Hilbert problems

E41774

historical mathematical program list of mathematical 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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All labels observed (25)

Label	Occurrences
Hilbert’s list of 23 problems	6
Hilbert’s problems	6
Hilbert's problems	3
Hilbert problems canonical	2
David Hilbert’s list of problems	1
Hilbert’s 1900 Paris lecture	1
Hilbert’s eighteenth problem	1
Hilbert’s eleventh problem	1
Hilbert’s fifteenth problem	1
Hilbert’s fifth problem	1
Hilbert’s first problem	1
Hilbert’s fourth problem	1
Hilbert’s nineteenth problem	1
Hilbert’s ninth problem	1
Hilbert’s seventh problem	1
Hilbert’s sixteenth problem	1
Hilbert’s sixth problem	1
Hilbert’s third problem	1
Hilbert’s thirteenth problem	1
Hilbert’s twentieth problem	1
Hilbert’s twenty-first problem	1
Mathematical Problems (Hilbert’s 1900 address)	1
Mathematische Probleme lecture	1
“Mathematical Problems”	1
“Mathematische Probleme”	1

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]

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
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’s eighteenth problem ⓘ linked to: Hilbert problems Hilbert’s eighth problem ⓘ linked to: Riemann hypothesis Hilbert’s eleventh problem ⓘ linked to: Hilbert problems Hilbert’s fifteenth problem ⓘ linked to: Hilbert problems Hilbert’s fifth problem ⓘ linked to: Hilbert problems Hilbert’s first problem ⓘ linked to: Hilbert problems Hilbert’s fourteenth problem ⓘ Hilbert’s fourth problem ⓘ linked to: Hilbert problems Hilbert’s nineteenth problem ⓘ linked to: Hilbert problems Hilbert’s ninth problem ⓘ linked to: Hilbert problems Hilbert’s second problem ⓘ Hilbert’s seventeenth problem ⓘ Hilbert’s seventh problem ⓘ linked to: Hilbert problems Hilbert’s sixteenth problem ⓘ linked to: Hilbert problems Hilbert’s sixth problem ⓘ linked to: Hilbert problems Hilbert’s tenth problem ⓘ Hilbert’s third problem ⓘ linked to: Hilbert problems Hilbert’s thirteenth problem ⓘ linked to: Hilbert problems Hilbert’s twelfth problem ⓘ Hilbert’s twentieth problem ⓘ linked to: Hilbert problems Hilbert’s twenty-first problem ⓘ linked to: Hilbert problems 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	Diophantine equations decision problem ⓘ linked to: Hilbert’s tenth problem Riemann hypothesis ⓘ consistency of arithmetic ⓘ continuum hypothesis ⓘ
numberOfItems	23 ⓘ
presentedAt	International Congress of Mathematicians ⓘ
presentedBy	David Hilbert ⓘ
presentedInCity	Paris ⓘ
presentedInYear	1900 ⓘ
publication	“Mathematical Problems” ⓘ linked to: Hilbert problems
publishedIn	Göttinger Nachrichten ⓘ
publishedInYear	1900 ⓘ
republishedIn	Bulletin of the American Mathematical Society ⓘ
status	partially solved ⓘ

How these facts were elicited

Referenced by (38)

Full triples — surface form annotated when it differs from this entity's canonical label.

David Hilbert → notableWork → Hilbert problems ⓘ

Millennium Prize Problem → inspiredBy → Hilbert problems ⓘ

Hilbert problems → hasPart → Hilbert’s first problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s third problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s fourth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s fifth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s sixth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s seventh problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s ninth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s eleventh problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s thirteenth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s fifteenth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s sixteenth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s eighteenth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s nineteenth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s twentieth problem ⓘ

linked to: Hilbert problems

Hilbert problems → hasPart → Hilbert’s twenty-first problem ⓘ

linked to: Hilbert problems

Hilbert problems → publication → “Mathematical Problems” ⓘ

linked to: Hilbert problems

Hilbert’s program → notableWork → Hilbert’s 1900 Paris lecture ⓘ

linked to: Hilbert problems

Riemann hypothesis → listedIn → Hilbert's problems ⓘ

linked to: Hilbert problems

continuum hypothesis → discussedIn → Hilbert's problems ⓘ

linked to: Hilbert problems

Hilbert’s second problem → partOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Hilbert’s second problem → originalPublication → “Mathematische Probleme” ⓘ

linked to: Hilbert problems

Hilbert’s seventeenth problem → partOf → Hilbert’s problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-second problem → partOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-second problem → sequence → Hilbert’s problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-second problem → originalPublication → Mathematische Probleme lecture ⓘ

linked to: Hilbert problems

Hilbert’s twenty-third problem → partOf → Hilbert’s problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-third problem → partOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-third problem → isLastProblemOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Hilbert’s twenty-third problem → appearsInWork → Mathematical Problems (Hilbert’s 1900 address) ⓘ

linked to: Hilbert problems

Hilbert’s tenth problem → partOf → Hilbert’s problems ⓘ

linked to: Hilbert problems

Hilbert’s fourteenth problem → partOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Göttinger Nachrichten → hasNotablePublication → David Hilbert’s list of problems ⓘ

linked to: Hilbert problems

Hilbert’s twelfth problem → partOf → Hilbert’s list of 23 problems ⓘ

linked to: Hilbert problems

Dehn invariant → relatedTo → Hilbert's problems ⓘ

linked to: Hilbert problems

Smale’s 18 problems → inspiredBy → Hilbert’s problems ⓘ

linked to: Hilbert problems

Smale’s 18 problems → relatedTo → Hilbert’s problems ⓘ

linked to: Hilbert problems

All labels observed (25)

How this entity was disambiguated Show

Statements (51)

How these facts were elicited Show

Referenced by (38)

How this entity was disambiguated

How these facts were elicited