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Several alternative methods for finding conserved quantities were developed in the 19th century, especially by [[William Rowan Hamilton]]. For example, he developed a theory of [[canonical transformation]]s which allowed changing coordinates so that some coordinates disappeared from the Lagrangian, as above, resulting in conserved canonical momenta. Another approach, and perhaps the most efficient for finding conserved quantities, is the [[Hamilton–Jacobi equation]].
Emmy Noether's work on the invariance theorem began in 1915 when she was helping [[Felix Klein]] and David Hilbert with their work related to [[Albert Einstein]]'s theory of general relativity<ref name="DickNoetherBio1981"/>{{rp|31}} By March 1918 she had most of the key ideas for the paper which would be published later in the year.<ref>{{Cite book |last=Rowe |first=David E. |url=https://link.springer.com/10.1007/978-3-030-63810-8 |title=Emmy Noether – Mathematician Extraordinaire |date=2021 |publisher=Springer International Publishing |isbn=978-3-030-63809-2 |___location=Cham |language=en |doi=10.1007/978-3-030-63810-8}}</ref>{{rp|81}}
==Mathematical expression==
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