Particular values of the Riemann zeta function

formal-conjectures · wikipedia · ams-11 · ams-33

$\zeta(5)$ is irrational.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/RiemannZetaValues.lean
Local target: Corpus.WikipediaRiemannZetaValues.irrational_five
Source SHA-256: 15da78c9102e5c32c5a232ca8e6aef4cd41d2afc0ce1d4b2c36a546af00999c7
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record