Emmy Noether: Biography, Theory & Contributions to Math

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Emmy Noether (1882-1935) was a German mathematician who helped to expand the study of abstract algebra in the early twentieth century. In this lesson, learn about her struggles to become a mathematician and the many contributions she made.

Early Life and Education

In Erlangen, Germany, around the beginning of the twentieth century, a young woman named Emmy Noether decided to break the rules. She had grown up in Erlangen, where her father worked as a mathematician and professor of mathematics at the University of Erlangen. As a child, she had studied languages, music, and other subjects deemed appropriate for young German ladies of the time.

However, now she was eighteen, and she wanted something different. She wanted to enroll in mathematics classes at the University of Erlangen, where her brother was also a student. She applied to the university, but her application was denied! It wasn't because she was unqualified. It was because she was a woman, and the university did not admit female students.

Despite the fact that she was a woman, Noether was determined to study mathematics like her father and brother, and she wasn't about to let the University of Erlangen's outdated rules stop her. The university finally agreed to allow her to audit some mathematics classes, even though they would not award her any credit for them.

For the next two years, she attended classes at the University of Erlangen and proved that she was as good as any of the other students when she passed a very difficult mathematics exam given to prospective graduate students. Armed with this hard evidence of her mathematical abilities, Noether attended graduate mathematics classes at the University of Gottingen for a year and then transferred back to the University of Erlangen when they finally began admitting female students in 1904. After four years of trying to prove herself, Emmy Noether was finally a full-time Ph.D. student in mathematics.

Emmy Noether made many contributions to the development of abstract algebra in the early twentieth century
Portrait of Emmy Noether

Early Research

When she graduated with a Ph.D. in mathematics in 1907, things did not get any easier for her. She was unable to find a paying job as a mathematician because women were not expected or allowed to pursue such careers at the time. Undeterred, she worked for several years at the Mathematical Institute of Erlangen for free, without any kind of title or recognition. She helped her father with his work there but also began to pursue her own research.

She began to collaborate with the famous mathematician Ernst Otto Fischer, and she became increasingly interested in abstract algebra. It was in this area of mathematics that she would go on to make her most important and substantial contributions.

Noether often sent postcards to her collaborator Ernst Fischer, filled with her ideas about abstract algebra.
Emmy Noether postcard

Noether's Theorem

In 1915, two mathematicians working at the University of Gottingen, Felix Klein and David Hilbert, were trying to refine the mathematics of Einstein's Theory of Relativity. When they realized that they needed help, they turned to Noether. They asked her to join them in Gottingen, and she agreed. Even though she was still not being paid, her status had improved somewhat because her name was now recognized in the world of mathematics.

Hilbert and Klein's faith in Noether's abilities was not misplaced. In a very short time, she came up with a new theorem, now known as Noether's theorem, that demonstrated that there was a clear relationship between quantities that were conserved in physics (such as energy and momentum) and physical symmetries in the system being analyzed. Einstein was impressed with her work right away, saying that Noether's theorem was a piece of ''penetrating mathematical thinking.'' Over the years, it has proven to be useful in many areas of theoretical physics and not just applicable to the theory of relativity.

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