Hilbert’s twenty-second problem

E220091

Hilbert problem mathematical 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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All labels observed (2)

Label	Occurrences
Hilbert’s twenty-first problem	1
Hilbert’s twenty-second problem canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T1859196 — 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-second problem
Context triple: [Hilbert problems, hasPart, Hilbert’s twenty-second problem]

A. 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.
B. 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.
C. 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.
D. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
E. "Invariante Variationsprobleme"
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
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-second problem
Target entity description: 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.

A. 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.
B. 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.
C. 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.
D. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
E. "Invariante Variationsprobleme"
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
F. None of above. chosen

Statements (44)

Predicate	Object
instanceOf	Hilbert problem ⓘ mathematical problem ⓘ
asksFor	construction of suitable Riemann surfaces for analytic functions ⓘ representation of multivalued analytic functions as single-valued functions ⓘ
category	unsolved and partially solved problems in mathematics ⓘ
concerns	representation of multivalued analytic functions ⓘ uniformization of analytic relations ⓘ
field	Riemann surface theory ⓘ analytic geometry ⓘ complex analysis ⓘ geometric function theory ⓘ
goal	global description of analytic relations via Riemann surfaces ⓘ systematic uniformization of analytic functions ⓘ
hasOrdinalPosition	twenty-second ⓘ
hasSubjectHeading	Riemann surfaces ⓘ surface form: Riemann surfaces and analytic relations uniformization of analytic functions ⓘ
historicalContext	turn of the 20th century mathematics ⓘ
influencedField	geometric theory of functions ⓘ modern complex analysis ⓘ theory of Riemann surfaces ⓘ
languageOfOriginalFormulation	German ⓘ
motivation	clarifying the global behavior of analytic functions ⓘ unifying local analytic data into global structures ⓘ
namedAfter	David Hilbert ⓘ
numberInSequence	22 ⓘ
originalPublication	Hilbert problems ⓘ surface form: Mathematische Probleme lecture
originalPublicationVenue	Göttinger Nachrichten ⓘ
originalPublicationYear	1902 ⓘ
partOf	Hilbert problems ⓘ surface form: Hilbert’s list of 23 problems
presentedAt	International Congress of Mathematicians ⓘ surface form: International Congress of Mathematicians in Paris
relatedConcept	Riemann surface ⓘ analytic continuation ⓘ analytic relation ⓘ multivalued analytic function ⓘ single-valued analytic function ⓘ uniformization theorem ⓘ
relatedTo	Hilbert’s twenty-second problem self-linksurface differs ⓘ surface form: Hilbert’s twenty-first problem Hilbert’s twenty-third problem ⓘ
requiresTool	conformal mapping theory ⓘ theory of covering spaces ⓘ topology of Riemann surfaces ⓘ
sequence	Hilbert problems ⓘ surface form: Hilbert’s problems
statedBy	David Hilbert ⓘ
statedInYear	1900 ⓘ

How these facts were elicited

Referenced by (2)

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

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

Hilbert’s twenty-second problem → relatedTo → Hilbert’s twenty-second problem self-linksurface differs ⓘ

this entity surface form: Hilbert’s twenty-first problem

All labels observed (2)

How this entity was disambiguated Show

Statements (44)

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Referenced by (2)

How this entity was disambiguated

How these facts were elicited