Hilbert's first problem
E628900
Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hilbert's first problem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6929769 — 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: Hilbert's first problem Context triple: [continuum hypothesis, positionInHilbertProblems, Hilbert's first problem]
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A.
Hilbert’s second problem
Hilbert’s second problem is one of David Hilbert’s famous list of 23 problems, asking for a proof of the consistency of arithmetic from a finite set of axioms using finitary methods.
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B.
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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C.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
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D.
Hilbert’s twenty-second problem
Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
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E.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
- 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: Hilbert's first problem Target entity description: Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.
-
A.
Hilbert’s second problem
Hilbert’s second problem is one of David Hilbert’s famous list of 23 problems, asking for a proof of the consistency of arithmetic from a finite set of axioms using finitary methods.
-
B.
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.
-
C.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
-
D.
Hilbert’s twenty-second problem
Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
-
E.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf | mathematical problem ⓘ |
| asksWhether |
there exists a set of cardinality strictly between the integers and the real numbers
ⓘ
there exists a set whose cardinality is strictly between aleph-null and the cardinality of the continuum ⓘ |
| concerns |
cardinality of infinite sets
ⓘ
continuum hypothesis NERFINISHED ⓘ foundations of mathematics ⓘ set theory ⓘ |
| equivalentToQuestion | Is the continuum hypothesis true? ⓘ |
| firstPublishedIn | 1900 ⓘ |
| formalContext |
Zermelo–Fraenkel set theory
NERFINISHED
ⓘ
Zermelo–Fraenkel set theory with Choice NERFINISHED ⓘ |
| hasPhilosophicalAspect |
completeness of axiomatic systems
ⓘ
nature of mathematical infinity ⓘ |
| hasSolutionType | independence result ⓘ |
| hasStandardFormulation | Is there a set whose cardinality is strictly between that of the integers and that of the real numbers? ⓘ |
| influencedField |
foundations of mathematics
ⓘ
mathematical logic ⓘ set theory ⓘ |
| involvesConcept |
aleph-null
ⓘ
cardinality of the continuum ⓘ integers ⓘ real numbers ⓘ set-theoretic independence ⓘ uncountable sets ⓘ |
| languageOfOriginalStatement | German ⓘ |
| namedAfter | David Hilbert NERFINISHED ⓘ |
| numberInHilbertList | 1 ⓘ |
| originalPublication | Mathematische Probleme (Hilbert's 1900 address) NERFINISHED ⓘ |
| partOf | Hilbert's list of 23 problems NERFINISHED ⓘ |
| presentedAt | International Congress of Mathematicians 1900 NERFINISHED ⓘ |
| presentedInCity | Paris NERFINISHED ⓘ |
| relatedTo |
Cantor's continuum hypothesis
NERFINISHED
ⓘ
generalized continuum hypothesis NERFINISHED ⓘ |
| resolutionYearPartial | 1938 ⓘ |
| resolutionYearPartial |
1940
ⓘ
1963 ⓘ |
| resolvedBy |
Kurt Gödel
NERFINISHED
ⓘ
Paul Cohen NERFINISHED ⓘ |
| resultByCohen |
continuum hypothesis is independent of ZF if ZF is consistent
NERFINISHED
ⓘ
continuum hypothesis is independent of ZFC if ZFC is consistent ⓘ |
| resultByGödel | continuum hypothesis is consistent with ZF if ZF is consistent ⓘ |
| resultByGödel | continuum hypothesis is consistent with ZFC if ZFC is consistent ⓘ |
| statedBy | David Hilbert NERFINISHED ⓘ |
| statusInZFC | independent ⓘ |
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: Hilbert's first problem Description of subject: Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.