When Albert Einstein wrote an obituary for Emmy Noether in 1935, he described her as “an inventive mathematical genius” who—despite “many years of devoted, important work”—did not receive the recognition she deserved.
Noether made groundbreaking contributions to mathematics at a time when women were barred from academia and Jews like herself faced persecution in Nazi Germany.
The year 2021 marked the 100th anniversary of Noether’s groundbreaking paper on ring theory, a branch of theoretical mathematics that remains fascinating and challenging for mathematicians like me today.
I remember when I first learned about Noether and the surprise I felt when my professor referred to the brilliant ring theorist as “he.” Even though I’m a woman interested in mathematics, I assumed Noether would be a man. I was surprised at how emotional I felt when I learned that she was also a woman.
His inspiring story is one that many people don’t know about.
A rare woman in mathematics
Noether was born in Erlangen, Germany, in 1882. His father was a mathematics professor, but it seemed unlikely that young Noether would follow in his footsteps. At that time, very few women were taking courses at German universities, and when they did, they could only supervise them. Teaching at the university was out of the question.
But in 1903, a few years after Noether graduated from the girls’ high school, the University of Erlangen began allowing women to enroll. Noether enrolled and eventually earned his doctorate in mathematics there.
This PhD should have been the end of his mathematics career. At that time, women were still not allowed to teach at universities in Germany. But Noether still remained loyal to mathematics, remaining in Erlangen and unofficially advising doctoral students for free. In 1915 she applied for a position at the prestigious University of Göttingen. The university’s dean, also a mathematician, was in favor of hiring Noether, even though her argument was far from feminist.
“I think the female brain is unsuited to mathematical production,” he wrote, but Noether stood out as “one of the rare exceptions.”
Unfortunately for Noether, the Prussian Ministry of Education would not allow a woman to serve on the university’s faculty, no matter how talented she was. Noether nevertheless remained in Göttingen, teaching courses listed under the name of a male lecturer.
He continued to do research during those years. Although still an unofficial lecturer, Noether made important contributions to theoretical physics and Einstein’s theory of relativity. The university finally granted him lecturer status in 1919, four years after he applied.
A revolution in ring theory
In 1921, just two years after becoming a formal lecturer, Noether published revolutionary discoveries in ring theory that mathematicians are still pondering and working on today. Noether’s work in ring theory is the main reason why I, like many mathematicians today, know his name.
Ring 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 elements that you can add, subtract and multiply, always obtaining another object in the set.
A classic example is the ring known as Z. It consists of all integers – positive and negative integers like 0, 1, 2, 3, -1, -2, -3 – and it is a ring because if you add, subtract, or multiply two integers, you always get another integer.
There are an infinite number of rings and each one is different. A ring can consist of numbers, functions, matrices, polynomials, or other abstract objects; As long as there is a way to add, subtract and multiply them.
One reason rings are so interesting to mathematicians is that it is often possible to tell that something is a ring, but it is difficult to know much about the properties of that ring. It’s like seeing a croissant in a fancy bakery. You know you see a croissant, but you may not know if it’s filled with almond butter, chocolate, or something else.
Rather than focusing on a single ring at a time, Noether showed that an entire class of easy-to-identify rings shared a common internal structure, like a set of houses with the same floor plan. These rings are now called Noether rings, and the structure they share is like a map that guides mathematicians who study them.
Noether rings appear all the time in modern mathematics. Mathematicians still use Noether’s map today, not only in ring theory but also in other fields such as number theory and algebraic geometry.
Escape from Nazi Germany
While teaching at Göttingen from 1919 to 1933, Noether published his famous ring theory paper and other important results in mathematics. But in the spring of 1933, the University of Göttingen received a telegram: six faculty members, including Noether, had to stop. I teach you immediately. The Nazis passed a law banning Jews from holding professorships.
Noether’s response was apparently calm. “This thing is much less terrible to me than to most other people,” he wrote in a letter to a mathematician friend. However, he was unemployed and no university in Germany could recruit him.
Help came from the USA. Bryn Mawr, a women’s college in Pennsylvania, offered Noether a professorship through a special fund for refugee German scholars. Noether accepted the offer and became a professor at Bryn Mawr, mentoring four young women (one doctoral student and three postdoctoral researchers) in advanced mathematics.
Noether’s time at Bryn Mawr was tragically short. In 1935, she had surgery to remove a tumor and died unexpectedly four days later.
At Noether’s funeral, mathematician Hermann Weyl likened her sudden death to “the echo of thunder.” In his short life, Noether shook up mathematics. She continued to teach and learn even when women and Jews were not welcome. A hundred years later, his mathematical genius and “unbreakable optimism” are admirable qualities.
This article is republished from The Conversation, an independent, nonprofit news organization providing facts and authoritative analysis to help you understand our complex world. Written by: Tamar Lichter Blanks, Rutgers University
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Tamar Lichter Blanks received funding from the National Science Foundation through the Graduate Research Fellowship Program. He is an American Association for the Advancement of Science (AAAS) Mass Communication Science and Engineering Fellow at The Conversation US, sponsored by the American Mathematical Society.