Following Eunice Foote and Dorothy Andersen; Emmy Noether is the third revolutionary woman featured in our series *Women in Science Lost in History.*

Noether was born into a German-Jewish family in 1882. Although Germany, at the time, was significantly less anti-Semitic than it would become in the 1930s (1), her father’s ancestors still deemed it necessary to change their surnames from ‘Samuel’ to ‘Nöther’, and then to ‘Noether’ in order to blend in with the locals.

Despite the attempts, there were ignorant perceptions and overlooking of Emmy’s accomplishments, and yet, it was not due to her status as a Jew.

As was the case with the two of the aforementioned women, the lack of acknowledgment towards Emmy was because she was born in a society that could not accept that women had any intellectual ability whatsoever. Her gender was the sole obstacle standing between her and attending university as women were not allowed to attend University classes in late 19th century Germany. Nonetheless, she was still able to grasp mathematics in its complex entirety. Since society would not accept her working as a mathematician, she pursued a teaching career in English and French, receiving the second-highest possible grade in the teaching exam (2).

But this did not satisfy her, so instead, she applied to Erlangen University, where her father served on the faculty, to study mathematics. Fortunately, her father was a well-respected mathematician at the Erlangen university, so, along with one other female student in the entire institution, she could unofficially attend mathematics classes. She later attended Göttingen University and spent two consecutive years, 1903 and 1904, under the tutoring of David Hilbert, Felix Klein, Hermann Minkowski, the teacher of Albert Einstein, and Karl Schwarzschild (3).

Emmy Noether (left) with mathematicians at Göttingen, Spring 1931 (Emmy Noether Mathematical Institute) In the spring of 1904, women were given permission to enroll at German universities, which caused the immediate return of Noether to Erlangen University in hopes of sitting the entrance exam. She passed and became one of the first women to join the first mixed-sex math courses in Germany. Noether then received her PhD from Erlangen in 1907 with a dissertation on algebraic invariants, passing with the highest honors possible. Her teachers were aware of her gift in mathematics; Colin McLarty stated that “her dissertation of 1908 with Gordan pursued a huge calculation that had stumped Gordan forty years before (…) [as] far as I know no one has ever completed it or even checked it as far as she went” and she “made no use of Gordan’s own work” (4).

Up until this point, her career in mathematics seemed to be going well. Almost as though her career has been foreshadowed by the other female scientists and their attempts, her luck came to an end. Hoping to pursue lecturing, Noether’s career prospects were not supported by the law that allowed the women to sit through lectures and get degrees but did not deem them capable of lecturing. Thus, her PhD was of no use for her in terms of getting her a job.

Her determined personality did not allow her to regard this as a downfall, but rather, caused her to stick to mathematics. Despite the obstacles, since her mother was the daughter of the wealthy Kaufmann family of Cologne, Noether did not have to earn money. When her father started suffering more and more from polio, he needed more time off his lectures, this posed an opportunity for Emmy who ended up becoming a temporary replacement. This allowed her to continue to engage with mathematics, remain in Erlangen, and publish papers.

Word of her gift in mathematics seemed to spread as in 1908, she was elected to the Circolo Matematico di Palermo (Mathematical Circle of Palermo), in 1909 she was invited to become a member of the Deutsche Mathematiker-Vereinigung, and in the same year, she was invited to Salzburg to address the annual meeting of the Society (5). In 1911, Ernst Sigismund Fischer, who inspired Noether’s work in abstract math, noticed her work.

In 1915, when Albert Einstein came up with the general theory of relativity, Noether’s mentors back in Göttingen, David Hilbert and Felix Klein came to think that the theory contradicted the law of conservation of mass. They needed the help of an experienced mathematician and asked Noether to come back to Göttingen. However, when she did, she wasn’t welcomed warmly. Hilbert’s suggestion that she should become an associate professor was replied with, “What will our soldiers think when they return to university and find that they are required to learn at the feet of a woman?” by a staff member. Thus, she was given the title ‘guest lecturer’.

By working on Einstein’s theory, Noether showed that it wasn’t at all contradictory, but rather, the problem was rooted in her two mentors’ reductionist approaches. She showed them how the law of conservation of mass wasn’t violated once gravity and matter were seen as a unified quantity. Noether discovered that there is a conservation of law for every invariant (symmetry) in the universe, and for every conservation law in physics, there is an invariant (6). On this discovery, Dutch mathematician Van der Waerden wrote, “She came and at once solved two important problems.” First, she focused on the question, “How can one obtain all differential covariants of any vector or tensor field in a Riemannian space?”. Second, she proved that “To every infinitesimal transformation of the Lorentz group there corresponds a Conservation Theorem”. She proved two theorems that were basic for both general relativity and elementary particle physics, one of them still being known as “Noether’s Theorem”. Frank Wilczek, a theoretical physicist from MIT, stated that the theorem “has been a guiding star to 20th and 21st-century physics,” (7). The theorem allowed practical calculations to be made and helped physicists determine whether to continue using a theorized system or abandon it.

Even after this, her gender was seen as a barrier that came before her intellectual ability. She was given the exception of being able to lecture, but only under the cover of Hilbert’s name.

She didn’t receive a salary until 1923, and ten years later, she was forced to quit as the government was now led by the Nazis. Her incapability of working due to her status as a woman coincided with the Nazis’ severe prejudice against the Jewish, being accused of holding leftist political beliefs (8), and once again, her bright soirees were destroyed. She then left for the United States to join the staff of Bryn Mawr College, Pennsylvania, before her death two years later at the age of fifty-three due to surgical complications.
Albert Einstein, in Noether’s obituary in 1935, described her as a “creative mathematical genius [that] never reached the academic standing due her in her own country” (9).

__Works Cited__

__https://encyclopedia.ushmm.org/content/en/article/antisemitism-in-history-nazi-antisemitism____https://www.britannica.com/biography/Emmy-Noether____https://www.famousscientists.org/emmy-noether/__McLarty, C. Emmy Noether’s first great mathematics and the culmination of first-phase logicism, formalism, and intuitionism.

*Arch. Hist. Exact Sci.***65,**99–117 (2011).__https://doi.org/10.1007/s00407-010-0073-y____https://mathshistory.st-andrews.ac.uk/Biographies/Noether_Emmy/____https://www.famousscientists.org/emmy-noether/__Wilczek, Frank.

__A Beautiful Question: in Pursuit of the Hidden Logic of the Universe__. Allen Lane, 2015.__https://www.nytimes.com/1935/05/04/archives/the-late-emmy-noether-professor-einstein-writes-in-appreciation-of.html__

## Comments