Hilbert’s sixteenth problem
E761264
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.
All labels observed (5)
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]
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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.
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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.
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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.
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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.
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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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hilbert’s sixteenth problem Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Hilbert’s sixteenth problem
linked to: Hilbert’s sixteenth problem
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