H10
E838585
H10 is the shorthand name for Hilbert’s tenth problem, a famous decision problem in number theory concerning the solvability of Diophantine equations.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Hilbert's tenth problem | 0 |
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
Hilbert's tenth problem
ⓘ
mathematical problem ⓘ |
| alsoKnownAs | Hilbert's tenth problem NERFINISHED ⓘ |
| answerType | negative ⓘ |
| asksAbout |
existence of an algorithm for Diophantine solvability
ⓘ
solvability of Diophantine equations ⓘ |
| classification | undecidable problem ⓘ |
| concerns |
Diophantine equations
ⓘ
algorithmic decidability ⓘ recursively enumerable sets ⓘ undecidability ⓘ |
| field |
mathematical logic
ⓘ
number theory ⓘ |
| hasComplexityProperty | recursively unsolvable ⓘ |
| historicalContext | turn of the 20th century foundational questions in mathematics ⓘ |
| implies | undecidability of Diophantine equation solvability ⓘ |
| influenceOn |
computability in number theory
ⓘ
logic and foundations of mathematics ⓘ |
| involves |
integer solutions
ⓘ
polynomial equations with integer coefficients ⓘ |
| keyResult | every recursively enumerable set is Diophantine ⓘ |
| language | originally formulated in German ⓘ |
| notation | H10 ⓘ |
| openVariant |
Hilbert's tenth problem over number fields
NERFINISHED
ⓘ
Hilbert's tenth problem over the rationals NERFINISHED ⓘ |
| originalQuestion | To devise a process according to which it can be determined in a finite number of operations whether a given Diophantine equation is solvable in integers GENERATED ⓘ |
| partOf | Hilbert's problems NERFINISHED ⓘ |
| posedBy | David Hilbert NERFINISHED ⓘ |
| positionInSeries | 10 ⓘ |
| presentedAt | International Congress of Mathematicians 1900 NERFINISHED ⓘ |
| relatedTo |
Church–Turing thesis
NERFINISHED
ⓘ
Davis–Putnam–Robinson–Matiyasevich theorem NERFINISHED ⓘ Hilbert's problems NERFINISHED ⓘ Turing machines NERFINISHED ⓘ computability theory ⓘ |
| solutionCollectiveName | MRDP theorem NERFINISHED ⓘ |
| solutionProperty | no algorithm exists that decides solvability of all Diophantine equations in integers ⓘ |
| solutionYear | 1970 ⓘ |
| solvedBy |
Hilary Putnam
NERFINISHED
ⓘ
Julia Robinson NERFINISHED ⓘ Martin Davis NERFINISHED ⓘ Yuri Matiyasevich NERFINISHED ⓘ |
| status | unsolvable as stated ⓘ |
| yearPosed | 1900 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.