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Hilbert’s tenth problem over the rationals

Undecidability over the integers does not automatically imply undecidability over the rationals.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

Undecidability over the integers does not automatically imply undecidability over the rationals. Enumerating rational solutions can confirm their existence but cannot generally confirm their absence.

This is a rational-solvability decision problem with variable dimension. It does not rule out decision algorithms for particular restricted polynomial classes.

Why it matters

If correct, resolves the rational version of a recognized undecidability problem, beyond the established integer case.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • This is a rational-solvability decision problem with variable dimension. It does not rule out decision algorithms for particular restricted polynomial classes.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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