Emmy Noether

emmy-noether

Summary: Amalie Emmy Noether was what some might have called a woman born out of time. Her work, in a world that was dominated by men, established her as a strong voice in the world of mathematics and algebra.

Early Life

Amalie Emmy Noether was born on March 23, 1882 in Erlangen, Germany. She was the oldest child (other three being boys) of Max Noether and Ida Kaufmann Noether. It might be said that her later interest in mathematics would have some connection to her father, who was a mathematics professor at the University of Erlangen. Interestingly, Max Noether did not have that in his lineage as his family worked in hardware.Her mother was of a well-to-do family from Cologne.

Although neither of her parents had Jewish names, their heritage was that of Jews. Her paternal great grandfather, Elias Samuel, ran a business in Bruchsal, Germany. In the year 1809, the government established a referendum that required all people of Jewish faith to take on German names. Thus Elias Samuel became Elias Noether.

Elias Noether also went the extra step of changing the first names of his children as well. One son, Hertz, became Hermann, who was the father of Max Noether. Hermann Noether left Bruchsal and set up a wholesale hardware business. Until the Nazis removed the business from the Noether’s in late 1930s, the family owned the business for almost a century.

Emmy Noether did the typical things young girls were brought up to learn. It was expected that she would someday marry and maintain a home like all the women of her era. Cooking, cleaning, running the home budget were all expectations and she did them. However, Emmy also loved studying mathematics (which again could be the influence of her father, the math professor at university). But studying and being able to become an instructor of the subject were two different things. It was man’s world and she understood that fact.

As mentioned, Emmy had three younger brothers. All three would suffer tragic fates in their lives. Alfred died early in his life after earning his doctorate in chemistry. Fritz went into the world of mathematics and left Germany in 1937 when the Nazis were in rule and prohibiting Jews from any kind of work. He left Germany and went to the Soviet Union. There was he arrested for sedition to the Communist rulers and summarily executed. The youngest Noether brother, Gustav was mentally disabled and lived in government care until his death at age 39.

In his book, Emmy Noether, A Dick describes Emmy in this way as a child,

Emmy did not appear exceptional as a child. Playing among her peers in the schoolyard on Fahrstrasse she probably was not especially noticeable – a near-sighted, plain-looking little girl, though not without charm. Her teachers and classmates knew Emmy as a clever, friendly, and likeable child. She had a slight lisp and was one of the few who attended classes in the Jewish religion.

The young Emmy spent much of her child years doing what was expected as mentioned. Besides handing domestics, she spent considerable time learning the art side of life rather than the sciences.

The young girl went to finishing school at Städtische Höhere Töchter Schule on Friedrichstrasse. She lived at home and attended there until 1897. Emmy Noether loved to dance and unlike her mother, who lived for piano, she loved attending parties during her high school years. Much of her studies were around literature and language. She intended at this part of her life to study to become a language teacher. Young Noether became a certified teacher, intending to work in girl’s schools instructing French and English.

University and Beyond

But Emmy Noether was not the typical woman of the early 1900’s. She made up her mind that she was going to follow her first love and learn mathematics at university. This would not be an easy task as women were not the norm in this field of study. The University of Erlangen required that for women to “sit in” on mathematics and science courses, they must first obtain permission from the instructing professor.

Once Emmy received the ok to attend the classes, she was a devout student…one of only two women that were auditing the classes at the time. Students could do an entrance exam that allowed them to any university. During her time of auditing, she was taking classes in languages, and Roman history. Emmy Noether planned to go to another university in hopes of science courses. Once passing her matriculation exam, Emmy entered into University of Gottingen. Unfortunately, again she could do was audit math classes.

She audited classes at Erlangen as one of two women among thousands of men, then took the entrance exam. She entered the University of Göttingen in 1903, again as an auditor, and transferred back to Erlangen in 1904 when the university finally let women enroll. She received her mathematics Ph.D. summa cum laude in 1907. In her field that was considered the highest possible accolade for a doctorate.

One aspect that helped her in her work for her doctorate was to study under noted mathematician Paul Gordan. Dr. Gordan had never allowed any one to work with him as a doctorate’s candidate. Making such an exception for Emmy Noether illustrated her intellectual status and ability to advance in the area of mathematics.

Paul Gordan was a scholar in the area of invariants, known as the “king of invariant theory”, along with David Hilbert. However, the two men looked at the subject from different perspectives.  To do her doctorate work, Emmy Followed the ideas of Gordan to conclude her thesis. Interestingly, she would later be working with David Hilbert.

Colin McLarty had this to say about her thesis;

her dissertation of 1908 with Gordan pursued a huge calculation that had stumped Gordan forty years before and which Noether could not complete either. So far as I know no one has ever completed it or even checked it as far as she went. It was old-fashioned at the time, a witness to the pleasant isolation of Erlangen, and made no use of Gordan’s own work building on Hilbert’s ideas.

Although Noether had her Ph.D. in mathematics, women were still being held back in the career aspect of the sciences. However, she was able to secure in 1908 as a lecturer in her specialty of math at University of Erlangen. Yes, an unpaid position but not because of her being a female. It was a common occurrence in Germany at this point of history.

Emmy Noether stayed in this uncompensated position for 7 years. During this period, she was also simply referred to as a lecturer; she had no title to her position on staff at university. Her parents had to help her in her economics as she was receiving no pay. Although it was a struggle for them; they felt she had much to offer in the area of mathematics.

Some of the lecturers she had sat under at Gottingen were now at Erlangen. Hilbert and Minkowski were two of the renowned gentleman that she would work with on projects. She spent time working with a known scholar in algebra, Ernst Otto Fischer. This collaboration would aid her in her studies of general Algebra. Fischer took a devoted interest in young Emmy’s ability and understanding of algebra. Emmy Noether once said of Fischer;

Above all I am indebted to Mr E Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work.

In 1915, Emmy Noether left Erlangen and went back to Gottingen. Mathematician David Hilbert had been working with Felix Klein on the general relativity theory of Albert Enstein. Hilbert realized he need various scholars to come and help them with their work. Noether was one of these candidates, and the only one that dealt in invariants and had studied the topic aggressively. Even though her work had been more in line with Paul Gordan; Noether jumped on the opportunity with both feet.

It should be mentioned that many professors from the language and history aspect of the university were livid with the idea of a woman lecturer. They felt that her coming to be a teacher of men was a slap in the face; although the scientific realm of the institution was more accepting of the idea. Because the humanities aspect of the university was more recognized, they appeared to be winning their case. So Emmy Noether ingeniously came up with a plan. He was willing to come as Hilbert’s assistant and any time she spoke it would be as such…thus again no remuneration. However, her father continued to aid in her financials needs.

Emmy Noether soon discovered that the work of assisting David Hilbert was more challenging than she first imagined. Because the work was less concept and more abstract, Noether soon found herself digging into Hilbert’s work on general relativity. She had to look at the problems with a mind towards abstract algebra. Through her continued diligence, Emmy soon came up with answers that Hilbert was looking for.

A note of interest is that whereas Noether had earlier prescribed to Gordan’s direct, or constructive, position of invariants; she found that Hilbert’s approach seemed to make more sense with the subject of relativity.

The problem Hilbert was having was that Relativity Theory did not answer one connect with a particular conservation laws of physics. The issue was that in physics, energy was not a quantity that could be ended or started from nothing. There is the concept that energy can be changed in form, but not totally done away with. Hilbert told Noether that in Relativity, an object losing energy would speed up (gravity waves emission). Conservation stated loss of energy meant the object should be losing speed. “Can you justify the idea?” was his basic question of her.

In General Relativity Theory however, there was a problem: it was possible for an object which lost energy by emitting gravity waves to speed up. An object with less energy should slow down, not speed up! It seemed that the conservation of energy law was being broken. Noether was able to establish that invariants could answer the problem of conservation principles of energy. This would become known as the “Noether Theory”.

Albert Einstein made a special mention of the work of Emmy Noether and her theory that allowed for conservation principles in physics to be coexistent through symmetries. In her, she found that she used mathematics with a deeper insight than many gentlemen of the discipline had been able to grasp. This high praise from the noted scientist did not escape Her attention.

Emmy Noether spent her years at Gottingen during the period of the first world war. Her financial situation did not improve; although her fellow professors like Hilbert continued to push for her position as a fellow full-time member of staff. In her politics she became a social democrat. She may not have been a participating member of the cause; Emmy no less remain convicted about the politics of socialism. She was a confirmed pacifist and deplored any form of armed conflict.

Achievements

Emmy Noether went on after this point of success to change from invariants to other aspects of algebra. Her success in other principles brought attention to her and she was invited to make speaking engagements; Bologna in 1928 and Zurich in 1932. Emmy Noether also received the Alfred Ackermann-Tuebner Memorial Prize for Advancement of Mathematical Knowledge in 1932.

Persecution and Final Years

The Nazi rise in Germany was not to allow Noether’s being Jewish go unnoticed. Even with the German name, she was known as a Jew and as such lost her position at Gottingen. Since she was no longer allowed to teach in any form, Emmy moved to the United States where she was able to find a teaching position at Bryn Mawr College.

In 1935, Emmy Noether was discovered to have a tumor. After what seemed to be a successful operation to remove the tumor; she passed away after the operation due to complications.

Emmy Noether’s work in mathematics was incredible for a woman at the time. To eventually receive the praise of noted men in the field as David Hilbert and Albert Einstein was indeed an accomplishment. Even though the two setbacks of her gender and her religion did not help her in her financial realm; Emmy Noether maintained her dignity and continued to accomplish what many thought she could not do.

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