Emmy Noether - Wikipedia, the free encyclopedia

Emmy Noether - Wikipedia, the free encyclopedia: Emmy Noether (German: [ˈnøːtɐ]; official name Amalie Emmy Noether;[1] 23 March 1882 – 14 April 1935) was an influential German mathematician known for her contributions to abstract algebra and theoretical physics. Described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics.[2][3] As one of the leading mathematicians of her time, she developed the theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.[4]

Noether was born to a Jewish family in the Franconian town of Erlangen; her father was mathematician Max Noether. She originally planned to teach French and English after passing the required examinations, but instead studied mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Gordan, she worked at the Mathematical Institute of Erlangen without pay for seven years. (At the time, women were largely excluded from academic positions.) In 1915, she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.

Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the "Noether boys". In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the leading expositor of Noether's ideas: her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra. By the time of her plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen was recognized around the world. The following year, Germany's Nazi government dismissed Jews from university positions, and Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of a recovery, died four days later at the age of 53.

Emmy Noether was born on 23 March 1882, the first of four children.   As a girl, Noether was well liked. She did not stand out academically although she was known for being clever and friendly. She was near-sighted and talked with a minor lisp during childhood.

In the spring of 1915, Noether was invited to return to the University of Göttingen by David Hilbert and Felix Klein. Their effort to recruit her, however, was blocked by the philologists and historians among the philosophical faculty: women, they insisted, should not become privatdozent. One faculty member protested: "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?"^{[26][27][28][29]} Hilbert responded with indignation, stating, "I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house."

Although Noether's theorem had a profound effect upon physics, among mathematicians she is best remembered for her seminal contributions to abstract algebra. As Nathan Jacobson says in his Introduction to Noether's Collected Papers,

The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her – in published papers, in lectures, and in personal influence on her contemporaries.

Noether's groundbreaking work in algebra began in 1920. In collaboration with W. Schmeidler, she then published a paper about the theory of ideals in which they defined left and right ideals in a ring. The following year she published a landmark paper called Idealtheorie in Ringbereichen, analyzing ascending chain conditions with regard to (mathematical) ideals. Noted algebraist Irving Kaplansky called this work "revolutionary";^[35] the publication gave rise to the term "Noetherian ring" and the naming of several other mathematical objects as Noetherian.

In 1924 a young Dutch mathematician, B. L. van der Waerden, arrived at the University of Göttingen. He immediately began working with Noether, who provided invaluable methods of abstract conceptualization. Van der Waerden later said that her originality was "absolute beyond comparison".^[38] In 1931 he published Moderne Algebra, a central text in the field; its second volume borrowed heavily from Noether's work. Although Noether did not seek recognition, he included as a note in the seventh edition "based in part on lectures by E. Artin and E. Noether".^[39][40][41] She sometimes allowed her colleagues and students to receive credit for her ideas, helping them develop their careers at the expense of her own.

In addition to her mathematical insight, Noether was respected for her consideration of others. Although she sometimes acted rudely toward those who disagreed with her, she nevertheless gained a reputation for constant helpfulness and patient guidance of new students. Her loyalty to mathematical precision caused one colleague to name her "a severe critic", but she combined this demand for accuracy with a nurturing attitude.^[48] A colleague later described her this way: "Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all."

Her frugal lifestyle at first was due to being denied pay for her work; however, even after the university began paying her a small salary in 1923, she continued to live a simple and modest life. She was paid more generously later in her life, but saved half of her salary to bequeath to her nephew, Gottfried E. Noether.

Noether spoke quickly—reflecting the speed of her thoughts, many said—and demanded great concentration from her students. Students who disliked her style often felt alienated.^[54][55] Some pupils felt that she relied too much on spontaneous discussions. Her most dedicated students, however, relished the enthusiasm with which she approached mathematics, especially since her lectures often built on earlier work they had done together.

She developed a close circle of colleagues and students who thought along similar lines and tended to exclude those who did not. "Outsiders" who occasionally visited Noether's lectures usually spent only 30 minutes in the room before leaving in frustration or confusion.

Theorems of abstract algebra are powerful because they are general; they govern many systems. It might be imagined that little could be concluded about objects defined with so few properties, but precisely therein lay Noether's gift: to discover the maximum that could be concluded from a given set of properties, or conversely, to identify the minimum set, the essential properties responsible for a particular observation. Unlike most mathematicians, she did not make abstractions by generalizing from known examples; rather, she worked directly with the abstractions. As van der Waerden recalled in his obituary of her,

The maxim by which Emmy Noether was guided throughout her work might be formulated as follows: "Any relationships between numbers, functions, and operations become transparent, generally applicable, and fully productive only after they have been isolated from their particular objects and been formulated as universally valid concepts."

This is the begriffliche Mathematik (purely conceptual mathematics) that was characteristic of Noether. This style of mathematics was consequently adopted by other mathematicians, especially in the (then new) field of abstract algebra.