Hilbert’s twenty-third problem

E221058

Hilbert problem mathematical 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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All labels observed (3)

Label	Occurrences
Hilbert’s twenty-third problem canonical	2
Hilbert problem 23	1
Problem 23 of Hilbert	1

How this entity was disambiguated

This entity first appeared as the object of triple T1859197 — 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 twenty-third problem
Context triple: [Hilbert problems, hasPart, Hilbert’s twenty-third problem]

A. 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.
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 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.
D. Hilbert’s seventeenth problem
Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
E. Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
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 twenty-third problem
Target entity description: 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.

A. 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.
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 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.
D. Hilbert’s seventeenth problem
Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
E. Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
F. None of above. chosen

Statements (42)

Predicate	Object
instanceOf	Hilbert problem ⓘ mathematical problem ⓘ
appearsInWork	Hilbert problems ⓘ surface form: Mathematical Problems (Hilbert’s 1900 address)
concerns	applications of variational methods to geometry ⓘ applications of variational methods to mechanics ⓘ applications of variational methods to physics ⓘ extension of variational methods ⓘ general theory of variational problems ⓘ methods of the calculus of variations ⓘ
field	calculus of variations ⓘ mathematical analysis ⓘ
focusesOn	calculus of variations ⓘ further development of the calculus of variations ⓘ systematic application of the calculus of variations ⓘ
formulatedInLanguage	German ⓘ
goal	to apply variational methods broadly in mathematics and physics ⓘ to extend the range of variational methods ⓘ to systematize the calculus of variations ⓘ
hasAlternativeName	Hilbert’s twenty-third problem ⓘ surface form: Hilbert problem 23 Hilbert’s twenty-third problem ⓘ surface form: Problem 23 of Hilbert
historicalPeriod	early 20th century mathematics ⓘ
influenced	20th-century research in the calculus of variations ⓘ applications of variational methods in partial differential equations ⓘ development of direct methods in the calculus of variations ⓘ modern functional analysis approaches to variational problems ⓘ
isLastProblemOf	Hilbert problems ⓘ surface form: Hilbert’s list of 23 problems
numberInHilbertList	23 ⓘ
partOf	Hilbert problems ⓘ surface form: Hilbert’s list of 23 problems Hilbert problems ⓘ surface form: Hilbert’s problems
presentedAt	International Congress of Mathematicians ⓘ surface form: International Congress of Mathematicians 1900
presentedInCity	Paris ⓘ
presentedInYear	1900 ⓘ
relatedTo	Euler–Lagrange equation ⓘ surface form: Euler–Lagrange equations direct methods in the calculus of variations ⓘ existence theorems in the calculus of variations ⓘ geodesics ⓘ minimal surfaces ⓘ variational inequalities ⓘ variational principles in physics ⓘ
statedBy	David Hilbert ⓘ
status	open in full generality ⓘ partially solved ⓘ

How these facts were elicited

Referenced by (4)

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

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

Hilbert’s twenty-second problem → relatedTo → Hilbert’s twenty-third problem ⓘ

Hilbert’s twenty-third problem → hasAlternativeName → Hilbert’s twenty-third problem ⓘ

this entity surface form: Problem 23 of Hilbert

Hilbert’s twenty-third problem → hasAlternativeName → Hilbert’s twenty-third problem ⓘ

this entity surface form: Hilbert problem 23

All labels observed (3)

How this entity was disambiguated Show

Statements (42)

How these facts were elicited Show

Referenced by (4)

How this entity was disambiguated

How these facts were elicited