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Emmy Noether

Ch. 1 of 8
— CH. 1 · THE WOMAN WHO WAS NOT A BATHHOUSE —

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Emmy Noether

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  • In a joint faculty meeting at the University of Göttingen, one professor protested aloud: "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?" The mathematician David Hilbert answered with indignation. His exact words have not been preserved, but he is often said to have remarked that the university was "not a bathhouse." The woman whose appointment caused this quarrel was Emmy Noether, a German mathematician born to a Jewish family in 1882. Albert Einstein, Pavel Alexandrov, Jean Dieudonné, Hermann Weyl, and Norbert Wiener would later call her the most important woman in the history of mathematics. Yet for much of her career she taught without pay, lectured under a man's name, and was barred from holding a regular professorship. How does someone excluded from the academy reshape its deepest ideas? Why did a result she proved in physics get compared to the Pythagorean theorem? And what happened to her when a new government in Germany decided that her ancestry made her unwelcome?

  • In early 1900, Emmy Noether passed an examination to teach French and English and earned the overall score of sehr gut, meaning very good. That result qualified her to teach languages at schools reserved for girls. She chose instead to study mathematics at the University of Erlangen-Nuremberg, where her father, Max Noether, was a professor. Two years earlier the university's Academic Senate had declared that mixed-sex education would "overthrow all academic order." Noether was one of just two women among 986 students, allowed only to audit classes and needing each professor's permission to attend. In 1903, restrictions on women's enrollment in Bavarian universities were lifted, and she officially reentered the university in October 1904. Under the supervision of Paul Gordan, known as the "king of invariant theory," she completed her doctoral dissertation in 1907 and graduated summa cum laude. Her thesis ended with a list of over 300 explicitly worked-out invariants. She later dismissed that early work, and similar papers, as "crap." All of her later work would be in a completely different field, one that would carry her name.

  • From 1908 to 1915, Noether taught at Erlangen's Mathematical Institute without a salary, sometimes substituting for her father when illness kept him from lecturing. She joined the Circolo Matematico di Palermo in 1908 and the Deutsche Mathematiker-Vereinigung in 1909. When Gordan retired in 1910, she taught under his successors, and one of them, Ernst Fischer, introduced her to the work of David Hilbert. Noether and Fischer found such lively enjoyment in mathematics that they discussed lectures long after they ended. She is known to have mailed Fischer postcards carrying her train of mathematical thought further. At Göttingen, after her invitation there in 1915, she again worked without an official position and without pay. Her lectures were advertised under Hilbert's name, with Noether listed only as providing "assistance." Even after a small salary arrived in 1923, she lived simply and saved half of it to bequeath to her nephew, Gottfried E. Noether.

  • On the 26th of July 1918, Felix Klein presented a paper titled Invariante Variationsprobleme to the Royal Society of Sciences at Göttingen. Its author, Emmy Noether, did not present it herself, because she was not a member of the society. Hilbert and Klein had brought her to Göttingen in 1915 precisely because they needed her command of invariant theory to help them understand Albert Einstein's general relativity. Hilbert had noticed that conservation of energy seemed to be violated in the theory, since gravitational energy could itself gravitate. Noether's paper resolved that paradox and gave physics a fundamental tool. Her result, now called Noether's theorem, shows that a conservation law is tied to any continuous symmetry of a physical system. If physical laws behave the same regardless of orientation in space, the theorem shows angular momentum must be conserved. A jagged asteroid tumbling through space conserves angular momentum despite its asymmetry, because the symmetry lies in the laws, not the object. Einstein wrote to Hilbert after reading her work: "The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff." The American physicists Leon M. Lederman and Christopher T. Hill have called the theorem possibly on a par with the Pythagorean theorem.

  • In 1921, Noether published Idealtheorie in Ringbereichen, or Theory of Ideals in Ring Domains, a paper the algebraist Irving Kaplansky called "revolutionary." In it she proved that in a ring satisfying the ascending chain condition on ideals, every ideal is finitely generated. The condition became so central that objects satisfying it are called Noetherian in her honor, a term coined by Claude Chevalley in 1943. The same paper established the Lasker-Noether theorem, which can be seen as a generalization of the fundamental theorem of arithmetic, the statement that any positive integer factors uniquely into primes. Her 1927 work characterized the rings now known as Dedekind domains through five conditions and introduced what are now called the isomorphism theorems. Nathan Jacobson wrote that abstract algebra is "largely due to her." Unlike most mathematicians, she did not generalize from known examples but worked directly with the abstractions. Van der Waerden recorded her guiding maxim: relationships between numbers, functions, and operations become "fully productive only after they have been isolated from their particular objects and been formulated as universally valid concepts." She called this begriffliche Mathematik, purely conceptual mathematics.

  • In Göttingen, Noether's students were sometimes called the "Noether Boys," and she supervised more than a dozen doctoral students, though most were registered formally with Edmund Landau because she was not permitted to supervise dissertations on her own. Her first, Grete Hermann, defended in February 1925 and later spoke reverently of her "dissertation-mother." In 1924 the Dutch mathematician Bartel Leendert van der Waerden arrived and soon became the leading expositor of her ideas. The second volume of his 1931 textbook Moderne Algebra borrowed heavily from her work, and he later said her originality was "absolute beyond comparison." Her devotion ran past the academic day. Once, when the building was closed for a state holiday, she gathered her class on the steps, led them through the woods, and lectured at a local coffee house. She did not follow a lesson plan, spoke quickly, and was hard to follow. Outsiders who visited often left within half an hour, and one regular student joked of such a departure: "The enemy has been defeated; he has cleared out." Olga Taussky-Todd recalled a luncheon where Noether, lost in mathematics, "gesticulated wildly" and spilled food on her dress, "completely unperturbed."

  • In 1932, Noether and Emil Artin shared the Ackermann-Teubner Memorial Award, seen as a long-overdue recognition of her work. That September she delivered a plenary address at the International Congress of Mathematicians in Zürich, an event attended by 800 people with only twenty-one plenary addresses given. The 1932 congress is sometimes described as the high point of her career. Yet her colleagues remained frustrated that she was never elected to the Göttingen academy of sciences and never promoted to full professor. When Adolf Hitler became Reichskanzler in January 1933, the attack came quickly. One young protester reportedly demanded: "Aryan students want Aryan mathematics and not Jewish mathematics." In April 1933 Noether received a notice withdrawing her right to teach, citing the Civil Service Code of the 7th of April 1933. She accepted the decision calmly. Hermann Weyl later wrote that she was "in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace." When a student appeared at her apartment in the uniform of the Sturmabteilung, she showed no agitation and reportedly laughed about it afterward.

  • After negotiations with the Rockefeller Foundation, a grant brought Noether to Bryn Mawr College in Pennsylvania, where she began in late 1933. There she gathered a group sometimes called the Noether girls, among them Grace Shover Quinn, Marie Johanna Weiss, Olga Taussky-Todd, and her only American doctoral student, Ruth Stauffer. In 1934 she also began lecturing at the Institute for Advanced Study in Princeton, though she remarked of nearby Princeton University that she was unwelcome at "the men's university, where nothing female is admitted." In April 1935 doctors found a tumor in her pelvis and discovered during surgery an ovarian cyst "the size of a large cantaloupe." For three days she seemed to recover normally. On the 14th of April she fell unconscious, her temperature soared to 109 degrees Fahrenheit, and she died. She was 53. Her body was cremated and the ashes interred under the walkway around the cloisters of the Old Library at Bryn Mawr. In a letter to a newspaper, Einstein called her the most significant creative mathematical genius produced since the higher education of women began. The historian Jeremy Gray put her legacy plainly: "Mathematicians simply do ring theory her way."

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20th-century German physicistsAcademic staff of the University of GöttingenEmigrants from Nazi Germany to the United StatesInstitute for Advanced Study visiting scholarsJewish emigrants from Nazi Germany to the United States

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Common questions

Who was Emmy Noether and why is she important?

Emmy Noether was a German mathematician, born on the 23rd of March 1882, who made fundamental contributions to abstract algebra and developed theories of rings, fields, and algebras. She also proved Noether's theorem, which connects symmetry and conservation laws in physics. Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener described her as the most important woman in the history of mathematics.

What is Noether's theorem in physics?

Noether's theorem shows that a conservation law is associated with any continuous, differentiable symmetry of a physical system. For example, if physical laws behave the same regardless of orientation in space, the theorem shows angular momentum must be conserved. Felix Klein presented the paper, Invariante Variationsprobleme, on the 26th of July 1918, and physicists Leon M. Lederman and Christopher T. Hill have called the theorem possibly on a par with the Pythagorean theorem.

Why did Emmy Noether work without pay at Göttingen?

When David Hilbert and Felix Klein invited Noether to the University of Göttingen in 1915, the philosophical faculty objected to a woman becoming a privatdozent. She had no official position and lectured under Hilbert's name for four years until her habilitation was approved in 1919. The university began paying her only a small salary in 1923.

What did Emmy Noether contribute to abstract algebra?

Noether developed the theory of ideals in commutative rings, and in her 1921 paper Idealtheorie in Ringbereichen she proved that every ideal in a ring satisfying the ascending chain condition is finitely generated. Objects satisfying the ascending chain condition are called Noetherian in her honor. Nathan Jacobson wrote that the development of abstract algebra is largely due to her.

Why did Emmy Noether leave Germany for the United States?

In April 1933, Germany's Nazi government withdrew Noether's right to teach at Göttingen under the Law for the Restoration of the Professional Civil Service, which removed Jews from university positions. After negotiations with the Rockefeller Foundation, she took a position at Bryn Mawr College in Pennsylvania starting in late 1933, and also lectured at the Institute for Advanced Study in Princeton.

How did Emmy Noether die?

Emmy Noether died on the 14th of April 1935 at the age of 53. In April 1935 doctors discovered a tumor in her pelvis and an ovarian cyst during surgery. She appeared to recover for three days, then fell unconscious as her temperature soared to 109 degrees Fahrenheit. Her ashes were interred under the walkway around the cloisters of the Old Library at Bryn Mawr.

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114 references cited across the entry

  1. 1Emmy Noether (1882–1935) – LebensläufeCordula Tollmien
  2. 2Lee Smolin on 'Special Relativity: Why Cant You Go Faster Than Light?' by W. Daniel Hillis; Hillis RespondsLee Smolin — Edge Foundation, Inc. — 21 March 1999
  3. 3The Impact of Emmy Noether's Theorems on XXIst Century PhysicsYuval Ne'eman
  4. 4In her short life, mathematician Emmy Noether changed the face of physicsEmily Conover — 12 June 2018
  5. 5NewsThe Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-MathematicianAlbert Einstein — 1 May 1935
  6. 7Emmy Noether's Contributions to the Theory of AlgebrasWinfried Scharlau
  7. 8Emmy Noether at the Institute for Advanced StudyArcGIS — 7 December 2019
  8. 9JournalThis Month in Physics History: March 23, 1882: Birth of Emmy NoetherAmerican Physical Society — March 2013
  9. 10Rowe, Koreuber (2020) p. 27–30Rowe, Koreuber — 2020
  10. 11The fundamental theorems of invariant theory classical, quantum and superGus Lehrer — University of Sydney — January 2015
  11. 12Emmy Noether's beautiful theoremPeter Lynch — 18 June 2015
  12. 13BookThe Philosophy and Physics of Noether's TheoremsJohn C. Baez — Cambridge University Press — 2022
  13. 14Noetherian inductionAndreas Klappenecker — Texas A&M University — Fall 2008
  14. 15Emmy Noether and TopologyFriedrich Hirzebruch
  15. 16Emmy-Noether Campus (ENC)University of Siegen
  16. 17Emmy Noether revolutionized mathematics — and still faced sexism all her lifeBrad Plumer — 23 March 2016
  17. 18Magazine100 Women of the YearMarch 5, 2020
  18. 19BookEmmy Noether: A Tribute to Her Life and WorkPavel S. Alexandrov — Marcel Dekker — 1981
  19. 20BookIntroduction to Commutative AlgebraMichael Atiyah et al. — Addison-Wesley and Avalon Publishing — 1994
  20. 21E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation LawsNina Byers — Bar-Ilan University — December 1996
  21. 22BookOut of the Shadows: Contributions of 20th Century Women to PhysicsNina Byers — Cambridge University Press — 2006
  22. 23BookIdeals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative AlgebraDavid A. Cox et al. — Springer — 2015
  23. 24JournalZur arithmetischen Theorie der algebraischen FunktionenMax Deuring — 1932
  24. 25BookEmmy Noether: 1882–1935Birkhäuser — 1981
  25. 26JournalChiungtze C. Tsen (1898–1940) and Tsen's theoremsShisun Ding et al. — 1999
  26. 27JournalInvariant theory, old and newJean A. Dieudonné et al. — 1970
  27. 28JournalUntersuchungen über einen verallgemeinerten GruppenbegriffWilhelm Dörnte — 1929
  28. 29ThesisVerzweigungen von Lösungen nichtlinearer DifferentialgleichungenHans Falckenberg — 1912
  29. 30JournalDie Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nicht kommutativen GruppenHans Fitting — 1933
  30. 31JournalThe Noether bound in invariant theory of finite groupsPeter Fleischmann — 2000
  31. 32JournalOn Noether's bound for polynomial invariants of a finite groupJohn Fogarty — 2001
  32. 33BookEmmy Noether: A Tribute to Her Life and WorkRobert Gilmer — Marcel Dekker — 1981
  33. 34BookIntroduction to Boolean AlgebrasSteven Givant et al. — Springer — 2009
  34. 35BookAn Introduction to Noncommutative Noetherian RingsKen R. Goodearl et al. — Cambridge University Press — 2004
  35. 36JournalDie simultanen Systeme binärer FormenPaul Gordan — 1870
  36. 37BookThe Princeton Companion to MathematicsPrinceton University Press — 2008
  37. 38BookA History of Abstract AlgebraJeremy Gray — Springer — 2018
  38. 39JournalBeziehungen zwischen den Idealen verschiedener RingeHeinrich Grell — 1927
  39. 40JournalReductive groups are geometrically reductiveWilliam J. Haboush — 1975
  40. 41JournalDie Struktur der R. Brauerschen Algebrenklassengruppe über einem algebraischen ZahlkörperHelmut Hasse — 1933
  41. 42BookAlgebraic GeometryRobin Hartshorne — Springer-Verlag — 1977
  42. 43JournalDie Frage der endlich vielen Schritte in der Theorie der Polynomideale. (Unter Benutzung nachgelassener Sätze von K. Hentzelt)Grete Hermann — 1926
  43. 44JournalUeber die Theorie der algebraischen FormenDavid Hilbert — December 1890
  44. 45JournalA Brief, Subjective History of Homology and Homotopy Theory in this CenturyPeter Hilton — 1988
  45. 46JournalZur Theorie der primären RingeRudolf Hölzer — 1927
  46. 47JournalEine Verallgemeinerung der Euler-Poincaréschen FormelHeinz Hopf — 1928
  47. 48BookDifferential Equations: A Dynamical Systems Approach. Part II: Higher-Dimensional SystemsJohn H. Hubbard et al. — Springer — 1991
  48. 49BookRemarkable Mathematicians from Euler to von NeumannIoan James — Cambridge University Press — 2002
  49. 50BookEmmy Noether: A Tribute to Her Life and WorkClark Kimberling — Marcel Dekker — 1981
  50. 51JournalEmmy Noether, Greatest Woman MathematicianClark Kimberling — National Council of Teachers of Mathematics — March 1982
  51. 52BookThe Noether Theorems: Invariance and Conservation Laws in the Twentieth CenturyYvette Kosmann-Schwarzbach — Springer — 2011
  52. 53BookEmmy Noether: A Tribute to Her Life and WorkTsit Yuen Lam — Marcel Dekker — 1981
  53. 54BookAlgebraSerge Lang — Springer-Verlag — 2002
  54. 55BookUndergraduate AlgebraSerge Lang — Springer-Verlag — 2005
  55. 56BookSymmetry and the Beautiful UniverseLeon M. Lederman et al. — Prometheus Books — 2004
  56. 57JournalÜber vollständig reduzible Ringe und UnterringeJakob Levitzki — 1931
  57. 58BookEmmy Noether: A Tribute to Her Life and WorkSaunders Mac Lane — Marcel Dekker — 1981
  58. 59Inverse Galois theoryGunter Malle et al. — Springer-Verlag — 1999
  59. 60BookEmmy Noether in Bryn Mawr: Proceedings of a Symposium Sponsored by the Association for Women in Mathematics in Honor of Emmy Noether's 100th BirthdayUta C. Merzbach — Springer — 1983
  60. 61JournalPoor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic PartyColin McLarty — 2005
  61. 62BookWomen of MathematicsGottfried E. Noether — Greenwood Press — 1987
  62. 63JournalPaul GordanMax Noether — 1914
  63. 64BookThe Biographical Dictionary of Women in Science: Pioneering Lives from Ancient Times to the Mid-Twentieth CenturyMarilyn Ogilvie et al. — Routledge — 2000
  64. 65JournalNoether Lasker Primary Decomposition RevisitedBarbara L. Osofsky — 1994
  65. 66BookQuantum Theory: Concepts and MethodsAsher Peres — Kluwer — 1993
  66. 67BookHilbertConstance Reid — Springer — 1996
  67. 68BookThe Brauer–Hasse–Noether theorem in historical perspectivePeter Roquette — 2005
  68. 69BookEmmy Noether – Mathematician ExtraordinaireSpringer — 2021
  69. 70BookProving It Her Way: Emmy Noether, a Life in MathematicsSpringer — 2020
  70. 71BookDictionary of Minor Planet NamesLutz D. Schmadel — Springer-Verlag — 2003
  71. 72BookVorlesungen über InvariantentheorieIssai Schur — Springer-Verlag — 1968
  72. 73BookMathematicians Under the NazisSanford L. Segal — Princeton University Press — 2003
  73. 74JournalDie Gesamtheit der kubischen und biquadratischen Gleichungen mit Affekt bei beliebigem RationalitätsbereichFritz Seidelmann — 1917
  74. 75JournalÜber gewisse Beziehungen zwischen der Arithmetik hyperkomplexer Zahlsysteme und algebraischer ZahlkörperOtto Schilling — 1935
  75. 76JournalThe Construction of a Normal Basis in a Separable Normal Extension FieldRuth Stauffer — July 1936
  76. 77BookGalois TheoryIan Stewart — CRC Press — 2015
  77. 78JournalInvariant rational functions and a problem of SteenrodRichard G Swan — 1969
  78. 79BookEmmy Noether: A Tribute to Her Life and WorkOlga Taussky — Marcel Dekker — 1981
  79. 80BookClassical MechanicsJohn R. Taylor — University Science Books — 2005
  80. 81The Heritage of Emmy NoetherBar-Ilan University, American Mathematical Society, Oxford University Press — 1999
  81. 82JournalDivisionsalgebren über FunktionenkörpernChiungtze C. Tsen — 1933
  82. 83JournalNachruf auf Emmy NoetherB. L. van der Waerden — 1935
  83. 84BookA History of Algebra: from al-Khwārizmī to Emmy NoetherB. L. van der Waerden — Springer-Verlag — 1985
  84. 85JournalIdealtheoretische Deutung der Darstellbarkeit beliebiger natürlicher Zahlen durch quadratische FormenWerner Weber — December 1930
  85. 86Emmy NoetherHermann Weyl — 1935
  86. 87David Hilbert and his mathematical workHermann Weyl — 1944
  87. 88JournalAnwendungen der p-adischen Theorie im NichtkommutativenWolfgang Wichmann — 1936
  88. 89JournalRiemann-Rochscher Satz und Z-Funktion im HyperkomplexenErnst Witt — 1935
  89. 90BookGroup Theory in a Nutshell for PhysicistsAnthony Zee — Princeton University Press — 2016
  90. 91Über die Bildung des Formensystems der ternären biquadratischen FormEmmy Noether — 1908
  91. 92Rationale FunktionenkörperEmmy Noether — 1913
  92. 93Der Endlichkeitssatz der Invarianten endlicher GruppenEmmy Noether — 1915
  93. 94Gleichungen mit vorgeschriebener GruppeEmmy Noether — 1918
  94. 95JournalInvariante VariationsproblemeEmmy Noether — 1918b
  95. 96JournalInvariante VariationsproblemeEmmy Noether — 1918c
  96. 97Idealtheorie in RingbereichenEmmy Noether — 1921
  97. 98Zur Theorie der Polynomideale und ResultantenEmmy Noether — 1923
  98. 99Eliminationstheorie und allgemeine IdealtheorieEmmy Noether — 1923b
  99. 100Eliminationstheorie und IdealtheorieEmmy Noether — 1924
  100. 101Der Endlichkeitsatz der Invarianten endlicher linearer Gruppen der Charakteristik pEmmy Noether — 1926
  101. 102Ableitung der Elementarteilertheorie aus der GruppentheorieEmmy Noether — 1926b
  102. 103Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und FunktionenkörpernEmmy Noether — 1927
  103. 104Über minimale Zerfällungskörper irreduzibler DarstellungenRichard Brauer et al. — 1927
  104. 105Hyperkomplexe Größen und DarstellungstheorieEmmy Noether — 1929
  105. 106Beweis eines Hauptsatzes in der Theorie der AlgebrenRichard Brauer et al. — 1932
  106. 107Nichtkommutative AlgebrenEmmy Noether — 1933
  107. 108Gesammelte AbhandlungenEmmy Noether — Springer-Verlag — 1983
  108. 109BookEinstein's Tutor: The Story of Emmy Noether and the Invention of Modern PhysicsLee Phillips — PublicAffairs — 2024
  109. 110BookHelmut Hasse und Emmy Noether – Die Korrespondenz 1925–1935Helmut Hasse et al. — Göttingen University — 2006
  110. 111NewsThe Mighty Mathematician You've Never Heard OfNatalie Angier — 26 March 2012
  111. 112Galois Theory and Noether's ProblemMeredith Blue — MAA Florida Section — 2001
  112. 113The female mathematician who changed the course of physicsbut couldn't get a jobLee Phillips — Condé Nast — 26 May 2015
  113. 114JournalSpecial Issue on Women in MathematicsAmerican Mathematical Society — September 1991
  114. 115JournalA Refugee Scholar from Nazi Germany: Emmy Noether and Bryn Mawr CollegeQinna Shen — September 2019

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