Hilbert problems
E41774
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.
All labels observed (25)
How this entity was disambiguated
This entity first appeared as the object of triple T326967 — 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 problems Context triple: [David Hilbert, notableWork, Hilbert problems]
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A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
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B.
David Hilbert
David Hilbert was a pioneering German mathematician whose foundational work in fields such as invariant theory, axiomatic systems, and functional analysis profoundly shaped modern mathematics.
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C.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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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.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- 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 problems Target entity description: 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.
-
A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
-
B.
David Hilbert
David Hilbert was a pioneering German mathematician whose foundational work in fields such as invariant theory, axiomatic systems, and functional analysis profoundly shaped modern mathematics.
-
C.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
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.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
historical mathematical program
ⓘ
list of mathematical problems ⓘ |
| aim | to guide future research in mathematics ⓘ |
| field | mathematics ⓘ |
| hasPart |
Hilbert problems
self-linksurface differs
ⓘ
surface form:
Hilbert’s eighteenth problem
Riemann hypothesis ⓘ
surface form:
Hilbert’s eighth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s eleventh problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s fifteenth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s fifth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s first problem
Hilbert’s fourteenth problem ⓘ Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s fourth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s nineteenth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s ninth problem
Hilbert’s second problem ⓘ Hilbert’s seventeenth problem ⓘ Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s seventh problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s sixteenth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s sixth problem
Hilbert’s tenth problem ⓘ Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s third problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s thirteenth problem
Hilbert’s twelfth problem ⓘ Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s twentieth problem
Hilbert problems self-linksurface differs ⓘ
surface form:
Hilbert’s twenty-first problem
Hilbert’s twenty-second problem ⓘ Hilbert’s twenty-third problem ⓘ |
| inception | 1900 ⓘ |
| influenced |
20th-century mathematics
ⓘ
algebraic geometry ⓘ analysis ⓘ foundations of mathematics ⓘ mathematical logic ⓘ number theory ⓘ set theory ⓘ |
| languageOfPresentation | German ⓘ |
| namedAfter | David Hilbert ⓘ |
| notableProblem |
Hilbert’s tenth problem
ⓘ
surface form:
Diophantine equations decision problem
Riemann hypothesis ⓘ consistency of arithmetic ⓘ continuum hypothesis ⓘ |
| numberOfItems | 23 ⓘ |
| presentedAt | International Congress of Mathematicians ⓘ |
| presentedBy | David Hilbert ⓘ |
| presentedInCity | Paris ⓘ |
| presentedInYear | 1900 ⓘ |
| publication |
Hilbert problems
self-linksurface differs
ⓘ
surface form:
“Mathematical Problems”
|
| publishedIn | Göttinger Nachrichten ⓘ |
| publishedInYear | 1900 ⓘ |
| republishedIn | Bulletin of the American Mathematical Society ⓘ |
| status | partially solved ⓘ |
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 problems Description of subject: 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.
Referenced by (38)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hilbert’s first problem
this entity surface form:
Hilbert’s third problem
this entity surface form:
Hilbert’s fourth problem
this entity surface form:
Hilbert’s fifth problem
this entity surface form:
Hilbert’s sixth problem
this entity surface form:
Hilbert’s seventh problem
this entity surface form:
Hilbert’s ninth problem
this entity surface form:
Hilbert’s eleventh problem
this entity surface form:
Hilbert’s thirteenth problem
this entity surface form:
Hilbert’s fifteenth problem
this entity surface form:
Hilbert’s sixteenth problem
this entity surface form:
Hilbert’s eighteenth problem
this entity surface form:
Hilbert’s nineteenth problem
this entity surface form:
Hilbert’s twentieth problem
this entity surface form:
Hilbert’s twenty-first problem
this entity surface form:
“Mathematical Problems”
this entity surface form:
Hilbert’s 1900 Paris lecture
this entity surface form:
Hilbert's problems
this entity surface form:
Hilbert's problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
“Mathematische Probleme”
this entity surface form:
Hilbert’s problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
Hilbert’s problems
this entity surface form:
Mathematische Probleme lecture
this entity surface form:
Hilbert’s problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
Mathematical Problems (Hilbert’s 1900 address)
this entity surface form:
Hilbert’s problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
David Hilbert’s list of problems
this entity surface form:
Hilbert’s list of 23 problems
this entity surface form:
Hilbert's problems
this entity surface form:
Hilbert’s problems
this entity surface form:
Hilbert’s problems