# Hilbert's tenth problem

- kind: problem
- status: refuted (evidence tier V3)
- year: 1900
- authors: David Hilbert

**Statement.** Find an algorithm that decides whether any Diophantine equation has an integer solution.

No such algorithm exists: every computably enumerable set is Diophantine, so a decision procedure would solve the halting problem. The version over the rationals is still open.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1900, David Hilbert. Closed 1970, Yuri Matiyasevich, completing Martin Davis, Hilary Putnam and Julia Robinson.

## Sources

- [Wikipedia: Hilbert's tenth problem](https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem)

[Algorithms](/wiki/Space:algorithms.md) · [Computation](/wiki/Continent:computation.md)

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