Emmy Noether, c. 1905

Amalie Emmy Noether (March 23, 1882 – April 14, 1935) was a German-born Jewish mathematician who worked in the fields of ring theory and abstract algebra. She is also remembered for Noether's theorem, which explains the connections between symmetry and conservation laws in theoretical physics. She is often described as the most important woman mathematician of all time.^[1][2] From Noethers age, this image appears to have been made in 1900 or 1910, so its definitely public domain. ... From Noethers age, this image appears to have been made in 1900 or 1910, so its definitely public domain. ... is the 82nd day of the year (83rd in leap years) in the Gregorian calendar. ... Year 1882 (MDCCCLXXXII) was a common year starting on Sunday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 12-day slower Julian calendar). ... is the 104th day of the year (105th in leap years) in the Gregorian calendar. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will display full calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... This article or section does not cite its references or sources. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world. ...

Born in the Bavarian town of Erlangen to the noted mathematician Max Noether and his wife, Emmy showed intellectual promise at a young age. Although she passed the examinations required to teach French and English, she continued her studies in mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Albert Gordan, she worked at the Mathematical Institute without pay for seven years. For other uses, see Bavaria (disambiguation). ... Erlangen around 1915 Erlangen is a German city in Middle Franconia. ... Max Noether (September 24, 1844 - December 13, 1921) was a German mathematician. ... The English language is a West Germanic language that originates in England. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Erlangen is a German city in Middle Franconia. ... Paul Albert Gordan (April 27, 1837 – December 21, 1912) was a German mathematician. ...

In 1915 she was invited by David Hilbert and Felix Klein to join mathematics department at the University of Göttingen. The Philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her Habilitation process was approved after that time, paving the way for her to obtain the rank of Privatdozent. She spent the next fourteen years gaining respect for her groundbreaking mathematics work, culminating with a major address at the 1932 International Congress of Mathematicians in Zürich, Switzerland. The following year, Germany's Nazi government fired her from Göttingen, and she moved to the United States, where she took a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of speedy recovery, died four days later. | name = David Hilbert | image = Hilbert1912. ... Felix Christian Klein (April 25, 1849, Düsseldorf, Germany – June 22, 1925, Göttingen) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Habilitation is the highest academic qualification a person can achieve by his/her own pursuit in certain European countries. ... Privatdozent (PD or Priv. ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... For other uses of Zurich, see Zurich (disambiguation). ... National Socialism redirects here. ... Bryn Mawr College (pronounced ) is a highly selective womens liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles northwest of Philadelphia. ... This article is about the U.S. State. ... Benign ovarian cyst. ...

Biography

Noether grew up in the Bavarian city of Erlangen, depicted here in a 1916 postcard.

The Noether family had descended from Jewish wholesale traders in Germany. Emmy's father, Max Noether, was an important mathematician who was largely self-taught. He had been paralyzed by polio at the age of fourteen, and even after regaining mobility was handicapped in one leg. He received a doctorate from the University of Heidelberg in 1868 – the first in his family to do so. After teaching there for seven years, he took a position in the Bavarian city of Erlangen, where he met and married Ida Amalia Kaufmann, the daughter of a prosperous Jewish merchant family.^[3] Image File history File links Download high resolution version (1616x1020, 783 KB) en:University-Street of Erlangen around 1915 de:Universitätsstraße in Erlangen um 1915 Scanned by Flominator File links The following pages link to this file: Erlangen ... Image File history File links Download high resolution version (1616x1020, 783 KB) en:University-Street of Erlangen around 1915 de:Universitätsstraße in Erlangen um 1915 Scanned by Flominator File links The following pages link to this file: Erlangen ... For other uses, see Bavaria (disambiguation). ... Erlangen around 1915 Erlangen is a German city in Middle Franconia. ... For the computer diagnostic tool, see POST card. ... The word Jew ( Hebrew: יהודי) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination of these attributes. ... Max Noether (September 24, 1844 - December 13, 1921) was a German mathematician. ... Autodidacticism (also autodidactism) is self-education or self-directed learning. ... Poliomyelitis (polio), or infantile paralysis, is a viral paralytic disease. ... The Ruprecht Karl University of Heidelberg (German Ruprecht-Karls-Universität Heidelberg; also known as simply University of Heidelberg) was established in the town of Heidelberg in the Rhineland in 1386. ... For other uses, see Bavaria (disambiguation). ... Erlangen around 1915 Erlangen is a German city in Middle Franconia. ...

Emmy Noether was born on 23 March 1882, the first of four children. Her first name was Amalie, after her mother and paternal grandmother, but she began using her middle name at a young age. As a girl, she was well-liked, although she did not stand out academically at school. Near-sighted and talking with a minor lisp, she was known for being clever and friendly. A family friend recounted a story years later about young Emmy quickly solving a brain teaser at a children's party, showing logical acumen at an early age.^[4] Emmy was taught to cook and clean – like most girls of the time – and took lessons on the piano. She pursued none of these activities with passion, although she loved to dance.^[5] is the 82nd day of the year (83rd in leap years) in the Gregorian calendar. ... Year 1882 (MDCCCLXXXII) was a common year starting on Sunday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 12-day slower Julian calendar). ... Normal vision for a achromatopsic colour-blind person. ... For the programming language, see Lisp (programming language). ... A brain teaser is a form of puzzle that involves a lot of thinking (mental/cognitive activity). ... A short grand piano, with the lid up. ...

Of her three brothers, only Fritz Noether is remembered for his academic accomplishments. Alfred, born in 1883, went on to study chemistry and received a doctorate from Erlangen in 1909; he died nine years later. The family's youngest child, Gustav Robert, was born in 1889. Very little is known about his life; he suffered from chronic illness and died in 1928. Fritz, however, made a reputation for himself in the field of applied mathematics after studying in Munich.^[6] Fritz Alexander Ernst Noether (born October 7, 1884 in Erlangen; died [September 10]], 1941 in Orel, Russia) was a German mathematician. ... Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ... For other uses, see Munich (disambiguation). ...

University of Erlangen

Originally interested in languages, Emmy Noether showed an early proficiency in French and English. In the spring of 1900, she took the examination for teachers of these languages and received an overall score of "sehr gut" (very good). Her performance qualified her to teach at girls' schools, but she chose instead to continue her studies at the University of Erlangen. This was an unconventional decision at the time; two years earlier, the Academic Senate of the university had declared that allowing coeducation would "overthrow all academic order".^[7] One of only two females in a school of 986, Noether was forced to audit classes and required permission of individual professors whose lectures she wished to attend. Despite the obstacles, on 14 July 1903 she passed the graduation exam at a Realgymnasium in Nuremberg.^[8] The English language is a West Germanic language that originates in England. ... Erlangen is a German city in Middle Franconia. ... Coeducation is the integrated education of males and females at the same school facilities. ... This article does not cite any references or sources. ... is the 195th day of the year (196th in leap years) in the Gregorian calendar. ... Year 1903 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Wednesday of the 13-day slower Julian calendar. ... Nürnberg redirects here. ...

Paul Albert Gordan supervised Noether's doctoral dissertation on invariants of biquadratic forms.

During the winter of 1903–04, she spent a semester studying as an auditor at the University of Göttingen, attending lectures from astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert. Soon thereafter, the law restricting women's rights in the university was rescinded, and Noether returned to Erlangen. She officially entered the school on 24 October 1904, and declared her intention to focus solely on mathematics. Working under the tutelage of Paul Albert Gordan, in 1907 she wrote her dissertation, Über die Bildung des Formensystems der ternären biquadratischen Form ("On Complete Systems of Invariants for Ternary Biquadratic Forms"). Although it was well received, Noether herself later referred to her thesis as "crap" and "a jungle of formulas".^[9] Paul Albert Gordan (April 27, 1837 – December 21, 1912) was a German mathematician. ... In mathematics, an invariant is something that does not change under a set of transformations. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ... Hermann Minkowski. ... Ludwig Otto Blumenthal (July 20, 1876 - November 12, 1944) was a German mathematician. ... Felix Christian Klein (April 25, 1849, Düsseldorf, Germany – June 22, 1925, Göttingen) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. ... | name = David Hilbert | image = Hilbert1912. ... is the 297th day of the year (298th in leap years) in the Gregorian calendar. ... 1904 (MCMIV) was a leap year starting on a Friday (see link for calendar). ... Paul Albert Gordan (April 27, 1837 – December 21, 1912) was a German mathematician. ...

For the next seven years she worked at the University of Erlangen's Mathematical Institute, without pay. Continuing her research on invariant theory, she occasionally substituted for her father when he was too ill to lecture. She also worked with Erhard Schmidt and Ernst Fischer, sometimes discussing advanced concepts with the latter through commentary on postcards.^[10] In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. ... Erhard Schmidt (January 13, 1876 - December 6, 1959) was a German mathematician born in Dorpat (now Tartu, Estonia). ... Ernst Sigismund Fischer (July 12, 1875 - November 14, 1954) was born in Vienna, Austria. ... For the computer diagnostic tool, see POST card. ...

University of Göttingen

David Hilbert invited Emmy Noether to join the mathematics department at the University of Göttingen in 1915, and defended her mathematical integrity against the gendered objections of his colleagues.

In the spring of 1915 Noether was invited by David Hilbert and Felix Klein to return to the University of Göttingen. Their effort to recruit her was blocked, however, by the philologists and historians in the Philosophical faculty; women, they insisted, should not be hired in the role of Privatdozent. One oppositional colleague 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?" Hilbert responded to this question with indignation: "I do not see that the sex of the candidate is an argument against her admission as Privatdozent," he said. "After all, we are a university, not a bath house."^[11] | name = David Hilbert | image = Hilbert1912. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Philology, etymologically, is the love of words. It is most accurately defined as an affinity toward the learning of the backgrounds as well as the current usages of spoken or written methods of human communication. The commonality of studied languages is more important than their origin or age (that is... For other uses, see Historian (disambiguation). ... Privatdozent (PD or Priv. ... // Public baths originated from a communal need for cleanliness. ...

Two weeks after Noether left for Göttingen, her mother died suddenly in Erlangen. She had previously received medical care for an eye malady, but its nature and impact on her death is unknown. Around the same time, Noether's father retired and her brother joined the army to serve in World War I. She returned to Erlangen for several weeks, mostly to care for her aging father.^[12] “The Great War ” redirects here. ...

During her first years at Göttingen, she worked in an unpaid and undefined role; her lectures were often advertised under Hilbert's name, with Noether providing "assistance". Soon after arriving, however, she demonstrated her value to the department by proving Noether's theorem, which shows that a conservation law can be derived from any differentiable symmetry of a physical system.^[13] US physicists Leon Lederman and Christopher T. Hill, in their book Symmetry and the Beautiful Universe, argue that Noether's theorem is "certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem."^[14] Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... This article is about derivatives and differentiation in mathematical calculus. ... This article or section does not cite its references or sources. ... Leon Max Lederman (born July 15, 1922) is an American experimental physicist who was awarded the Nobel Prize in Physics in 1988 for his work on neutrinos. ... Christopher T. Hill (born 1951, Neenah, Wisconsin) a theoretical physicist at the Fermi National Accelerator Laboratory. ... Look up theorem in Wiktionary, the free dictionary. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ...

When World War I ended, the German Revolution of 1918-19 brought a significant change in social attitudes, including more equal rights for women. In 1919 the University of Göttingen allowed her to proceed with the Habilitation, a process to obtain the rank of Privatdozent. Her oral examination took place in late May, and she successfully delivered her Habilitation lecture in June. Three years later she was made an "unofficial associate professor", which – despite its official title – still did not provide her with a salary. Not until she was appointed to the special position of Lehrauftrag für Algebra a year later was she paid for her lectures.^[15] Habilitation is the highest academic qualification a person can achieve by his/her own pursuit in certain European countries. ...

The mathematics department at the University of Göttingen allowed Noether's Habilitation in 1919, four years after she began lecturing at the school.

In 1920 Noether collaborated with a colleague named W. Schmeidler on a paper about the theory of ideals. Their work was the first to define left and right ideals. One year later she published a landmark paper called Idealtheorie in Ringbereichen, which analyzed ascending chain conditions with regard to ideals. Canadian mathematician Irving Kaplansky called this work "revolutionary",^[16] and its importance is seen in the use of the term "Noetherian ring" to describe a ring which adheres to ascending chain conditions.^[17] Image File history File links Size of this preview: 800 × 354 pixelsFull resolution (3612 × 1600 pixel, file size: 1. ... Image File history File links Size of this preview: 800 × 354 pixelsFull resolution (3612 × 1600 pixel, file size: 1. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Habilitation is the highest academic qualification a person can achieve by his/her own pursuit in certain European countries. ... In mathematics, ideal theory is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra. ... In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. ... In mathematics, a poset P is said to satisfy the ascending chain condition (ACC) if every ascending chain a1 ≤ a2 ≤ ... of elements of P is eventually stationary, that is, there is some positive integer n such that am = an for all m > n. ... Irving Kaplansky (March 22, 1917) is a Canada mathematician. ... In abstract algebra, a Noetherian ring is a ring that satisfies the ascending chain condition on ideals. ... In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. ...

Soon afterwards, she began supervising doctoral students, including Grete Hermann, who later spoke reverently of her "dissertation-mother".^[18] Noether also sponsored the doctoral work of Max Deuring, who distinguished himself as an undergraduate and went on to contribute significantly to the field of arithmetic geometry; Hans Fitting, who established Fitting's theorem as well as the Fitting lemma; and Zeng Jiongzhi, who proved Tsen's theorem. She also worked closely with Wolfgang Krull, originator of Krull's theorem.^[19] Grete Hermann (1901-1984) was a German mathematician and philosopher. ... In mathematics, a Diophantine equation is a polynomial equation that only allows the variables to be integers. ... Hans Fitting (13 November 1906 München-Gladbach (now Mönchengladbach) – 15 June 1938 Königsberg (now Kaliningrad)) was a mathematician who worked in group theory. ... The Fitting lemma, named after the mathematician Hans Fitting, is a basic statement in abstract algebra. ... In mathematics, Tsens theorem states that a function field K of an algebraic curve over an algebraically closed field is quasi-algebraically closed. ... Wolfgang Krull (1899 - 1971) was a German mathematician, after whom Krull dimension, the Krull topology, and Krulls principal ideal theorem are named. ... In mathematics, more specifically in ring theory, Krulls theorem, named after Wolfgang Krull, proves the existence of maximal ideals in any unital commutative ring. ...

Dutch mathematician Bartel Leendert van der Waerden came to the University of Göttingen in 1924. He began working immediately with Noether, who provided invaluable methods of abstract conceptualization. He said later that her originality was "absolute beyond comparison".^[20] In 1931 he published Moderne Algebra, a central text in the field; its second volume borrows heavily from Noether's work. He acknowledged his debt to her in a note for the seventh edition reading "Based in part on lectures by E. Artin and E. Noether".^[21] In other instances she allowed her colleagues and students to receive credit for her ideas, helping them develop their careers rather than demanding tribute.^[22] Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician. ... Emil Artin (March 3, 1898-December 20, 1962) was an Austrian mathematician born in Vienna who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. ...

Van der Waerden's visit was part of an international convergence on Göttingen, which became a central hub of activity among mathematicians worldwide. From 1926 to 1930, Russian topologist Pavel Alexandrov lectured at the university, and quickly became good friends with Noether. He began referring to her as der Noether, a term of endearment signifying his respect for her. She tried to arrange for him to obtain a position at Göttingen as a regular professor, but was only able to help him secure a scholarship from the Rockefeller Foundation.^[23] They met regularly and enjoyed ongoing discussions about the intersections of algebra and topology. In his 1935 memorial address, Alexandrov named her "the greatest woman mathematician of all time".^[24] A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Pavel Sergeevich Alexandrov (Па́вел Серге́евич Алекса́ндров, sometimes romanized Alexandroff or Aleksandrov) (born May 7, 1896 - died November 16, 1982) was a Russian mathematician. ... For the 1983 romantic-drama film, see Terms Of Endearment (movie). ... The Rockefeller Foundation (RF) is a prominent philanthropic organization based at 420 Fifth Avenue, New York City. ...

Moscow

Noether taught at the University of Moscow during the winter of 1928–29.

In the winter of 1928–29, Noether accepted an invitation to the University of Moscow, where she continued working with Alexandrov and his colleagues. In addition to her own research work, she taught classes in abstract algebra and algebraic geometry. She worked with the topologist Lev Pontryagin and N.G. Tschebotaröw, who later praised her contributions to the development of Galois theory.^[25] Moscow State University M.V. Lomonosov Moscow State University (Russian: Московский государственный университет имени Ðœ.Ð’.Ломоносова, often abbreviated МГУ, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: Московский государственный университет имени Ðœ.Ð’.Ломоносова, often abbreviated МГУ, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problematics of geometry. ... Lev Semenovich Pontryagin (Russian: Лев Семёнович Понтрягин) (3 September 1908- 3 May 1988) was a Soviet/Russian mathematician. ... In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. ...

Although politics were not central to her life, Noether took a keen interest in political matters, and according to Alexandrov showed considerable support for the Russian revolution. She was especially happy to see Soviet advancements in the fields of science and mathematics, which she considered indicative of new opportunities made possible by the Bolshevik project. This attitude caused her problems in Germany, culminating in her eviction from a pension building, after student leaders complained of living with "a Marxist-leaning Jewess".^[26] The Russian Revolution (1917) was a series of economic and social upheavals in Russia, involving first the overthrow of the tsarist autocracy, and then the overthrow of the liberal and moderate-socialist Provisional Government, resulting in the establishment of Soviet power under the control of the Bolshevik party. ... Soviet redirects here. ... For other uses, see Bolshevik (disambiguation). ... A pension is a family-owned owned guesthouse. ...

After her time at the University of Moscow, Noether planned to return – an effort for which she received support from Alexandrov. After leaving Germany in 1933, he tried to help her gain a chair at Moscow through the Commissariat of Education. Although this effort was unsuccessful, they corresponded frequently during the 1930s, and in 1935 she made plans for a return to the Soviet Union.^[26] Her brother Fritz, meanwhile, took a position at the Research Institute for Mathematics and Mechanics in Tomsk, Siberia after losing his job in Germany.^[27] Fritz Alexander Ernst Noether (born October 7, 1884 in Erlangen; died [September 10]], 1941 in Orel, Russia) was a German mathematician. ... Flag Seal Location Tomsk and Oblast on the map of Russia Coordinates , Government Oblast Tomsk Mayor Aleksandr Makarov Geographical characteristics Area     City 294,6 km²     Land   294,6 km²     Water   0 km² Population     City (end of 2005) 509,568     Density   1,730/km² Elevation +100 m Website: Municipality website Main... This article is about Siberia as a whole. ...

Personality

Noether was commonly regarded as a generous and caring woman, fiercely dedicated to her fields of study. Although she sometimes acted rudely to 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.^[28] Van der Waerden 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."^[29]

Her frugal lifestyle was at first a necessity of not receiving a salary; even after the university began paying her modestly in 1923, she lived 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.^[30] Mostly unconcerned about appearance and manners, she focused on her studies to the exclusion of romance and fashion. Czech-American mathematician Olga Taussky-Todd described a luncheon wherein Noether, wholly engrossed by a discussion of mathematics, "gesticulated wildly" as she ate and "spilled her food constantly and wiped it off from her dress, completely unperturbed".^[31] Her appearance-conscious students cringed as she retrieved the handkerchief from her blouse and ignored her hair's growing disarray during a lecture. Two female pupils once approached her during a break in a two-hour class to express their concern, but were unable to break through the energetic mathematics discussion she was having with other students.^[32] A bequest is the disposition of property by will. ... Olga Taussky Todd (August 30, 1906, Olomouc, then Austria-Hungary - October 7, 1995, Pasadena, California) was a mathematician. ... Linen handkerchief A handkerchief or hanky is a square of fabric, usually carried in the pocket, for personal hygiene purposes such as wiping ones hands or blowing ones nose, but also used as a decorative accessory in a suit pocket. ...

Her lectures are described as enlightening but intense. She spoke quickly (to reflect the speed of her thoughts, many said), and demanded focused concentration from her students. Some pupils felt that she relied too much on spontaneous discussions; one wrote in a notebook with regard to a class which ended at 1:00 PM: "It's 12:50, thank God!"^[33] Her most dedicated students, however, relished the enthusiasm with which she approached mathematics, especially since her lectures often built upon earlier work they had done together. She developed a close circle of colleagues and students, who thought along similar lines and frequently excluded those who did not. When "outsiders" visited Noether's lectures, it took only thirty minutes for them to leave in frustration or confusion. A regular student at one such instance was heard to remark: "The enemy has been defeated; he has cleared out."^[34] Noether showed a devotion to the subject and her students that went beyond the regular school day. Once when the building was closed for a state holiday, she gathered the class on the steps outside, led them through the woods, and lectured at a local coffee house.^[35]

1932

Noether and the Austrian mathematician Emil Artin were awarded the Ackermann–Teubner Memorial Award in 1932, for their contributions to mathematics. The prize came with a sum of 500 Reichsmarks (about US$120) and was seen as a long-overdue official recognition of her considerable work in the field. Her colleagues have expressed frustration at the fact that she was never elected to the Göttingen Gesellschaft der Wissenschaften (Academy of Sciences) and was never promoted to the position of Ordentlicher Professor.^[36] Emil Artin (March 3, 1898-December 20, 1962) was an Austrian mathematician born in Vienna who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. ... User(s) Germany Subunit 1/100 Reichspfennig Symbol RM Reichspfennig Rpf. ...

Noether visited Zürich in 1932 to deliver a major address at the International Congress of Mathematicians.

1932 was also Noether's fiftieth birthday, and her colleagues celebrated it with a typical mathematical style. Helmut Hasse dedicated an article to her in the Mathematische Annalen, wherein he confirmed her theory about the increased regularity of the laws governing noncommutative algebra compared to those of commutative. He also sent her a mathematical riddle, which she solved with great speed.^[36] Image File history File links Download high resolution version (3456x2304, 1691 KB) Die vier grossen Kirchen in der Altstadt von Zürich: links vorne: Predigerkirche links hinten: Grossmünster mitte: Fraumünster rechts: St. ... Image File history File links Download high resolution version (3456x2304, 1691 KB) Die vier grossen Kirchen in der Altstadt von Zürich: links vorne: Predigerkirche links hinten: Grossmünster mitte: Fraumünster rechts: St. ... For other uses of Zurich, see Zurich (disambiguation). ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... Helmut Hasse (pronounced HAHS uh) (25 August 1898- 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry (Hasse principle), and to local zeta functions. ... The Mathematische Annalen is a German mathematical research journal published by Springer-Verlag. ... In mathematics, there is a close relationship between spaces, which are geometric in nature, and the numerical functions on them. ... In abstract algebra, commutative algebra studies commutative rings, their ideals, and modules over such rings. ...

In September of the same year, Noether delivered a major address (grosse Vorträge) at the International Congress of Mathematicians in Zürich, Switzerland. The conference was attended by 800 people, with 420 official participants. Her talk, on "Hyper-complex systems in their relations to commutative algebra and to number theory", was one of 21 major addresses at the congress. Notable participants of the 1932 ICM included Hermann Weyl, Edmund Landau, and Wolfgang Krull. Because her prominent speaking position was a recognition of her importance to the field of mathematics, the congress is sometimes described as the high point of her career.^[37] The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... For other uses of Zurich, see Zurich (disambiguation). ... Hermann Klaus Hugo Weyl (November 9, 1885 – December 9, 1955) was a German mathematician. ... Edmund Georg Hermann (Yehezkel) Landau (February 14, 1877 – February 19, 1938) was a German Jew mathematician and author of over 250 papers on number theory. ... Wolfgang Krull (1899 - 1971) was a German mathematician, after whom Krull dimension, the Krull topology, and Krulls principal ideal theorem are named. ...

Expulsion

When Adolf Hitler became Chancellor of Germany in January 1933, Nazi activity around the country – including at the University of Göttingen – increased dramatically. The campus German Students Association led the charge against the "un-German Spirit", aided by a Privatdozent named Werner Weber, a former student of Noether. Anti-Semitic attitudes created a climate hostile to Jewish professors; one young protester reportedly demanded: "Aryan students want Aryan mathematics and not Jewish mathematics."^[38] Several of Noether's colleagues, including Max Born and Richard Courant, had their positions revoked.^[39] Hitler redirects here. ... For other uses, see Chancellor (disambiguation). ... National Socialism redirects here. ... The Eternal Jew: 1937 German poster. ... Aryan (/eÉ™rjÉ™n/ or /ɑːrjÉ™n/, Sanskrit: ) is a Sanskrit and Avestan word meaning noble/spiritual one. ... Max Born (December 11, 1882 – January 5, 1970) was a German physicist and mathematician. ... Richard Courant (born January 8, 1888 at Lublinitz, today Poland, died January 27, 1972 at New York/USA) was a German and American mathematician. ...

In April Noether received a notice from the Prussian Ministry for Sciences, Art, and Public Education which read: "On the basis of paragraph 3 of the Civil Service Code of April 7, 1933, I hereby withdraw from you the right to teach at the University of Göttingen."^[39] Noether accepted the decision calmly, providing support for others during the difficult time. Weyl wrote later: "Emmy Noether–her courage, her frankness, her unconcern about her own fate, her conciliatory spirit–was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace."^[38] As usual, Noether remained focused on mathematics, gathering students in her apartment to discuss class field theory. When one of her students appeared in the uniform of the Nazi paramilitary organization Sturmabteilung (SA), she showed no sign of agitation, and reportedly even laughed about it later.^[39] In mathematics, class field theory is a major branch of algebraic number theory. ... The seal of SA The  , abbreviated SA, (German for Storm division or Storm section, usually translated as stormtroop(er)s), functioned as a paramilitary organization of the NSDAP — the German Nazi party. ...

Bryn-Mawr

Bryn Mawr College provided a pleasant home for Noether during the last two years of her life.

As dozens of newly-unemployed professors began searching for positions outside of Germany, their colleagues in the United States worked to provide assistance and opportunities. Einstein and Weyl were welcomed by Princeton University, while others worked to find the sponsor required for legal immigration. Noether was contacted by representatives of two schools, Bryn Mawr College and Oxford University; after a series of negotiations with the Rockefeller Foundation, it was decided that she would take a position at Bryn Mawr starting in the winter of 1933–34.^[40] Bryn Mawr College (pronounced ) is a highly selective womens liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles northwest of Philadelphia. ... Princeton University is a private coeducational research university located in Princeton, New Jersey. ... Bryn Mawr College (pronounced ) is a highly selective womens liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles northwest of Philadelphia. ... The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ... The Rockefeller Foundation (RF) is a prominent philanthropic organization based at 420 Fifth Avenue, New York City. ...

At Bryn Mawr, Noether met and befriended Anna Johnson Pell Wheeler, who had studied at Göttingen just before Noether arrived there. Another source of support at the college was Bryn Mawr President Marion Edwards Park, who enthusiastically invited mathematicians in the area to "see Dr. Noether in action!"^[41] Noether and a small team of students worked quickly through van der Waerden's 1930 book Algebra I and parts of Erich Hecke's Theorie der algebraischen Zahlen (Theory of Algebraic Numbers, 1908).^[42] Erich Hecke (September 20, 1887 – February 13, 1947) was a German mathematician. ...

In 1934 Noether began lecturing at Princeton's Institute for Advanced Study, since – in her words – she was not welcome at the "men's university, where nothing female is admitted".^[43] In addition to Abraham Flexner and Oswald Veblen, who had invited her, she worked with and supervised Abraham Adrian Albert and Harry Vandiver.^[44] Her time in the US was pleasant, surrounded as she was by supportive colleagues and ensconced in her favorite subjects.^[45] In the summer of 1934, she returned to Germany to see Artin and her brother Fritz before he left for Siberia. Although the universities had been cleared of many of her former colleagues, she was able to use the library as a "foreign scholar".^[46] Fuld Hall The Institute for Advanced Study, located in Princeton, New Jersey, United States, is one of the world’s leading centers for theoretical research and intellectual inquiry. ... Abraham Flexner (November 13, 1866-September 21, 1959) was an American educator. ... Oswald Veblen (24 June 1880 - 10 August 1960) was an American mathematician. ... Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was a mathematician of Russian ancestry. ... Harry Schultz Vandiver (21 October 1882-9 January 1973) was an American mathematician, known for work in number theory. ...

Noether's remains are buried under the walkway surrounding the cloisters of Bryn Mawr's M. Carey Thomas Library.

Image File history File linksMetadata Size of this preview: 800 × 600 pixel Image in higher resolution (1984 × 1488 pixel, file size: 1. ... Image File history File linksMetadata Size of this preview: 800 × 600 pixel Image in higher resolution (1984 × 1488 pixel, file size: 1. ... Bryn Mawr College (pronounced ) is a highly selective womens liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles northwest of Philadelphia. ...

Death

In April 1935, doctors discovered a tumor in Noether's pelvis. Because they were worried about complications from surgery, they ordered two days of bed rest first. During the operation, they discovered an ovarian cyst "the size of a large cantaloupe". Two smaller tumors in her uterus appeared to be benign and were not removed, to avoid prolonging the surgery. For three days she appeared to convalesce normally, and recovered quickly from a circulatory collapse on the fourth. On 14 April, she fell unconscious, her temperature soared to 109 °F (40 °C), and she died. "[I]t is not easy to say what had occurred in Dr. Noether," one of the physicians wrote. "It is possible that there was some form of unusual and virulent infection, which struck the base of the brain where the heat centers are supposed to be located."^[47] For malignant tumors specifically, see cancer. ... The pelvis (pl. ... Benign ovarian cyst. ... Trinomial name Cucumis melo cantalupensis Cucumis melo reticulatus Naudin. ... This article is about female reproductive anatomy. ... Look up Benign in Wiktionary, the free dictionary. ... For transport in plants, see Vascular tissue. ... An infection is the detrimental colonization of a host organism by a foreign species. ...

Several days after Noether's death, her friends and associates at Bryn Mawr gathered at President Park's house, where a small memorial service took place. Hermann Weyl and Richard Brauer traveled from Princeton, and spoke with Wheeler and Taussky about their departed colleague. In the months which followed, written tributes began to appear around the globe: Albert Einstein joined van der Waerden, Weyl, and Alexandroff in paying respects. Her body was cremated, and the ashes interred under the walkway around the cloisters of the M. Carey Thomas Library at Bryn Mawr.^[48] Richard Dagobert Brauer (February 10, 1901 - April 17, 1977) was a leading German and American mathematician. ... Bryn Mawr College (pronounced ) is a highly selective womens liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles northwest of Philadelphia. ...

Contributions to mathematics and physics

Noether's contributions to mathematics extended into the fields of theoretical physics and topology. Her interest in and skill with abstract algebra created revolutionary connections between the worlds of physical science and mathematics.^[49] Although she is best known for her pioneering work in ring theory, she was never satisfied with a single area of research, and worked with many different mathematicians in a variety of fields.^[50] Several results in algebraic geometry, such as the Brill–Noether theorem, the Noether–Lefschetz theorem, and several other Noether theorems, are named after her father Max Noether. Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. ... Max Noether (September 24, 1844 - December 13, 1921) was a German mathematician. ...

Physics

In 1915, her first year at Göttingen, Noether proved Noether's theorem,^[51] which has become a fundamental tool of modern theoretical physics. Her theorem states that there is a conserved quantity for every continuous symmetry of the Lagrangian of a physical system. The Lagrangian of a physical system is a function from which the system's behavior can be determined by the principle of least action. For illustration, if a physical system behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved.^[52] The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. As another example, if a physical experiment has the same outcome regardless of place or time (working the same, say, in Cleveland on Tuesday and Samaria on Wednesday), then its Lagrangian is symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively. Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world. ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... The principle of least action was first formulated by Pierre-Louis Moreau de Maupertuis, who said that Nature is thrifty in all its actions. See action (physics). ... This gyroscope remains upright while spinning due to its angular momentum. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... This article is about momentum in physics. ...

Noether's theorem is profoundly important, both because of the insight it gives into conservation laws, but also as a practical calculation tool. It allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it allows researchers to consider whole classes of hypothetical Lagrangians to describe a physical system. For illustration, suppose that a new field is discovered that conserves a quantity X. Using Noether's theorem, the types of Lagrangians that conserve X because of a continuous symmetry can be determined, and then their fitness judged by other criteria. The converse of Noether's theorem is not always true; not every conservation law corresponds to a continuous symmetry.^[52]

Algebra

Noether sometimes used postcards to discuss abstract algebra with her colleague Ernst Sigismund Fischer. This card was postmarked 10 April 1915.

First and foremost, Noether is remembered as an algebraist. She showed an acute propensity for abstract thought, which allowed her to approach problems of mathematics in fresh and original ways.^[53] Her friend and colleague Hermann Weyl described her scholarly output in three epochs. The first, from 1908 to 1919, began with her dissertation on invariants, supervised and heavily influenced by Paul Albert Gordan. The first epoch also included her work with David Hilbert and Ernst Sigismund Fischer. The second epoch, 1920–1926, was more abstract, examining what was then called the "general theory of ideals" (now ring theory).^[54] The third epoch, in the eight years before her death, focused on noncommutative algebra, linear transformations, and commutative number fields.^[55] For the computer diagnostic tool, see Postcard (computing). ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... Ernst Sigismund Fischer (July 12, 1875 - November 14, 1954) was born in Vienna, Austria. ... An example of a postmark A postmark is a postal marking made on a letter, package, postcard or the like indicating the (more or less precise) date and time that the item was delivered into the care of the postal service. ... is the 100th day of the year (101st in leap years) in the Gregorian calendar. ... Year 1915 (MCMXV) was a common year starting on Friday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Thursday[1] of the 13-day-slower Julian calendar). ... Hermann Klaus Hugo Weyl (November 9, 1885 – December 9, 1955) was a German mathematician. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... Paul Albert Gordan (April 27, 1837 – December 21, 1912) was a German mathematician. ... | name = David Hilbert | image = Hilbert1912. ... Ernst Sigismund Fischer (July 12, 1875 - November 14, 1954) was born in Vienna, Austria. ... In mathematics, there is a close relationship between spaces, which are geometric in nature, and the numerical functions on them. ... In mathematics, a linear map (also called a linear transformation or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. ...

Historical context

In the century from 1832 to Noether's death in 1935, the field of mathematics – specifically algebra – underwent a profound revolution, whose reverberations are still being felt.^[56] Mathematicians of previous centuries had worked on practical methods for solving specific types of equations, e.g., cubic, quartic and quintic equations, and on the related problem of constructing regular polygons using compass and straightedge. Beginning with Évariste Galois' theory of groups in 1832 and William Rowan Hamilton's discovery of quaternions in 1843, however, research turned to determining the properties of ever-more-abstract systems defined by ever-more-primitive rules. Much work on hypercomplex numbers and the representations of groups was carried out in the 19th and early 20th centuries; but this disparate work was united by Noether, who gave the first general representation theory of groups and algebras.^[57] Briefly, Noether subsumed the structure theory of abstract algebras and the representation theory of groups into a single arithmetic theory of modules and ideals in rings that satisfy certain finiteness conditions. This single work had a profound impact on the development of modern algebra.^[56] This article is about the branch of mathematics. ... Polynomial of degree 3 In mathematics, a cubic function is a function of the form where b is nonzero; or in other words, a polynomial of degree three. ... In mathematics, a quartic equation is the result of setting a quartic function equal to zero. ... Graph of a polynomial of degree 5, with 4 critical points. ... In mathematics, the nth roots of unity, or de Moivre numbers, are all the complex numbers which yield 1 when raised to a given power n. ... A regular pentagon A regular polygon is a simple polygon (a polygon which does not intersect itself anywhere) which is equiangular (all angles are equal) and equilateral (all sides have the same length). ... Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ... Galois at the age of fifteen from the pencil of a classmate. ... This picture illustrates how the hours on a clock form a group under modular addition. ... For other persons named William Hamilton, see William Hamilton (disambiguation). ... Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = -k, ij = -ji This page describes the mathematical entity. ... The term hypercomplex number has been used in mathematics for the elements of algebras that extend or go beyond complex number arithmetic. ... Group representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... Universal algebra (sometimes called General algebra) is the field of mathematics that studies the ideas common to all algebraic structures. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, where instead of requiring the scalars to lie in a field, the scalars may lie in an arbitrary ring. ... In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. ... In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. ...

Commutative rings, ideals and modules

Her 1921 paper Idealtheorie in Ringbereichen,^[58] is the foundation of general commutative ring theory, and gives the first general definition of a commutative ring. Before this paper, most results in commutative algebra were restricted to special examples of commutative rings, such as polynomial rings over fields or rings of algebraic integers. Noether proved that in a ring which satisfies the ascending chain condition on ideals, every ideal is finitely generated. In 1943, French mathematician Claude Chevalley coined the term "Noetherian ring" to describe this property.^[59] A Noetherian module is a module that satisfies the ascending chain condition on submodules, where the submodules are partially ordered by inclusion. (A Noetherian topological space is one that satisfies a similar ascending cha