Hilbert’s sixteenth problem

E761264

Hilbert problem

Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.

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All labels observed (5)

Label	Occurrences
Hilbert's sixteenth problem	1
Hilbert’s sixteenth problem canonical	1
Hilbert’s sixteenth problem (first part)	1
Hilbert’s sixteenth problem (second part)	1
Hilbert’s sixteenth problem on limit cycles	1

How this entity was disambiguated

This entity first appeared as the object of triple T8850260 — 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 sixteenth problem
Context triple: [Hilbert’s seventeenth problem, relatedTo, Hilbert’s sixteenth 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’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.
C. Smale’s 18 problems
Smale’s 18 problems are a celebrated list of major open questions in mathematics proposed by Stephen Smale in 1998 as a successor in spirit to Hilbert’s famous problems.
D. Hilbert’s twenty-third 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.
E. Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
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 sixteenth problem
Target entity description: Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.

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’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.
C. Smale’s 18 problems
Smale’s 18 problems are a celebrated list of major open questions in mathematics proposed by Stephen Smale in 1998 as a successor in spirit to Hilbert’s famous problems.
D. Hilbert’s twenty-third 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.
E. Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
F. None of above. chosen

Statements (44)

Predicate	Object
instanceOf	Hilbert problem ⓘ
appearsIn	“Mathematische Probleme” (Hilbert’s 1900 address) ⓘ linked to: Hilbert problems
asks	whether there is a uniform upper bound on the number of limit cycles of a polynomial vector field of given degree ⓘ which configurations of ovals can occur for real plane algebraic curves of degree n ⓘ
concerns	arrangement of algebraic curves ⓘ arrangement of algebraic surfaces ⓘ limit cycles of polynomial vector fields on the plane ⓘ number of ovals of real algebraic curves ⓘ position of ovals of real algebraic curves ⓘ possible arrangements of components of real algebraic curves of given degree ⓘ qualitative theory of real polynomial differential equations ⓘ relative position of ovals of real plane algebraic curves ⓘ topology of algebraic curves ⓘ topology of algebraic surfaces ⓘ
degreeOfCurvesMentioned	plane algebraic curves of degree n ⓘ
field	algebraic geometry ⓘ differential equations ⓘ topology ⓘ
hasHilbertProblemNumber	XVI ⓘ
hasKeyword	limit cycles ⓘ ovals ⓘ polynomial vector fields ⓘ qualitative behavior of solutions ⓘ real algebraic curves ⓘ
hasPart	Hilbert’s sixteenth problem (first part) ⓘ linked to: Hilbert’s sixteenth problem Hilbert’s sixteenth problem (second part) ⓘ linked to: Hilbert’s sixteenth problem
influenced	qualitative theory of dynamical systems ⓘ real algebraic geometry ⓘ linked to: Tarski–Seidenberg theorem topology of real plane curves ⓘ
languageOfOriginalStatement	German ⓘ
namedAfter	David Hilbert ⓘ
numberInList	16 ⓘ
partOf	Hilbert’s list of 23 problems ⓘ linked to: Hilbert problems
posedBy	David Hilbert ⓘ
presentedAt	International Congress of Mathematicians in Paris ⓘ linked to: International Congress of Mathematicians
relatedTo	Gudkov’s conjecture ⓘ Harnack’s inequality ⓘ Hilbert’s problems ⓘ linked to: Hilbert problems Hilbert’s sixteenth problem on limit cycles ⓘ linked to: Hilbert’s sixteenth problem Rokhlin’s complex orientation formula ⓘ linked to: Rokhlin invariant
statedIn	1900 ⓘ
status	open ⓘ partially solved ⓘ unsolved in full generality ⓘ

How these facts were elicited

Referenced by (5)

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

Hilbert’s seventeenth problem → relatedTo → Hilbert’s sixteenth problem ⓘ

Bendixson–Dulac criterion → relatedTo → Hilbert's sixteenth problem ⓘ

linked to: Hilbert’s sixteenth problem

Hilbert’s sixteenth problem → hasPart → Hilbert’s sixteenth problem (first part) ⓘ

linked to: Hilbert’s sixteenth problem

Hilbert’s sixteenth problem → hasPart → Hilbert’s sixteenth problem (second part) ⓘ

linked to: Hilbert’s sixteenth problem

Hilbert’s sixteenth problem (second part) → relatedTo → Hilbert’s sixteenth problem on limit cycles ⓘ

subject linked to: Hilbert’s sixteenth problem

linked to: Hilbert’s sixteenth problem

All labels observed (5)

How this entity was disambiguated Show

Statements (44)

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Referenced by (5)

How this entity was disambiguated

How these facts were elicited