Noether's theorems/Chronology

Noether's theorems: map
Reading the volume How to read this volume Notation Glossary Index of symmetries Figure gallery
Reading by level Start here: the plain-language primer The first theorem, stated and proved The second theorem, stated and proved The two theorems side by side The mathematics: Lie groups and Lie algebras The applications: General relativity and the energy question The history: Göttingen and the energy problem
Sources Sources Bibliography Chronology Further reading
Related Hamilton's principle On Physical Lines of Force

A chronology from Lie to the anomaly

Every dated entry below is established on the history track. Entries whose date or attribution rests on secondary literature rather than on a primary text are marked.

A caution that applies to the whole of 1918. Neither Noether's paper nor Klein's second note reached its final form until September, after both had been presented in July. What was said at either July session is not recoverable from the printed papers, and this chronology dates the presentations and the manuscripts separately for that reason.

date	event	source
1891	Lie, Grundlagen für die Theorie der unendlichen kontinuierlichen Transformationsgruppen. Cited by Noether at three points	her footnotes
Nov 1915	Einstein publishes the field equations of general relativity	secondary
20 Nov 1915	Hilbert presents Die Grundlagen der Physik, first communication	secondary
23 Dec 1916	Hilbert presents the second communication	secondary
25 Jan 1918	Klein presents his first note, on Hilbert's first communication. At the same session Klein presents Noether's Invarianten beliebiger Differentialausdrücke	secondary
15 Feb 1918	Noether, in a postcard to Klein from Erlangen, sketches the second theorem in a particular case	secondary
12 Mar 1918	Noether's letter to Klein gives a preliminary formulation of its essential consequence	secondary
spring 1918	Weyl, Gravitation und Elektrizität. Presented to the Berlin Academy; sources disagree between April and May, and the disagreement is unresolved	secondary
19 Jul 1918	Klein presents his second note, on the differential laws for the conservation of momentum and energy	primary, his paper
23 Jul 1918	Noether presents her results to the Göttingen Mathematical Society	secondary
26 Jul 1918	Klein presents Invariante Variationsprobleme to the Göttingen Scientific Society	primary, printed on the paper
mid-Sep 1918	Klein's manuscript reaches final form	primary, his footnote
end Sep 1918	Noether's manuscript reaches final form	primary, her footnote
1918	Invariante Variationsprobleme published, Nachrichten pages 235 to 257	primary
Sep 1921	Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik. Divergence invariance enters here	secondary; the paper was not reached
1921	Klein's collected works appear, with a footnote restating both of Noether's theorems and Hilbert's assertion	secondary
1924	Hilbert reprints both communications, crediting Klein with the general derivation of the identities and Noether with the general proof	secondary
1934	first proper citation of Bessel-Hagen's paper, on the account of a study of its reception. This is a fact about his paper and not about Noether's	secondary
1939, 1940	Belinfante and Rosenfeld, the improvement of the stress-energy tensor	secondary, unverified
from 1949	Bergmann and the constrained-Hamiltonian programme	secondary, unverified
1951	Hill's review article, commonly credited with putting the theorem before physicists	secondary, unverified
1954	Yang and Mills	secondary, unverified
1956, 1961	Utiyama, then Kibble, extend the gauge idea to gravitation	secondary, unverified
from 1962	Trautman on conservation laws in general relativity	secondary, unverified
1971	Tavel's English translation, in Transport Theory and Statistical Physics	primary, located; under copyright
2004, 2011	Kosmann-Schwarzbach's study of the theorems, in French and then English	secondary
2018	centenary; renewed work returning to the paper itself	secondary

Entries from 1939 onward are the route the secondary literature commonly gives. None of the papers named there was read, and the page that carries them says so.