Grundlagen der Mathematik
E602274
Grundlagen der Mathematik is a foundational two-volume work in mathematical logic and the philosophy of mathematics, co-authored by David Hilbert and Paul Bernays, that systematically develops proof theory and formalizes large parts of mathematics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Grundlagen der Mathematik canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6572447 — 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: Grundlagen der Mathematik Context triple: [Paul Bernays, coAuthored, Grundlagen der Mathematik]
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A.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
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B.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
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C.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
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D.
Einleitung in die Mengenlehre
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
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E.
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.
- 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: Grundlagen der Mathematik Target entity description: Grundlagen der Mathematik is a foundational two-volume work in mathematical logic and the philosophy of mathematics, co-authored by David Hilbert and Paul Bernays, that systematically develops proof theory and formalizes large parts of mathematics.
-
A.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
-
B.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
-
C.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
-
D.
Einleitung in die Mengenlehre
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
-
E.
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.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
foundational work in the philosophy of mathematics
ⓘ
mathematics book ⓘ work in mathematical logic ⓘ |
| aim |
to formalize large parts of classical mathematics
ⓘ
to provide a systematic exposition of proof theory ⓘ |
| approach |
axiomatic
ⓘ
finitistic ⓘ |
| author |
David Hilbert
ⓘ
Paul Bernays ⓘ |
| coAuthorRole |
David Hilbert was the leading proponent of the Hilbert program
ⓘ
linked to:
David Hilbert
Paul Bernays contributed detailed technical development and editing ⓘ |
| contains |
formalization of analysis
ⓘ
formalization of arithmetic ⓘ formalization of set-theoretic reasoning ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ proof theory ⓘ |
| genre | technical monograph ⓘ |
| historicalContext | written in the context of the Hilbert program ⓘ |
| impact |
classic in the foundations of mathematics literature
ⓘ
standard reference in proof theory ⓘ |
| influenced |
development of proof theory
ⓘ
philosophy of mathematics in the 20th century ⓘ subsequent work in mathematical logic ⓘ |
| intendedAudience |
logicians
ⓘ
philosophers of mathematics ⓘ professional mathematicians ⓘ |
| language | German ⓘ |
| numberOfVolumes | 2 ⓘ |
| publisherRole | published by a German academic publisher ⓘ |
| relatedTo |
Gödel incompleteness theorems
ⓘ
linked to:
Gödel's incompleteness theorems
consistency problem for arithmetic ⓘ formalization of logical inference rules ⓘ |
| subject |
Hilbert program
ⓘ
linked to:
Hilbert’s program
axiomatic method ⓘ completeness questions ⓘ consistency proofs ⓘ finitism ⓘ formal systems ⓘ formalization of mathematics ⓘ metamathematics ⓘ primitive recursive arithmetic ⓘ proof calculi ⓘ syntactic consistency ⓘ |
| titleTranslation | Foundations of Mathematics ⓘ |
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: Grundlagen der Mathematik Description of subject: Grundlagen der Mathematik is a foundational two-volume work in mathematical logic and the philosophy of mathematics, co-authored by David Hilbert and Paul Bernays, that systematically develops proof theory and formalizes large parts of mathematics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.