Theorems

Noether's Theorem

NUR-ter, German [ˈnøːtɐ]; named for Emmy Noether

Also Known As Noether's First Theorem

Mathematical Physics

Citation Formats

General Reference

Mathematics Atlas. "Noether's Theorem." Accessed August 30, 2026. https://dev-mathematics.interactiveatlas.org/theorems/noethers-theorem.

APA Style

Mathematics Atlas. (n.d.). Noether's Theorem. Retrieved August 30, 2026, from https://dev-mathematics.interactiveatlas.org/theorems/noethers-theorem

BibTeX

@misc{mathematicsatlas-noether-s-theorem,
  author = {Mathematics Atlas},
  title = {Noether's Theorem},
  year = {2026},
  url = {https://dev-mathematics.interactiveatlas.org/theorems/noethers-theorem},
  note = {Accessed August 30, 2026}
}

Noether's theorem states that every continuous symmetry of a physical system's action corresponds to a conserved quantity: rotational symmetry yields conservation of angular momentum, translational symmetry yields conservation of momentum, and time-translation symmetry yields conservation of energy. Emmy Noether proved it in 1918, and it has become one of the most cited results connecting mathematics to physics.

Facts

Statement

For every continuous symmetry of the action of a physical system, there is a corresponding conservation law. 1

Proof Year

1918 1

Cross-Tradition Connections