Emmy Amalie Noether

1882-1935

German-born American Mathematician

In the world of early twentieth-century German mathematics, Emmy Noether had two strikes against her: she was a woman, and she was Jewish. Through perseverance and outstanding contributions to abstract algebra and other disciplines, Noether overcame the barrier posed by the first fact. Ironically, just when it seemed she had gained acceptance, the Nazi takeover of Germany forced her to begin her career again in America.

Noether was born on March 23, 1882, in Erlangen, Germany, the daughter of Max and Ida Kaufmann Noether. Max was a well-known mathematics professor at the University of Erlangen, noted for his work on the theory of algebraic functions. Later, two of Noether's three brothers earned distinction in mathematics and science—Fritz as a mathematician, and Alfred as a chemist.

Such careers seemed blocked to Noether, who could not enroll in the gymnasium, or college preparatory school, simply because girls were not allowed to do so. Instead, she entered a teachers' college for women, and in 1900 passed the Bavarian state teaching examinations. Determined to study at the University of Erlangen, however, Noether received permission to audit classes, and in 1903 was able to take the matriculation exam, which she passed easily.

She even had the opportunity to attend the distinguished University of Göttingen, where she studied under a number of influential figures. Among these was David Hilbert (1862-1943), destined to become a lifelong friend. By 1904, Erlangen had opened its doors to women, so she undertook her doctoral studies under Paul Gordan, a friend of her family. In 1908, she earned her Ph.D. summa cum laude with the dissertation "On Complete Systems of Invariants for Ternary Biquadratic Forms."

On the invitation of Hilbert and Felix Klein (1849-1925), Noether joined them at the Mathematical Institute in Göttingen to work on problems relating to the general theory of relativity. Specifically, Noether was concerned with the problem of invariance under transformation, or laws that remain the same regardless of changes in space and time. This led her to the development of Noether's Theorem, which established the correspondence between an invariance property and a law of conservation. She also formulated a theorem concerning the relationship between invariance, equations of motion, and the existence of certain integrals.

Despite this groundbreaking work, Noether was unable to obtain a permanent, paying job in mathematics; fortunately, family money allowed her to work without pay at Göttingen. Hilbert also helped her immensely, arranging for her to lecture his classes in mathematical physics. After a long struggle in the late 1910s and early 1920s, Noether—a popular and enthusiastic instructor—obtained a position as adjunct teacher.

Because so much of her early career had been devoted to simply gaining the right to participate in mathematics, Noether defied the usual pattern for mathematicians, who typically produce their most important work in their thirties or even their twenties. Beginning with the publication of a paper in 1920, Noether began to delve into an abstract and generalized approach to the axiomatic development of algebra, a method dubbed "epoch-making" by renowned mathematician Hermann Weyl (1885-1955).

Weyl tried but failed to help her gain a better position at Göttingen, yet in 1932 Noether was honored as co-recipient of the Alfred Acker-mann-Teubner Memorial Prize. Also in that year, the algebra faculty at Göttingen held a celebration in honor of her fiftieth birthday, and Helmut Hasse (1898-1979) presented a paper validating one of her concepts of non-communicative algebra.

It seemed that Noether had finally gained acceptance. Then, less than nine months after she turned 50, the Nazis took power. On April 7, 1933, she was officially informed that she could no longer continue teaching in Germany.

Through the help of the Emergency Committee to Aid Displaced German Scholars, as well as a grant from the Rockefeller Foundation, Noether obtained a professorship at Bryn Mawr, a women's college in Pennsylvania. She soon became involved with the Institute for Advanced Study at Princeton, where she delivered weekly lectures. Once again, it seemed that she had begun a new career, but on April 10, 1935, she developed an extremely high fever following surgery to remove a uterine tumor. Losing consciousness, she died four days later.

JUDSON KNIGHT