Emmy Noether

German mathematician

• Born: March 23, 1882; Erlangen, Germany
• Died: April 14, 1935; Bryn Mawr, Pennsylvania

As one of the founders of the study of abstract algebra, German mathematician Emmy Noether formulated Noether’s theorem, an important development in the theory of general relativity that has become fundamental in the study of classical and quantum physics.

Also known as: Amalie Emmy Noether

Primary field: Mathematics

Specialty: Algebra

Early Life

Amalie Emmy Noether was born on March 23, 1882, in Erlangen, Bavaria, Germany. Her parents, Ida Amalia Kaufmann and Max Noether, both came from financially well-off Jewish families. In 1809, when anti-Semitic laws had forced Max’s grandfather to change his surname from Samuel, he had chosen Nöther; Max’s father kept the name but used the form Noether. Emmy Noether would eventually have three younger brothers.

Because there were no college preparatory schools for girls in Germany at the time, Noether spent her high-school years preparing to become a language instructor in a girls’ school. In 1900, at age eighteen, she earned a certification to teach both English and French. She never taught languages, however, but instead decided to audit classes at the University of Erlangen. Women were prohibited from earning college credits or degrees, so she had to ask for permission from individual professors—most of them friends of her father, who was a mathematics professor at the university—to allow her to sit in their classrooms and listen to the lectures. She did this for two years, during which time only one other woman audited classes at the university. Thus Noether began her formal study of mathematics.

In 1903, Noether passed the entrance examination and began studies at the University of Göttingen. She attended lectures by highly respected mathematicians, including David Hilbert, Felix Klein, and Hermann Minkowski. In 1904, however, she returned to the University of Erlangen, which had begun allowing women to earn degrees. Studying under her father’s friend Paul Gordan, Noether completed her thesis and was granted a doctorate in mathematics in 1907, at the age of twenty-five.

Life’s Work

From 1908 until 1915, Noether worked at the University of Erlangen without pay or an official position. She published several papers in mathematical journals during these years, all of which demonstrated the formal style of formula manipulation that she had learned under her thesis adviser, Gordan. She took on more of her father’s duties at the university as his health began to fail.

In 1915, Hilbert and Klein invited Noether to join them at the University of Göttingen. She accepted and stayed there for most of the rest of her career. Noether was beginning to employ more of an abstract approach in her mathematical thinking, a style championed by Hilbert in particular. He and Klein hoped that Noether could help them in their efforts to provide a mathematical framework for parts of Albert Einstein’s general theory of relativity. In fact, she was responsible for several key developments in this area, and her reputation, already beginning to spread, grew quickly in the worldwide mathematical community. Her results, known as Noether’s theorem, are fundamental in physics.

Unfortunately for Noether, her mathematical success did not translate to success in her workplace. A 1908 law prohibited women from being lecturers in German universities. Nevertheless, Hilbert, Klein, and others worked hard to persuade their fellow Göttingen professors to allow Noether to deliver her “habilitation” lecture, part of the process that all professors had to complete in order to be hired at a university in Germany. Her lecture was well attended due to the controversy surrounding her potential appointment. Although the lecture was well received, her application for employment was denied; the government would permit her to lecture only as Hilbert’s assistant, still for no pay. Ultimately, in the 1920s, the government allowed her to be appointed to the faculty, though without a salary. The university managed to provide her with a small stipend.

Throughout the 1920s, Noether continued her work of publishing papers, educating a generally small circle of graduate students, and engaging in dialogue with mathematicians throughout Europe. She became a leader of the movement to employ highly abstract thinking as an approach to discovering the underlying relationships among mathematical objects. The highest validation of her work came in 1932 when she became the first woman invited to address the International Congress of Mathematicians. Her lecture was widely regarded as a great success.

In January of 1933, Adolf Hitler became chancellor of Germany. Not long after, the science ministry published a list of all German professors who were of Jewish ancestry. Noether, who was one of six Göttingen professors on the list, was soon fired. She was so well regarded that even her Aryan students appealed for her reinstatement, but it was not to be. Friends sought positions for her at Oxford University and in Moscow, but when neither of those materialized, she accepted an offer from Bryn Mawr College in the United States. There, she became close friends with the chair of the mathematics department, Anna Pell Wheeler.

Noether’s time at Bryn Mawr was short, however. In April of 1935, less than two years after coming to the United States, she underwent surgery to remove a large ovarian cyst; four days later, on April 14, 1935, she died at the age of fifty-three, probably as a result of a postoperative infection.

Impact

Noether’s great contribution to mathematics was her pioneering use of a highly abstract way of approaching problems. She sought to strip the problem or mathematical object of its particular characteristics and to discover the underlying relationships that governed the behavior of the objects in question. Her 1921 paper “Theory of Ideals and Rings” was essential for the development of abstract algebra in the twentieth century, an area that is one of the most significant in modern mathematics. Even before she died, terms such as Noetherian rings were becoming commonplace in mathematics. Her students spread the influence of her new approach so well that forty years after the appearance of her paper, there was an education revolution in the United States, the so-called new math of the 1960s and 1970s. Even though the initial fad died away, much of her abstract approach remains a central feature of math education.

Bibliography

Dick, Auguste. Emmy Noether, 1882-1935. Trans. H. I. Blocher. Boston: Birkhäuser, 1981. Print. The first biography of Noether and still the source of most of what is known of her life and background.

Kimberling, Clark. “Emmy Noether.” American Mathematical Monthly 79.2 (1972): 136–49. Print. Draws from obituaries and from P. S. Alexandroff’s unpublished 1935 address before the Moscow Mathematical Society to shed light on Noether’s accomplishments. Includes Einstein’s letter to the editor of the New York Times commemorating Noether, reprinted in full.

Kleiner, Israel. A History of Abstract Algebra. Boston: Birkhäuser, 2007. Print. Includes the chapter “Emmy Noether and the Advent of Abstract Algebra” the only one in the book dedicated to the work of a single individual. Also features biographical sketches of Noether and five other mathematicians at the end of the book.

Silverberg, Alice. “Emmy Noether in Erlangen.” Mathematical Intelligencer 23.3 (2001): 44–49. Print. Relates details of Noether’s early life by taking readers on a virtual tour of Erlangen. Includes several photos.