{"id":"noethers-theorem","domain":"mathematical-physics","type":"Theorem","title":"Noether's Theorem","slug":"noethers-theorem","url":"/mathematics/mathematical-physics/noethers-theorem/","proved":"1915 (published 1918), Emmy Noether","summary":"Every continuous symmetry of a physical system corresponds to a conserved quantity. Time symmetry->energy conservation, translation->momentum, rotation->angular momentum.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Noether, E. (1918). Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 235-257."},{"tier":1,"citation":"Goldstein, H., Poole, C. and Safko, J. (2002). Classical Mechanics. 3rd ed. Addison Wesley."},{"tier":2,"citation":"Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. Springer."},{"tier":3,"citation":"Byers, N. (1998). E. Noether's discovery of the deep connection between symmetries and conservation laws. arXiv:physics/9807044."}],"relationships":[{"type":"key_person","target":"ring","label":"Emmy Noether — also founded abstract ring theory"},{"type":"uses","target":"group","label":"Group — symmetry groups"},{"type":"uses","target":"integral","label":"Integral — action integral"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.7"}