetries of the Universe allows us to know which things are invariant, know more about the nature of reality and assess any new theories by checking whether they also produce the same conserved quantities.*

Here's a nice video which talks about Noether's Thereom.




Her male colleagues Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener described Noether as the most important woman in the history of mathematics - a compliment which betrays the biases of the times in comparing her only to those of the same sex. She was quite simply, one of the most important mathematicians period, and her impact on physics was tremendous. (My portrait betrays my own biases, focusing on the physics of Noether's Theorem, rather than her contributions to mathematics... but there you are. I'm a physicist by training, not a mathematician).

Born in Erlangen, Germany, Emmy Noether initially planned to teach girls English and French, rather than follow in her father's footsteps and become a professor of mathematics. But ultimately, she choose to study mathematics at the University of Erlangen, where he was a lecturer. Pursuing mathematics was unconventional for a woman; the university had recently declared that mixed-sex education would "overthrow all academic order" and as one of 2 female students (out of 986) she was only able to audit classes at the discretion of professors. She nonetheless managed to pass the graduation exam in 1903 and was granted a degree. She spent the winter semester at the University of Göttingen attending lectures from astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert, before returning to Erlanger. She completed a dissertation supervised by Paul Gordan, On Complete Systems of Invariants for Ternary Biquadratic Forms (1907) using the "computational" approach to invariants, later superseded by Hilbert's more abstract and general approach. She later referred to this well-received thesis and the first few similar papers as "crap". She continued to work at the university for 7 years, but as a woman she was excluded from an academic position and in fact forced to worked without pay.

In 1915 she was recruited to come to the renown University of Göttingen and work with famed mathematicians David Hilbert and Felix Klein. However, some philologists and historians in the philosophical department protested that a woman must not become a Privatdozent, an additional post-doctoral rank required in Germany and certain other European nations to act as a university professor. Famously, a faculty member protested "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?" but Hilbert defended her indignantly, with one of my favourite lines in response to such entrenched academic sexism: "I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house." There she still faced hurdles and had to rely on her family to support her financially, as she was unpaid and could only lecture under Hilbert's name until 1919  despite already having published her eponymous Noether's Theorem in 1918! After Einstein published his theory of general relativity in 1915 and Noether responded by applying her invariance work to some of its complexities and this eventually lead her to prove her famous theorem. As Einstein wrote when he read her paper, "Yesterday I received from Miss Noether a very interesting paper on invariants. I'm impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff."

The end of WWI and German Revolution of 1918-1919 lead to social change and increased rights for women. Her habilitation was approved and she obtained the rank of Privatdozent in 1919. Three years later she was promoted to an untenured professor (nicht beamteter ausserordentlicher Professor) but her work remained unpaid until the next year when she was finally granted a special position (Lehrbeauftragte für Algebra).
 
Until 1919 she focused on theories of algebraic invariants and number fields. While her incredible contribution to physics had already occurred in 1918, mathematicians remember her for her central role in the 20th century revolution in mathematics, the development of abstract algebra, and her prolific work including Ring Theory from 1920 to 1926, as well as Noetherian rings, Noether groups, Noether equations, Noether modules and more. Her revolutionary 1921 paper Theory of Ideals in Ring Domains is considered a classic and objects which satisfy the ascending chain condition are named Noetherian, in her honour. In the final stage of her career, she focused on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. She was a leader in the strong University of Göttingen math department until 1933. Her colleague Dutch mathematician B. L. van der Waerden made her work the foundation of the second volume of his influential 1931 textbook, Moderne Algebra; it was typical of her to allow students and colleagues to receive credit for her ideas. She supervised more than a dozen doctoral students. She was known for her patient guidance but insistence on accuracy. van der Waerden wrote that she was, "Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all." She learned to live frugally, having gone so long without a salary, and took no concern about her manners, housework or appearance. She used her lecturers as a time for spontaneous discussions of the latest mathematics with students and a place to explore ideas (many of which would become major publications of those students). She spent the winter of 1928–29 at Moscow State University, working with P. S. Alexandrov. She was interested in and supportive of the Russian Revolution and her political opinions got her evicted from her lodging back in Germany when students there complained of living with "a Marxist-leaning Jewess". In 1932, she won the received the Ackermann–Teubner Memorial prize for her contributions to mathematics, which came with 500 Reichsmarks and she gave the plenary address at the 1932 International Congress of Mathematicians in Zürich, a sign of her international stature in the field. Colleagues complained that she was however never elected to the Göttingen Gesellschaft der Wissenschaften (academy of sciences) or promoted to full professor. Within a year Nazi Germany moved to dismiss her and all Jewish academics from university positions. The German Student Association, aided by one of Noether's own former students, a privatdozent named Werner Weber, led the attack on Jews at the University of Göttingen. She merely laughed when students showed up dressed as Hilter's brownshirts. Dedicated to her students, she invited them to her home to discuss math and their plans for the future. Herman Weyl wrote "Emmy Noether—her courage, her frankness, her unconcern about her own fate, her conciliatory spirit—was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace." Emmy Noether was able to find a position at Bryn Mawr College in Pennsylvania in 1933, where she finally gained the appreciation she deserved. In 1934 she lectured at the Institute for Advanced Study in Princeton, but remarked that she was not welcome at the "men's university, where nothing female is admitted." Tragically, she died 4 days after surgery to remove an ovarian cyst in 1935 when she was only 53.

Noether's theorem remains fundamental to physics, and has been especially vital to particle physics in the decades since her death. Her originality in mathematics was beyond compare and in Weyl's words she "changed the face of algebra by her work."

References
Emmy Noether, wikipedia article access June 6, 2018

Noether E (1918). "Invariante Variationsprobleme". Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse. 1918: 235–257.

M. A. Tavel's English translation of Noether's Theorems (1918)

Matthew R. Francis, Mathematician to know: Emmy Noether, Symmetry Magazine, June 18, 2015.

Natalie Angier, The Mighty Mathematician You’ve Never Heard Of, The New York Times, March 26, 2012

*Now, if you're interested in the equation itself here's one good online explation (if say, you have most of an undergraduate degree in physics or more). A more intuitive a bit more straightforward explanation is here. The original paper is here and can be found in translation here.