‘The most significant creative mathematical genius thus far produced since the higher education of women began': Emmy Noether

Authored by Izzy Maundrill

This article investigates the work and life of Emmy Noether, a mathematician and scientist who invented an incredibly important theory and worked alongside major male scientists at a time where women’s advanced education was rare. She is characterized by her friend and colleague Einstein as ‘the most significant creative mathematical genius thus far produced since the higher education of women began’, and yet she faced much discrimination in her field for her sex and religion. Despite being somewhat credited for her work it was nowhere near proportionate to how influential her work has been, with Nobel Prize winner in physics Wigner stating in 1963 how ‘we physicists pay lip service to the great accomplishments of Noether, but we do not really use her work… it should have excited physicists more than it did… but most physicists know little about her’.

 

Emmy Noether was born in 1882 into a family of mathematicians. She was described by a later coworker, Professor Quinn, as a woman with dark cropped hair, wearing thick glasses, and a way of turning her head aside and looking into the distance when trying to think. Her personality was described as ‘sincere, straightforward, kindly, thoughtful, and considerate’. She began her career as an English and French teacher but decided to change paths and study Mathematics at the University of Erlangen instead. This change in path was not welcomed by society as women were not allowed to study at universities without permission of the professor; this is not something she received. Determined to pursue her want of higher education, Noether moved to Gottingen University where she studied until the University of Erlangen would allow her to study within the Philosophical faculty. She achieved a PhD in 1907 with a dissertation in algebraic invariants. She remained at the university for a further eight years assisting her father on mathematical research for his projects and lecturing under his name. This all had to be done without pay as a woman could not officially work at the university.  

Then she was offered by Einstein a worthy and spectacular opportunity to explore the recently published Theory of Relativity with other scholars at the University of Gottingen. During this period, she also fulfilled her wish to teach, however this did not come without pushback. Faculty members disapproved of a woman teaching at the university and so she taught under her colleague and friends name Hilbert. Hilbert helped to stand against the universities discrimination of Noether saying how ‘I do not see that the sex of the candidate is an argument against her admission as a privatdozent. After all, we are a university not a bathing establishment’. During this time Noether developed her two theorems. I will try to explain her theorems as best I can while not being especially well versed in physics. The definition given is that she discovered and explained the link between physical systems and conservation laws. A physical system is a collection of physical objects that have a physical relationship and are observed as one unit or group. Her theorems looks at when a physical system is impacted by the changing of kinetic or potential energy and how that links to the three major conservation laws – Conservation of linear movement, angular momentum, and energy. The theory allows one to find what symmetries a physical system has, this is the physical or mathematical feature of a system that remains unchanged when a transformation, such as movement, occurs, this can then be calculated to find a quantifiable way to identify conserved energies. Examples of this include spatial translation symmetry leading to knowledge of the conservation of linear momentum, or rotational symmetry leading to knowledge of the conservation of angular momentum.

If, like me, that makes your head spin, just know that it draws together many potent mathematical developments and is described by a professor at Syracuse University as ‘forming one of the cornerstones of work in general relativity as well as certain aspects of elementary particles physics’.

 

Noether became an official lecturer in 1919 with her work being first recognised in 1920 by Schmeidler in his academic writing. From here she thrived as a professor, researching within the department, and editing for the Mathematische annalen. Her influence over both colleagues and students is huge with nods to her theory appearing in other professors’ publications and her insight being seen in the students’ work. Her academic influence had a wide geographical range with her teaching in the University of Moscow in 1928 for a few months, and later at various universities in the United States of America.

However, her struggles and barriers to success were not yet over. She was dismissed as a professor in 1933 when Nazis came to power for her Jewish beliefs. She continued to teach in her apartment in secret but eventually had to flee to the United States due to the endangerment of her life. She made the most of this situation and became a visiting professor at Bryn Mawr College and conducted research at Princeton University. It was in the US where she passed away from an ovarian cyst at 53.

 

Despite her seemingly huge influence in mathematics and physics over her colleagues and students, her work was mostly unpaid and unrecognised until recent. Kimberling says that she was ‘only given a footnote in E.T. Bells men of mathematics, and hardly more in compatible books. Little can be found about her in other than three obituary addresses and a biography published about her in 1971’. Her dismissal as a professor and academic based purely off of her sex and religion is shocking considering how she was the creator of such a fundamental concept in physics.