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	Mathematical Problems (Hilbert’s 1900 address) ⓘ linked to: Hilbert problems
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 problem 23 ⓘ linked to: Hilbert’s twenty-third problem Problem 23 of Hilbert ⓘ linked to: Hilbert’s twenty-third problem
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’s list of 23 problems ⓘ linked to: Hilbert problems
numberInHilbertList	23 ⓘ
partOf	Hilbert’s list of 23 problems ⓘ linked to: Hilbert problems Hilbert’s problems ⓘ linked to: Hilbert problems
presentedAt	International Congress of Mathematicians 1900 ⓘ linked to: International Congress of Mathematicians
presentedInCity	Paris ⓘ
presentedInYear	1900 ⓘ
relatedTo	Euler–Lagrange equations ⓘ linked to: Euler–Lagrange equation 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 → Problem 23 of Hilbert ⓘ

linked to: Hilbert’s twenty-third problem

Hilbert’s twenty-third problem → hasAlternativeName → Hilbert problem 23 ⓘ