Emmy Noether is the most accomplished mathematician you probably never heard of. She helped Albert Einstein with the math required to formulate his Theory of Relativity. And then she came up with what is known as Noether's theorem.
Noether's theorem validated Einstein's theory. And to this day it provides the foundation for a unified theory that combines gravity and quantum mechanics.
Similarly impressive is her long list of accomplishments while battling double prejudices: she was a woman and Jewish.
Forge Your Own Path
Noether (1882-1935) was born in Erlangen, Germany. At first, she followed the traditional path for single women at the time. The only acceptable occupation was teaching languages. She passed the required exams and was licensed to teach French and English to girls.
But she had a passion for math. It perhaps arose from her professor father, Max Noether, himself a widely respected mathematician. Back then, though, women were not permitted to take classes as matriculated students. However, they were on occasion allowed to audit them. That's what Noether did, in part thanks to her father.
Ironically, in a kind of twisted logic, the women auditing classes — only two at Erlangen University out of 986 students — were forbidden to take exams in individual subject areas during the course of the year. But they could take a graduation exam.
Noether passed easily. And she immediately began postgraduate studies — still only permitted to audit — spending a semester at the University of Göttingen. She studied with two of the greatest mathematicians of the time, Felix Klein and David Hilbert.
Take It To The Next Level
In 1904, she returned to Erlangen. Now permitted to enroll as a matriculated student, she earned her Ph.D. with honors in 1907. But what next? Women were not permitted to hold academic posts. But that didn't deter her, either. She hadn't pursued the degree in order to get a job. She was hungry for knowledge and research experience. So she stayed at Erlangen as her father's unpaid assistant.
While not ideal, it allowed her to continue her research. She also joined several mathematical societies, attended their meetings, discussed her work, and slowly but assuredly built an international reputation.
Later, when her father became ill, she began to teach his courses as a permanent and unpaid substitute, even supervising Ph.D. students. All this was allowed because of her obvious brilliance. Yet at the same time, less talented mathematicians who'd graduated with her won positions at universities and rose up the academic ranks.
Keep A Positive Attitude
Noether didn't let the discrimination hold her back. Lee Phillips, author of "Einstein's Tutor: The Story of Emmy Noether and the Invention of Modern Physics," told IBD he didn't find any bitterness or self-pity in any of her correspondence or speeches.
"It wasn't that she was accepting of her second-class status," Phillips said. "She knew that she couldn't go to school, that she couldn't teach. It was like the air you breathe. You have to swim in the ocean in which you were born. Yes, she accepted reality, but she wasn't going to be deterred from pursuing her academic interest because of institutional backwardness."
It was a sign of her intellectual flexibility. She wasn't locked into a single school of thought and was willing to change if she saw a better or more interesting way.
Elevate Your Knowledge
Noether had been trained in classical algebra. But when exposed to a more abstract methodology, she quickly shifted gears. Instead of standard algebraic formulas, she found a more theoretical approach far more appealing. Rather than focusing on specific answers, she focused on the rules that govern the entire system.
By 1915, her reputation was such that she was invited back to Göttingen to work with Klein and Hilbert — unofficially and without pay. Women were still not permitted on the faculty.
It was during this period that she corresponded with Einstein, who, as Phillips wrote, "expressed his wonderment at what happened to his equations in her hands."
In fact, Einstein wrote to Hilbert: "You know that (Ms.) Noether is continually advising me in my projects, and it is really through her that I have become competent in the subject."
Be Willing To Help
While kind, the letter was unnecessary. Hilbert already knew the quality of her intellect. He himself hit a wall when trying to figure out a theory on energy conservation, so he asked for her help.
Though she wasn't particularly interested in physics at the time, she did what became a hallmark of her work: homework. She came prepared and soon built a reputation as a thorough and always prepared scholar who read the literature both past and present.
But her accomplishments were not sufficient to traverse the complicated German process to earn a teaching license, called habilitation. It required her to submit a thesis or research paper, and only then, if deemed competent, could she be elevated to privatdozent — a high academic level.
Rely On Your Skill
She forged her path not through confrontation, but the sheer force of her intellect.
It took three attempts over several years to earn that title in 1919. In the interim, she taught classes under Hilbert's name. But the indignities continued. It took another three years, until 1922, before she finally was promoted to assistant professor. But that came with a caveat. Yes, she could teach, but not be a member of the civil service or receive a pension.
Still, she soon developed a rabid following, familiar and appreciative of her eccentricities. She never planned her lectures, inventing new ways to prove theorems on the fly. It could be maddening for less advanced students who couldn't follow her rapid-fire calculations on the chalkboard.
But her advanced students were devoted to her and took special delight when newcomers fled her classroom.
Share Your Knowledge
Moreover, she was extremely generous, often giving young students results of her research she hadn't yet published. However, she'd insisted the young scholars develop the idea further and that she receive no credit when they published.
An interesting anecdote from Phillips' "Einstein's Tutor" involved one of Noether's young associates, B.L. van der Waerden. He wrote a paper he was excited about. Then, he showed it to Noether, who suggested how he might improve its organization and encouraged him to send it off for publication.
He did so, under his own name. Noether even reviewed it. Only later did van der Waerden learn from a fellow student that Noether had reached the same conclusions years ago, and had presented them in a class the student had attended.
Stay Modest
Also, considered one of the finest mathematical minds in the world, Noether was not caught up in her status.
One of her doctoral students, Olga Taussky, got into a classroom tussle with her when she thought the professor unfairly criticized one of her published proofs. Everyone in the class got tense, because you didn't talk back to a professor that way. But nothing happened. Taussky later said, "I realize for the first time that she was a person who did not mind criticism."
All went relatively well until 1933, when the Nazis gained control of Germany. Noether was one of the first academics dismissed. Despite the inherent dangers, Noether defied the authorities by holding secret classes for her students in her apartment.
"When you are that single-minded and that enthusiastic about a subject to the exclusion of all else, you can't explain it," Phillips said. "She wouldn't — couldn't — stop teaching though she knew the dangers."
Find Your Path
Fortunately, thanks to the intercession of several aid organizations, Noether was able to emigrate to the U.S., where she landed a job at Bryn Mawr College just outside Philadelphia.
She was charged with a complicated task: bringing modern algebra to America. As she encountered early on in Germany, her lectures could occasionally be beyond the grasp of some students. So she adjusted them for her new American student audience. "I'm beginning to realize I must be careful after all," she said.
She described her time at Bryn Mawr (during which she also lectured at the Institute for Advanced Study at Princeton) as "the happiest" time of her life. Sadly, it was all too brief. She died from complications following surgery to remove several tumors in April 1935.
Emmy Noether's Keys
- One of the finest mathematic minds of the modern age.
- Overcame: Prejudices against women academics.
- Lesson: "I do not see why I should not be able to do mathematics."
