The Andrews-Curtis conjecture

formal-conjectures · wikipedia · ams-20

The conjecture says that every normally generating n-tuple in the free group
on n generators is Andrews-Curtis equivalent to the standard free basis.

**The Andrews-Curtis conjecture.**

Every normally generating n-tuple in the free group of rank n is
Andrews-Curtis equivalent to the standard tuple of free generators.

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/Andrews%E2%80%93Curtis_conjecture
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/math/0302080
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/AndrewsCurtis.lean
Local target: Corpus.WikipediaAndrewsCurtis.andrews_curtis_conjecture
Source SHA-256: ece885a268da08b336202f337a871a555fa5d25c1adeabd7fec39de74c98fec9
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