"Invariante Variationsprobleme"
E157399
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| "Invariante Variationsprobleme" canonical | 1 |
| Invariante Variationsprobleme | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382796 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: "Invariante Variationsprobleme" Context triple: [Noether's theorem, publishedIn, "Invariante Variationsprobleme"]
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A.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
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B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
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C.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
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D.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
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E.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: "Invariante Variationsprobleme" Target entity description: "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
-
A.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
-
B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
C.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
D.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
E.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics paper
ⓘ
physics paper ⓘ scientific paper ⓘ |
| appliesTo |
Hamiltonian systems
ⓘ
Lagrangian mechanics ⓘ classical field theory ⓘ general relativity ⓘ |
| author | Emmy Noether ⓘ |
| centuryOfPublication | 20th century ⓘ |
| contains |
Noether's theorem
ⓘ
surface form:
first Noether theorem
Noether's theorem ⓘ
surface form:
second Noether theorem
|
| countryOfOrigin | Germany ⓘ |
| field |
calculus of variations
ⓘ
conservation laws ⓘ mathematical physics ⓘ symmetry theory ⓘ theoretical physics ⓘ |
| focusesOn |
invariance of action integrals
ⓘ
relationship between invariance and integrals of motion ⓘ |
| historicalSignificance |
cornerstone of modern gauge theories
ⓘ
foundational work in modern theoretical physics ⓘ key work in the development of symmetry methods in physics ⓘ |
| influenced |
Noetherian approaches in mathematics and physics
ⓘ
gauge theory ⓘ modern differential geometry ⓘ particle physics ⓘ quantum field theory ⓘ |
| language | German ⓘ |
| mainContribution |
development of invariant methods in the calculus of variations
ⓘ
establishing connection between symmetries and conservation laws ⓘ formulation of Noether's theorem ⓘ |
| originalTitle |
"Invariante Variationsprobleme"
self-link
ⓘ
surface form:
Invariante Variationsprobleme
|
| publicationYear | 1918 ⓘ |
| relatedConcept |
Noether charge
ⓘ
Noether current ⓘ Noether's theorem ⓘ
surface form:
Noether symmetry
|
| relatedTo |
Erlangen Program
ⓘ
surface form:
Felix Klein's Erlangen program
Hilbert's work on general relativity ⓘ |
| topic |
Euler–Lagrange equation
ⓘ
surface form:
Euler–Lagrange equations
Lie groups of transformations ⓘ Noether currents ⓘ conserved currents ⓘ continuous symmetries ⓘ energy–momentum conservation ⓘ variational principles ⓘ |
How these facts were elicited
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You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: "Invariante Variationsprobleme" Description of subject: "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.