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For a long time, we have been using Noether’s theorem to have useful insights into numerous theories in physics. For example, it has played a fundamental role in emphasizing the beautiful relationship between the symmetries in nature and various conservation laws. However, the woman behind this appealing theorem has always remained away from the limelight, and we have rarely heard or read about her. Let’s have a peep into the life of Emmy Noether, the genius who made unmatched contributions to mathematical sciences, despite all the hardships that she had to face because of her gender.

Emmy Noether
Emmy Noether

Early life and education

Born on March 23, 1882, in Erlangen, Germany, Amalie Emmy Noether belonged to a Jewish family. Her father, Max Noether, was one of the most respected mathematicians of his time and served as a mathematics professor at the University of Erlangen. During her childhood, Emmy spent most of her time learning the arts expected out of girls at that time. Since the girls in the nineteenth century were not allowed to attend college preparatory schools, Emmy went to a general finishing school where she got certified to teach English and French. However, she wanted to go into the field of mathematics instead of teaching languages.

To chase her dreams of becoming a mathematician, Emmy applied to join the mathematics classes at the University of Erlangen. But due to her gender, she wasn’t allowed to do so; instead, she was asked to audit the classes. Again when she entered the University of Gottingen, she was given entry as an auditor only. However, in 1904, the University of Erlangen finally let women enroll. Eventually, Emmy Noether joined the university to finally receive her Ph.D. in mathematics in 1907 by defending her dissertation on invariants of biquadratic form under Paul Gordan’s guidance.

The Woman Who Wrote the Most Crucial Theorem To Guide Modern Physics. 1
Paul Gordan, the man who supervised Noether’s Ph.D. thesis

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Professional appointments and and personal hardships

Even after completing her Ph.D. in mathematics, she was not accepted as a faculty member at the University of Erlangen because of its policy against women professors. So in the initial years of her career, she decided to help her father at the Mathematics Institute in Erlangen. While being with her father, she helped him by teaching his classes and gradually began to conduct her independent research and soon began to publish papers on her work.

After World War I ended, Felix Klein and David Hilbert, who were working on one of Einstein’s theories at the University of Gottingen, realized that Emmy Noether’s expertise could help them in their work. Hence, they asked her to come and join them there. Although no women were on the faculty earlier, Noether worked really hard and eventually bagged a job there as a lecturer. Even though she still was not paid for her efforts, it was for the first time that Noether was teaching under her own name. Slowly and steadily, her efforts got paid off, and she started receiving a small salary for her work.

However, In 1933, Hitler and the Nazis came into power in Germany. As per their known policies, the Nazis demanded all the Jews to be thrown out of the universities. Following this, Emmy Noether also had to bid farewell to the University of Gottingen. She moved to the United States, where Bryn Mawr College had offered her a teaching position in a women’s college. This job appointment enabled Noether to work with female colleagues for the first time in her life, and she continued to teach there until she died in 1935.

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Emmy Noether (Image: Credit: Pictorial Parade/Hulton Archive/Getty)

Contributions to mathematics and physics

Throughout her mathematics career, Emmy Noether made some remarkable contributions to mathematical science. She was responsible for developing some of the most beautiful theories of rings, fields, and algebras. Emmy’s entire contribution to physics and mathematics has been categorized into three main epochs.

The work done by Emmy Noether between 1908 and 1919 is put under the first epoch. During these years, she contributed explicitly to the theories of algebraic invariants and number fields. Moreover, Emmy’s work on differential invariants in the calculus of variations and her Noether’s theorem has been termed as “one of the most important mathematical theorems ever proved in guiding the development of modern physics.”

In her widely recognized Noether’s theorem, Emmy brought together the differential symmetry and the conservation laws under a single frame. She stated that every differentiable symmetry of the action of a physical system has a corresponding conservation law. For instance, the invariance of physical systems with respect to spatial translation (translational symmetry) gives the law of conservation of linear momentum, the invariance with respect to rotation (rotational symmetry) leads to the law of conservation of angular momentum, and the invariance with respect to time translation (temporal translational symmetry) gives the well-known law of conservation of energy.

Not only this, but Noether’s theorem can also be used to calculate the entropy of stationary black holes and remains one of the most celebrated works of Emmy Noether.

When Einstein came to know about this work of hers, he wrote to Hilbert as follows:
“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.“

After this, Emmy contributed six years of her life to change the face of abstract algebra. She worked in this regime from 1920 to 1926, and this period was known as her second epoch. In 1921, Emmy Noether published a paper titled Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains), where she developed the theory of ideals in commutative rings into a tool with wide-ranging applications. Noether further made elegant use of the ascending chain condition, and the objects satisfying it were termed as Noetherian in her honor.

In her final and third epoch of intellectual contributions between 1927 and 1935, Emmy published numerous works on non-commutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals.

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Emmy Noether as a teacher

Emmy was known for her intellectual abilities and was also loved for her considerate attitude towards her students. She was a warm person who cared deeply about her students and considered them as her family members. Although Emmy’s teaching style was challenging to follow, those who could catch on to her unique style eventually became her loyal followers. Noether’s teaching methodology provided her students a room to grow as individuals and led them on a path to develop their original ideas. As a result, many of her students went on to become great mathematicians themselves.

Indeed, despite all the obstacles in Emmy’s path towards becoming a mathematician, she overcame them all with flying colors. She became a woman to make significant contributions to mathematics and physics and inspired many to follow in her footsteps in the future.

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