Über die Hypothesen, welche der Geometrie zu Grunde liegen
E47356
"Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
All labels observed (2)
How this entity was disambiguated
This entity first appeared as the object of triple T373793 — 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.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Über die Hypothesen, welche der Geometrie zu Grunde liegen Context triple: [Bernhard Riemann, notableWork, Über die Hypothesen, welche der Geometrie zu Grunde liegen]
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A.
Grundlagen der Geometrie
Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
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B.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
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C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
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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.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Über die Hypothesen, welche der Geometrie zu Grunde liegen Target entity description: "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
-
A.
Grundlagen der Geometrie
Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
-
B.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
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.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
foundational text in geometry
ⓘ
mathematical lecture ⓘ scientific work ⓘ |
| anticipated |
geometrization of gravitation
ⓘ
use of curved spacetime in physics ⓘ |
| author | Bernhard Riemann ⓘ |
| authorOccupation | mathematician ⓘ |
| considered |
foundational work of Riemannian geometry
ⓘ
milestone in history of geometry ⓘ revolutionary for concept of space ⓘ |
| context | habilitation lecture ⓘ |
| countryOfOrigin |
Duchy of Brunswick-Lüneburg
ⓘ
surface form:
Kingdom of Hanover
|
| dateOfLecture | 1854 ⓘ |
| field |
differential geometry
ⓘ
foundations of geometry ⓘ geometry ⓘ mathematical physics ⓘ mathematics ⓘ |
| hasKeyConcept |
line element
ⓘ
local vs global properties of space ⓘ |
| impactOn |
development of differential geometry
ⓘ
general relativity ⓘ mathematical physics ⓘ modern geometry ⓘ |
| influencedBy |
Carl Friedrich Gauss
ⓘ
Euclidean space ⓘ
surface form:
Euclidean geometry
non-Euclidean geometry ⓘ |
| introduces |
Riemannian manifolds
ⓘ
surface form:
Riemannian geometry
Riemannian manifolds ⓘ
surface form:
Riemannian manifold
Riemannian manifolds ⓘ
surface form:
Riemannian metric
concept of n-dimensional manifold ⓘ variable curvature of space ⓘ |
| language | German ⓘ |
| laterPublishedIn | Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen ⓘ |
| originalTitle | Über die Hypothesen, welche der Geometrie zu Grunde liegen self-link ⓘ |
| philosophicalAspect |
nature of space
ⓘ
relation between geometry and physical reality ⓘ |
| placeOfLecture |
University of Göttingen
ⓘ
surface form:
Georg-August-Universität Göttingen
Göttingen ⓘ |
| publicationType | journal article ⓘ |
| purpose | habilitation in mathematics ⓘ |
| supervisor | Carl Friedrich Gauss ⓘ |
| titleInEnglish | On the Hypotheses which Lie at the Foundations of Geometry ⓘ |
| topic |
axioms of geometry
ⓘ
curved spaces ⓘ foundations of space and geometry ⓘ generalization of Euclidean geometry ⓘ metric structure of space ⓘ |
| year | 1854 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
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.
Input
Subject: Über die Hypothesen, welche der Geometrie zu Grunde liegen Description of subject: "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
Über die Hypothesen, welche der Geometrie zu Grunde liegen
→
originalTitle
→
Über die Hypothesen, welche der Geometrie zu Grunde liegen
self-link
ⓘ
subject surface form:
Friedrich Bernhard Riemann
this entity surface form:
Habilitation thesis on the hypotheses which lie at the foundations of geometry