Emmy Noether: The Captivating Woman Who Revolutionized Mathematics

Introduction

In a world where the thought of a woman separating herself from the kitchen, let alone the possibility of one breaking ground in the world of higher education, was unheard of, Emmy Noether was a shining light, the pioneer that defied all formerly accepted “truths” about women in STEM. Noether, a Jewish woman, who taught in Nazi Germany, survived by fleeing the country and emigrating to the United States in 1933. She’d been targeted by the Nazi regime not just because she was a Jewish woman, but because she was a Jewish professor– at the time, one of the most prominent pieces of Nazi propaganda was that “Jewish mathematics” and “Jewish science” were flat out untrue and unreliable, whereas “Aryan mathematics and science” were valid and dependable. Despite their attempt to erase Jewish history and scientific discoveries, Noether’s work couldn’t be effaced. Her revolutionary ideas held strong through the years, and today, she is still credited as one of the most brilliant minds in mathematics and praised for her rewriting of algebra. 

Early Work 

While one could probably tell you that Albert Einstein called Noether “the most significant creative mathematical genius thus far produced since the higher education of women began,” or that Pavel Aleksandrov addressed her as “one of the most captivating human beings I have ever known,” it’s important that we don’t simply value female scientists by the adjectives and praises that their male peers assign to them– in Noether’s case, this is easy, because her work speaks for herself. 

Emmy Noether was raised like most upper middle class girls, to invest in the arts and not to seek anything higher than what she was given. In the late 1800s, girls weren’t allowed to attend college preparatory school, so instead, she completed a general “finishing school,” and would later be certified in teaching English and French in 1900. Rather than pursuing a career in teaching, however, Noether sought after a higher education in mathematics. After auditing classes at the university, Erlangen, as one of two women among thousands of men, she took the entrance exam– and passed. She entered the University of Göttingen in 1903 as an auditor, as women still weren’t allowed enrollment, and then transferred back to Erlangen in 1904 when the university began allowing women to enroll. In 1907, she received her Ph.D. in mathematics, becoming one of the first women to receive their Ph.D.. Without allotting her pay or title, the Mathematical Institute of Erlangen employed her. It would be here, between 1908 and 1915, where she worked with algebraist Ernst Otto Fischer, and where she would begin her work on theoretical algebra. In 1915, she joined the Mathematical Institute in Göttingen and began her work on Einstein’s general relativity theory. Her work there would lead her to prove two theorems that set the basis for both general relativity and elementary particle physics– one now known as “Noether’s Theorem.” 

Noether’s Theorem

Noether’s Theorem, confirmed by Emmy Noether in 1918 during her time at the Mathematical Institute in Göttingen, is now a hailed standard in theoretical physics. While you’ll typically, and likely first, come across Noether’s Theorem in quantum physics, this work of genius also shows up regularly in classical field theory. Noether’s Theorem allows physicists to obtain quantities from symmetries of laws of nature. Put simply, “Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.” (Baez 2020) 

Post-Theorem Work

Even after her ground-breaking discoveries had begun, she was still unable to join the faculty at Göttingen due to her gender and was only allowed to lecture under her male superior’s name. Because of her colleagues, Albert Einstein and David Hilbert, interceding for her, she was finally given permission to lecture in 1919, although without salary. In 1922, she became an associate professor without tenure and received a small salary. Her status remained non-existent while she remained at Göttingen, which she owes to the fact that she was a woman, a Jew, a Social Democrat, and a pacifist. All throughout the 1920s, Noether worked on abstract algebra, group theory, ring theory, group representations, and number theory. Though her work was controversial, physicists and crystallographers would benefit greatly from her work during this period. Baez 2020 states that “Noether's conceptual approach to algebra led to a body of principles unifying algebra, geometry, linear algebra, topology, and logic.” 

Moscow State University 

In the late 1920s, Noether would go on to teach in Zurich and Moscow– more specifically, she was granted a position lecturing at Moscow State University, where she worked with her close friend P.S Alexandrov. Here, she carried on her research and lectured on abstract algebra and algebraic geometry. Additionally, she worked with prominent topologists Lev Pontryagin and Nikolai Chebotaryov, who later praised her contributions to the development of Galois theory. 

Noether took an interest in Russian politics and was an avid supporter of the Russian Revolution. She supported the Soviets and was particularly fond of their contributions to math and science, of which there were many. According to historian, Colin McLarty, "she was not a Bolshevist but was not afraid to be called one." This was a controversial take at the time, relative to the rest of the world– but we know opinions such as these, unconventional ones, are typical for her. 

​​ Noether’s work teaching in Moscow would win the Ackermann-Teubner Memorial Prize in mathematics. 

Nazi Germany’s Impact on Her Work and Life

In 1933, Adolf Hitler was appointed Chancellor of Germany and the Nazi Party took control of the country. Noether was approached by both Bryn Mawr College, in the United States and the University of Oxford, in England. After many negotiations, she took a grant position at Bryn Mawr, where she’d take a position in 1933. She’d later teach at Princeton, where, though her colleagues were very accepting of her, she noted she did not feel welcome as a woman by the student body. 

Though she enjoyed her time in America, she and Alexandrov would write back and forth, with whom she made plans to return to the Soviet Union in 1935. 

Death

Tragically, in 1935, she was found to have a tumor in her pelvis. After her operation, though technically successful in removing the tumor, she developed a postoperative infection, which killed her at the age of 53. 

Conclusion 

Dr. Emmy Noether was a brilliant, creative, and revolutionary woman whose contributions to algebra and physics were unconventional and trailblazing. For a woman in her time, at her age, to make so much progress in her field– one that was severely male-dominated– and for her to persevere through no title, no pay, no recognition, was praiseworthy and brilliant. Noether knew what an impact she’d have if she persisted and didn’t let the roadblocks she faced stop her by any means. A woman commendable in every way, Noether is who we owe the way we think about physics and mathematics today. 

Works Cited

Conover, Emily. “In Her Short Life, Mathematician Emmy Noether Changed the Face of Physics | Science News.” Science News, 12 June 2018, www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math.

Cavna, Michael. “Emmy Noether Google Doodle: Why Einstein Called Her a “Creative Mathematical Genius.” Washington Post, 24 Oct. 2021, www.washingtonpost.com/news/comic-riffs/wp/2015/03/23/emmy-noether-google-doodle-why-einstein-called-her-a-creative-mathematical-genius/.

“Emmy Noether: Creative Mathematical Genius.” Www.sdsc.edu, www.sdsc.edu/ScienceWomen/noether.html.

Baez, John. “Noether.” Math.ucr.edu, 17 Feb. 2020, math.ucr.edu/home/baez/noether.html.