When Albert Einstein wrote an obituary for Emmy Noether in 1935, he described her as a “creative mathematical genius” who – despite “unselfish, significant work over a period of many years” – did not get the recognition she deserved.Noether made groundbreaking contributions to mathematics at a time when women were barred from academia and when Jewish people like herself faced persecution in Nazi Germany, where she lived.2021 marked the 100th anniversary of Noether’s landmark paper on ring theory, a branch of theoretical mathematics that is still fascinating and challenging mathematicians like me today.AdvertisementAdvertisementI remember the first time I learned about Noether and the surprise I felt when my professor referred to the brilliant ring theorist as “she.” Even though I am a woman doing mathematics, I had assumed Noether would be a man. I was surprised at how moved I was to learn she was a woman, too.Her inspiring story is one that not many people know.A rare woman in mathematicsNoether was born in 1882 in Erlangen, Germany. Her father was a math professor, but it must have seemed unlikely to a young Noether that she would follow in his footsteps. At the time, few women took classes at German universities, and when they did they could only audit them. Teaching at a university was out of the question.But in 1903 – a few years after Noether graduated from a high school for girls – Erlangen University started to let women enroll. Noether signed up and eventually earned her doctorate in mathematics there.AdvertisementAdvertisementThat doctorate should have been the end of her mathematical career. At the time, women were still not allowed to teach at universities in Germany. But Noether stuck with mathematics anyway, staying in Erlangen and unofficially supervising doctoral students without pay. In 1915, she applied for a position at the prestigious University of Göttingen. The dean at the university, also a mathematician, was in favor of hiring Noether, although his argument was far from feminist.“I think the female brain is unsuitable for mathematical production,” he wrote, but Noether stood out as “one of the rare exceptions.”Unfortunately for Noether, the Prussian Ministry of Education would not give the university permission to have a woman on their faculty, no matter how talented. Noether stayed in Göttingen anyway and taught courses listed under the name of a male faculty member.During those years, she kept doing research. While she was still an unofficial lecturer, Noether made important contributions to theoretical physics and Einstein’s theory of relativity. The university finally granted her lecturer status in 1919 – four years after she applied.A revolution in ring theoryIn 1921, only two years after becoming an official lecturer, Noether published revolutionary discoveries in ring theory that mathematicians are still pondering and building upon today. Noether’s work in ring theory is the main reason that I, like many mathematicians today, know her name.AdvertisementAdvertisementRing theory is the study of mathematical objects called rings. Despite the name, these rings have nothing to do with circles or ring-shaped objects – theoretical or otherwise. In mathematics, a ring is a set of items you can add, subtract and multiply and always get another object that is in the set.More in U.S.A classic example is the ring known as Z. It is made of all the integers – positive and negative whole numbers like 0, 1, 2, 3, -1, -2, -3 and so on – and it is a ring because if you add, subtract or multiply two integers, you always get another integer.There are infinitely many rings, …
