You’ve probably never heard of German mathematician Emmy Noether, but that doesn’t stop her from being one of the most influential mathematicians of the 20th century. Noether’s work included studying invariants in algebra and abstract algebra. In less than 30 years, she made impressive advances, helped shape growing fields, and made an impact on some of the biggest names of the day, including Albert Einstein.

“In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.” —Albert Einstein

Noether’s biggest contribution to the world is what has become known as ‘Noether’s Theorem.’ Using abstract algebra, Noether was able to prove that every symmetry found in nature has a corresponding law of conservation. For example, the fact that physical laws work the same way today as they did yesterday (time symmetry) is related to the fact that energy can be neither created nor destroyed (law of conservation of energy).

If none of that made a whole lot of sense (we’re not all Noether’s and Einstein’s), consider this: time and energy are two very different concepts, and Noether was able to prove a link between them. Furthermore, she was able to show a connection between abstract algebraic functions and physics, something that had never been done before. Fundamentally, she changed the way mathematicians think about their subject.

“She taught us to think in simple, and thus general, terms… and not in complicated algebraic calculations.” —P.S. Alexandroff

Despite her discoveries and successes, nothing about Noether’s life as a mathematician was easy, except maybe the math. Born in 1882, she lived during a time when women weren’t exactly welcome in academia, or in university at all. Just getting a university education proved difficult. Noether audited classes at the University of Erlangen and the University of Gottingen for a number of years, before the University of Erlangen finally allowed women to enroll in 1904.

Even completing her dissertation didn’t make life easy for Noether. She worked at both the Mathematical Institute of Erlangen and the mathematics department at the University of Gottingen, but for 15 years, never received a single cent in payment for her work. For her first four years at Gottingen, she lectured under the name of a male colleague due to objections from the philosophical faculty. Eventually, Noether was granted the title ‘associate professor without tenure’ and began to receive a small salary, but even then was considered, and treated, as ‘lesser than’ her male colleagues.

“Surprisingly few could say exactly who she was or why she was important.” —physicist David Goldberg in 2012, referring to his colleagues and students

Noether lived most of her life in the background, and lives in obscurity even today. That hasn’t, however, stopped her work from having a powerful impact. Noether’s theorem underpins much of modern day physics, and her initial work on symmetries spurred other scientists to hunt for more symmetries. Because of her theorem, scientists were able to predict the existence of new particles, including the Higgs Boson — predictions that were later confirmed to be accurate.

Noether’s story proves that you don’t have to be well-known to make an impact. Not everyone can be famous, or popular, or stand out from the shadows of others, but everyone has the ability to produce influential work. Living in obscurity can be okay, and often, leaving behind a body of work is more important than leaving behind a well-known name.

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**Emmy Noether revolutionized mathematics — and still faced sexism all her life**

*Image Credit: Huffington Post *