What did Emmy Noether contribute to the theory of integral invariants that wasn't already done by, e.g., Sophus Lie in his 1902 Über Integralinvarianten und Differentialgleichungen?


1 Answer 1


Noether was the first to, as she said in the abstract of her 1918 "Invariant Variational Problems" paper (The Noether Theorems p. 3), formulate

a combination of the methods of the formal calculus of variations and of Lie’s theory of groups.

She says

For those differential equations that arise from variational problems, the statements that can be formulated are much more precise than for the arbitrary differential equations that are invariant under a group, which are the subject of Lie’s researches.

and recognized that

For certain groups and variational problems this combination is not new


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