Amalie Emmy Noether
A German #mathematician behind the Noether’s Theorem, who framed modern physics and algebra, but was not fully appreciated by the scientific society of her time due to her gender.
Featuring artwork by Miler Ximena Lopez & words by Dr. Roopali Chaudhary, Sci-Illustrate Stories. Set in motion by Dr. Radhika Patnala.
“In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematician thus far produced since the higher education of women began.” — Albert Einstein, New York Times 1935
Many mathematicians and physicists have heard of Noether’s Theorem, but may not know the legacy of the woman behind it. Emmy Noether was a woman who made groundbreaking contributions to abstract algebra and theoretical physics, all the while overcoming deeply rooted sexism in her line of work. She was known as an extremely intelligent person who was not fully appreciated by the scientific society of her time due to her gender. This is not to say that she did not have any supporters. In fact, upon her unexpected death in 1935, the crème of the crop physicists and mathematicians wrote letters about her to their local newspapers. They wanted the world to celebrate her brilliance, her courage and her work that illuminated powerful new principles about our universe.
Early Life
Noether was born on 23 March 1882 in Erlangen, Germany to Ida Amalia and Max Noether, as the first of 4 children. Her father was noted German mathematician known in the algebraic geometry field. Noether was raised with the expectation to follow a typical female life trajectory of the time, i.e. focus on arts and languages, get married and have a family. In Spring of 1900, she took the examinations for teachers for English & French, qualifying her to teach languages at girls schools. But she had a greater interest in continuing her studies, and decided to pursue mathematics. This decision was considered unruly for the time, but her family was in full support.
Noether’s father, who she shared a kinship with over mathematics, taught at the University of Erlangen, and he arranged for her audit classes. This was not as easy as it sounds. Erlangen had a university policy that mixed-sex education would “overthrow all academic order”. Thus she had to get special permission from individual professors if she could sit in their course. She was only one of 2 women who were allowed in the school.
Though she was not officially registered in university, Noether took and passed the graduation exam at prep school in Nuremberg to earn her bachelor’s in mathematics in 1903. The winter of 1903–1904, she joined University of Göttingen, learning from well-known mathematicians, but soon women’s participation in Göttingen was revoked. Noether returned to Erlangen, not having her passion for mathematics dissuaded. She worked under Paul Gordon, and in 1907 earned her PhD in Mathematics with her dissertation on classical invariant theory where she provided a list of 300 calculated invariants and publishing a number of papers on them for the next few years.
Passion & Determination
After her PhD, Noether began lecturing at Erlangen without pay for the next 7 years (1908–1915), many times covering her father’s lectures. Though she had earned her PhD, in Germany at the time, an advanced degree was required to become a professor, one that she was banned from taking due to her gender. But this did not discourage her from pursing mathematics further.
When Paul Gordon retired in 1910, his successor, Ernst Fischer introduced Noether to David Hilbert’s methods on mathematical objects. Noether was fascinated, and she published several papers from 1913–1916 extending Hilber’s work to the abstract and general approach to invariants. This began her transition to abstract algebra, a fairly young field at the time.
Her publications did not go unnoticed. In fact, David Hilbert, along with Felix Klein, two leading mathematicians of their time invited her to University of Göttingen to help them understand the Theory of Relativity. In 1915, Albert Einstein published his general theory of relativity in which he determined that massive objects cause a distortion in space-time, which is felt by gravity. Conservation laws of nature were well understood at this time, so the theory of relativity was confusing to many mathematicians (it did not seem to follow the conservation laws). Hilbert and Klein hoped that Noether’s expertise in invariants would help them with the unresolved issues. Though the university refused to give her a formal position, Hilbert offered her an unofficial unpaid position. Noether took the challenge head on and quickly resolved the problem with her own theorem, which argued that since time and energy were linked, Einstein’s proposed relationship between space and time was possible without ignoring physical laws when physicists considered a large enough space.
Taking note of her brilliance, and with massive push & backing of Hilbert, Göttingen administration allowed for her to lecture, though this had to be done under Hilber’s name with her providing “assistance”. So Noether trekked on, unpaid but just as passionate about algebra.
Only a few months later, Noether developed her second theorem, now known as the Neother’s Theorem. Noether’s Theorem forged a link between symmetries in nature and conservation of energy, momentum, and electric charge. Generations of physicists have relied on her theorem to understand everything from subatomic particles to black holes. Essentially, her work framed the way we look at modern physics.
Recognition
“In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.” — Albert Einstein
After publishing her theorem in 1918, Noether reverted her attention back to solving abstract algebra, her true passion. WW1 had come to an end and there was a social change in Germany, especially for women’s rights. In 1919, over the objection of many faculty members, University of Göttingen allowed for Noether her eligibility for tenure, which she passed. However this did not come with any pay. After publishing her ground-breaking work, the only material improvement Noether saw was that the university, under pressure from Einstein, Hilbert, and Klein, allowed her finally to lecture to students under her own name. She developed multiple mathematical theories such as the ring theory, noncumulative algebra, linear transformations, and more!
In 1922, Noether was given the title of “extraordinary” professorship by Prussian minister for Science, Art & Public Education, recognizing the importance of her work. However, this title also did not come with any pay. Her family, completely supporting her academic work, continued to help pay for room to board. In 1923, Noether was appointed to a special position as a Lecturer in Algebra, finally earning a small stipend.
In 1932, Noether received the Ackermann–Teubner Memorial Award for her contribution to mathematics, finally receiving international formal recognition. The award came with a monetary prize, long over due for her contributions! She never did make full professor nor was elected into the Academy of Sciences. Her plenary address at the International Congress of Mathematics in the same year have been described as high points of formal recognition of her career.
However, as Nazi Germany gained political power, Noether was one of the first people whose position was revoked at University of Göttingen, stripped off her hard-earned right to teach in Germany. She had 3 strikes against her: she was female, Jewish ancestry, and a pacifist. Germany saw a huge loss of academics during this time.
With Einstein’s help, Noether found a job at Bryn Mawr University outside of Philadelphia and she occasionally lectured at Princeton. Her time in the US however was short lived; only 18 months after moving, Noether was diagnosed with ovarian cysts and underwent surgery. Though the surgery was successful, and Noether did well in recovery for 3 days, she fell ill suddenly and passed away on 14 April 1935.
Who was she?
Noether was known to be a very happy woman, always found smiling in her pictures and laughing often. She was known to be charismatic, but also a terrible lecturer! She rarely had a teaching plan, and used her classrooms for open discussions and advise on how to think through problems. She spoke at great speeds through her lectures, leaving many students dazed and confused. Only a handful of students shared her enthusiasm of mathematics, getting the nick name Noether’s boys.
She was known for her enthusiasm for math, so much so that if her hair was to fall loose out of her hairpins in the excitement, she let it! She was known to be empathetic to her students. She taught and mentored numerous mathematicians who went on to become academics themselves, though she was yet to be paid. She would hold lectures in coffee shop if the university were closed; sometimes even holding dinner parties to discuss the future of her students in math. She supervised more than a dozen doctorate students, including a female Grete Hermann who defended her dissertation in 1925.
She lived frugally, partially because she was not paid, but partially because she preferred a modest lifestyle. Noether left little record of how she felt about the difficulties she faced as a woman, or of her personal and emotional life generally. After meeting the young Czech math star Olga Taussky in 1930, Noether told friends how happy she was that women were finally gaining acceptance in the field.
There’s no doubt that despite being described as a most affable person, Noether must have had a great deal of determination to overcome the difficulties and hurdles placed in front of her. Noether helped change the world and show that women could make successful professors. This helped change the advancement of women in science! She was a woman at a time when women’s opportunities were limited, but she changed the world she lived in, and she changed the world for the better.
Timeline:
1882 Born to Amalia and Max Noether in Erlangen, Germany
1900 Completed examinations for teaching English and French, but instead decided to pursue Mathematics, following her father’s footsteps
1903 Earned her Bachelor’s in Mathematics despite only being allowed to audit courses at the University of Erlangen
1907 Earned her PhD in Mathematics focusing on invariants
1908–1915 Taught, without pay, at University of Erlangen and began developing the field of abstract algebra; supervised 2 PhD students
1916 Invited to work, unofficially and unpaid, at University of Göttingen; begins teaching under Dr. David Hilbert’s name
1916 Solves the relationship between space and time as proposed by Einstein’s Theory of Relativity
1918 Publishes the Noether’s Theorem that links symmetries in nature to conservation laws aka Noether’s Theorem
1919 Allowed to teach under her own name
1922 Receives title of “extraordinary” professorship from Prussian minister for Science, Art & Public Education
1923 Appointed to a special position as a Lecturer in Algebra; finally with a stipend
1932 Gives plenary address at International Congress of Mathematics and receives Ackermann–Teubner Memorial Award
1933 Flees Germany for the USA; begins teaching at Bryn Mawr University
1935 Dies during recovery from surgery for ovarian cysts
Sources:
About the author:
DR. ROOPALI CHAUDHARY
Content Editor Women in Science, Sci-Illustrate Stories
Dr. Chaudhary has an MSc in Genetics (University of Waterloo, Canada) studying Drosophila embryogenesis (fruit fly embryo development), and a PhD in Cellular & Molecular Biology (McMaster University, Canada) studying intestinal inflammation in a novel mouse model. She furthered her career in a 3-year post-doctoral fellowship studying the immune memory in food allergies (McMaster University, Canada). Dr. Chaudhary’s continually strives to make science accessible, be with through her edible science art (custom cakes), teaching or her outreach activities.
About the artist:
MILER XIMENA LÓPEZ
Contributing Artist Women in Science, Sci-Illustrate stories
Expressing myself graphically has always been a source of great satisfaction for me. With my work, I can provide many things to others in different positive ways, as well as get a lot in return, because in every goal achieved, in every process, there is a lot to learn.
About this series:
Not enough can be said about the amazing Women in Science who did and continue to do their part in moving the world forward.
Every month, through the artwork & words of the Sci-Illustrate team, we will bring to you profiles of women who touched our hearts (and brains) with their scientific works, and of many more who currently hold the flag high in their own fields!
-Dr. Radhika Patnala, Series Director
