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Mathematical Physics

Picture of Amalie Emmy Noether

Emmy Noether

1882 - 1935
Additional Information

Important Contributions

Proved that a physical system described by a Lagrangian invariant with respect to the symmetry transformations of a Lie group has, in the case of a group with a finite (or countably infinite) number of independent, infinitesimal generators, a conservation law for each such generator, and certain `dependencies' in the case of a larger infinite number of generators. The latter case applies, for example, to the general theory of relativity and gives the Bianchi identities. These `dependencies' lead to understanding of energy-momentum conservation in the general theory. Her paper proves both the theorems described above and their converses.These are collectively referred to by physicists as Noether's Theorem.

The key to the relation of symmetry laws to conservation laws is Emmy Noether's celebrated Theorem. ... Before Noether's Theorem the principle of conservation of energy was shrouded in mystery, leading to the obscure physical systems of Mach and Ostwald. Noether's simple and profound mathematical formulation did much to demystify physics. --- Feza Gursey [encp1983nj]

An historical account of how she came to make this discovery is given in E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws.

The main body of her work was in the creation of modern abstract algebra. As the topologist P. S. Alexandrov wrote

    It was she who taught us to think in terms of simple and general algebraic concepts - homomorphic mappings, groups and rings with operators, ideals ...theorems such as the `homomorphism and isomorphism theorems', concepts such as the ascending and descending chain conditions for subgroups and ideals, or the notion of groups with operators were first introduced by Emmy Noether and have entered into the daily practice of a wide range of mathematical disciplines. ... glance at Pontryagin's work on ..continuous groups, Kolmogorov on ... combinatorial topology ..., ... Hopf on continuous mappings, ... van der Waerden on algebraic geometry, ... to sense the influence of Emmy Noether's ideas. This influence is also keenly felt in H. Weyl' book Gruppentheories und Quantenmechanik. ---[en1981ad]

Specifically, Nathan Jacobson writes

    Abstract algebra can be dated from the publication of two papers by Noether, the first a joint paper with Schmeidler and .. a truly monumental work Idealtheorie in Ringbereichen [which] belongs to one of the mainstreams of abstract algebra, commutative ring theory, and may be regarded as the first paper in this vast subject ... [encp1983nj]

And Hermann Weyl writes of her important later work

    The theory of non-commutative algebras and their representations wa built up by Emmy Noether in a new unified, purely conceptual manner by making use of all the results that has been accumulated by the ingenious labors of decades by Frobenius, Dickson, Wedderburn and others. ---[sm1935hw]

Some Important Publications

"Invariante Variationsprobleme," Nachr. v. d. Ges. d. Wiss. zu Göttingen 1918, pp 235-257      English translation by M. A. Tavel.

"Moduln in nichtkommutativen bereichen, insobesondere aus Differential- und Differen-zenaus-drucken," Math. Zs. 8:1 (1920) with W. Schmeidler.

"Idealtheories in Ringbereichen," Math. Ann. 83:24 (1921).

"Hyperkomplexe Grossen und Darstellungstheorie," Math. Zs. 30:641 (1929).

"Beweis eines Hauptsatzes in der Theorie de Algebren," Journal f. d. reine u. amgew. Math. 167:399 (1932) with R. Brauer and H. Hasse.

"Nichtkommutative Algebren," Math. Zs. 37:514 (1933).


1907 Doctorate summa cum laude University of Erlangen

1908 member of the Circolo mathematico di Palermo [en1981ad]

1909 member Deutsche Mathematiker Vereinigung (DMV) [en1981ad]

1932 Co-winner, Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge

1958 A conference at the University of Erlangen was held to commemorate the 50th anniversary of Noether's doctorate.

1982 Emmy Noether Gymnasium, a co-educational school emphasizing mathematics, natural sciences and language, opened in Erlangen, Germany on the 100th anniversary of Noether's birth.

1992 Emmy Noether Institute for Mathematical Research established in Bar Ilan University, Tel Aviv, Israel.


1908-1915 unpaid lecturer and supervisor of doctoral student in University of Erlangen.

1916-1922 unpaid lecturer and member of Hilbert's research team in the University of Göttingen.

1922-1933 nicht-beamteter ausserordentlicher Professor (adjunct, not-ordinary Professor - untenured), University of Göttingen.

1922-1933 Lehrauftrag for algebra - which brought her a small stipend; "the first and only salary she was ever paid in Göttingen." [h1970cr]

1933-1935 Visiting Professor, Bryn Mawr College.


1903 Reifeprüfung, Königliches Realgymnasium, Nuremburg

1907 Doctorate in Mathematics, University of Erlangen

1919 habilitation, University of Göttingen

References [en1981ad],[encp1983nj],[oibdpp1996nb], [h1970cr]

Additional Information/Comments

Emmy Noether's name is used to designate many concepts specific to abstract algebra ; for example,

  • a ring is called Noetherian if each ideal has a finite basis;
  • a group is called Noetherian if each subgroup can be generated by a finite basis;
  • and mathematicians speak of Noetherian equations, Noetherian modules, Noetherian factor systems, etc..

She was never elected to the Königl. Gesellschaft der Wissenschaften zu Göttingen . [h1970cr]
Her great 1918 paper on symmetries and conservation laws was communicated to the Gesellschaft by Felix Klein.

Auguste Dick raises interesting questions regarding the fact that Noether wa never appointed to a paid position in the faculty of the University of Göttingen:

How was it then that in her academic career she did not go beyond the [unpaid] level of nicht-beamteter ausserordentlicher Professor? ... Was it because she was Jewish? There were several Jewish Ordinarii in Göttingen. Was it because she was a member of the social- democratic party? ... Or was it her firm stance as a pacifist that was frowned upon? ..." -- [en1981ad]

As a Jewish woman, in 1933 Emmy Noether was fired from her position as a privat docent in Göttingen. By decree no Jew was allowed to teach after Hitler came to power. (In 1934 women were dismissed from University posts.)

Hermann Weyl wrote about her in this period

    " A stormy time of struggle like this one we spent in Göttingen in the summer of 1933 draws people closely together; thus I have a vivid recollection of these months. Emmy Noether - her courage, her frankness, her unconcern about her own fate, her conciliatory spirit - was in the midst of all the hatred and meaness, despair and sorrow surrounding us, a moral solace." [sm1935hw]

Part of a Letter to the Editor of the New York Times that Albert Einstein wrote on the occasion of her untimely death:

    ``The efforts of most human beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. ... There is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and thinker have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.''[NYT1935ae]


Recommended further reading on Emmy Noether's contributions to mathematics:

There are two papers by Nina Byers on her contributions to physics:

Field Editor: Nina Byers


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