ProofWiki:Mathematicians/Emmy Noether

Amalie ("Emmy") Noether was a German-born mathematician who made considerable contributions to abstract algebra and theoretical physics.

Most famous for Noether's Theorem which makes the fundamental connection between symmetry and various laws of conservation.

Her philosophy and outlook were fundamental in the development of ideas that led to the establishment of the field of category theory.

Daughter of Max Noether.

One of the top 100 people that Matt Westwood is looking forward to meeting when he dies.

Nationality

German

History

• Born: 23 March 1882, Erlangen, Bavaria, Germany.
• 1900 - 1902: Attended courses at the University of Erlangen.
• 1903: Passed matriculation examination at Nürnberg, started attending University of Göttingen.
• 1903 - 1904: Attended lectures by Blumenthal, Hilbert, Klein and Minkowski.
• 1904: Matriculated at Göttingen.
• 1907: Granted a doctorate, having studied under Paul Gordan.
• 1908: Elected to the Circolo Matematico di Palermo.
• 1909: Invited to become a member of the Deutsche Mathematiker-Vereinigung.
• 1913: Lectured in Vienna.
• 1915: Hilbert and Klein invited her to return to Göttingen.
• 1919: Finally granted permission to join the Mathematics Facility at the University of Göttingen.
• 1933: Dismissed from her position for being Jewish. Emigrated to USA, and accepted visiting professorship at Bryn Mawr College, Pennsylvania.
• Died: 14 April 1935, Bryn Mawr, Pennsylvania, USA.

Theorems and Definitions

• Noether's Theorem
• Noether Normalization Lemma
• Noetherian: a categorization which can apply to a range of objects, including:
  • Noetherian Ring
  • Noetherian Module
  • Noetherian Topological Space

• Lasker-Noether Theorem (with Emanuel Lasker)

Lectures and Courses Delivered

• At Göttingen:
  • Winter 1924/25: Gruppentheorie und hyperkomplexe Zahlen (Group Theory and Hypercomplex Numbers)
  • Winter 1927/28: Hyperkomplexe Grössen und Darstellungstheorie (Hypercomplex Quantities and Representation Theory)
  • Summer 1928: Nichtkommutative Algebra (Noncommutative Algebra)
  • Summer 1929: Nichtkommutative Arithmetik (Noncommutative Arithmetic)
  • Winter 1929/30: Algebra der hyperkomplexen Grössen (Algebra of Hypercomplex Quantities)

Books and Papers

• 1907: Über die Bildung des Formensystems der ternären biquadratischen Form (On Complete Systems of Invariants for Ternary Biquadratic Forms)
• 1913: Rationale Funkionenkörper (Rational Function Fields)
• 1915: Der Endlichkeitssatz der Invarianten endlicher Gruppen (The Finiteness Theorem for Invariants of Finite Groups)
• 1918: Gleichungen mit vorgeschriebener Gruppe (Equations with Prescribed Group)
• 1918: Invariante Variationsprobleme (Invariant Variation Problems)
• 1921: Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains)
• 1923: Zur Theorie der Polynomideale und Resultanten
• 1923: Eliminationstheorie und allgemeine Idealtheorie
• 1924: Eliminationstheorie und Idealtheorie
• 1926: Der Endlichkeitsatz der Invarianten endlicher linearer Gruppen der Charakteristik p (Proof of the Finiteness of the Invariants of Finite Linear Groups of Characteristic p)
• 1926: Ableitung der Elementarteilertheorie aus der Gruppentheorie (Derivation of the Theory of Elementary Divisor from Group Theory)
• 1927: Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern (Abstract Structure of the Theory of Ideals in Algebraic Number Field)
• 1927: Über minimale Zerfällungskörper irreduzibler Darstellungen (On the Minimum Splitting Fields of Irreducible Representations) (with Richard Brauer)
• 1929: Hyperkomplexe Grössen und Darstellungstheorie (Hypercomplex Quantities and the Theory of Representations)
• 1932: Beweis eines Hauptsatzes in der Theorie der Algebren (Proof of a Main Theorem in the Theory of Algebras) (with Richard Brauer and Helmut Hasse)
• 1933: Nichtkommutative Algebren (Noncommutative Algebras)

Also see

• John J. O'Connor and Edmund F. Robertson: "Emmy Noether": MacTutor History of Mathematics archive