Recent Synthetic Differential Geometry
E855795
"Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Recent Synthetic Differential Geometry canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10313527 — 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: Recent Synthetic Differential Geometry Context triple: [Herbert Busemann, notableWork, Recent Synthetic Differential Geometry]
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A.
Archive of Formal Proofs
The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
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B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
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C.
The Calculus of Computation
The Calculus of Computation is a textbook that introduces the mathematical foundations of verification, focusing on logic-based methods for specifying and proving properties of computational systems.
-
D.
Isabelle/ML
Isabelle/ML is the ML-based implementation and extension language used to develop and script the Isabelle interactive theorem prover.
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E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- 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: Recent Synthetic Differential Geometry Target entity description: "Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
-
A.
Archive of Formal Proofs
The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
-
B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
-
C.
The Calculus of Computation
The Calculus of Computation is a textbook that introduces the mathematical foundations of verification, focusing on logic-based methods for specifying and proving properties of computational systems.
-
D.
Isabelle/ML
Isabelle/ML is the ML-based implementation and extension language used to develop and script the Isabelle interactive theorem prover.
-
E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| aimsAt |
foundational clarity in differential geometry
ⓘ
minimizing reliance on calculus ⓘ |
| approach |
axiomatic
ⓘ
non-analytic ⓘ synthetic ⓘ |
| author | Herbert Busemann ⓘ |
| contrastsWith | classical analytic differential geometry ⓘ |
| emphasizes |
geometric intuition over analytic computation
ⓘ
synthetic treatment of curvature ⓘ |
| field |
differential geometry
ⓘ
synthetic differential geometry ⓘ |
| focusesOn |
development of differential geometry from axioms
ⓘ
geometric methods independent of coordinates ⓘ |
| hasAuthorNationality |
Herbert Busemann – German-American mathematician
ⓘ
linked to:
Herbert Busemann
|
| hasMainTheme | reformulation of differential-geometric notions in synthetic terms ⓘ |
| hasMathematicalSubject |
curvature
ⓘ
foundations of geometry ⓘ geodesics ⓘ metric spaces ⓘ |
| intendedAudience |
advanced graduate students in geometry
ⓘ
research mathematicians ⓘ |
| language | English ⓘ |
| relatedTo |
axiomatic geometry
ⓘ
global differential geometry ⓘ metric geometry ⓘ |
| subject |
geometry of curves and surfaces
ⓘ
metric and geodesic concepts in synthetic form ⓘ |
| uses |
axioms for distance and geodesics
ⓘ
synthetic definitions of curvature ⓘ |
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: Recent Synthetic Differential Geometry Description of subject: "Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.