# Collatz conjecture

- kind: problem
- status: open
- year: 1937
- authors: Lothar Collatz

**Statement.** Halving even numbers and sending odd n to 3n + 1 always reaches 1.

A child can run it and nobody can prove it. Terence Tao showed in 2019 that almost all orbits reach almost bounded values, the strongest result so far. Conway showed that natural generalizations are undecidable, which hints that the specific numbers 3 and 1 matter. A counterexample would be a number a computer can check, which makes this one of the few famous problems where a finite search could still end it.

Posed 1937, Lothar Collatz.

## What would settle it

Lean statement in formal-conjectures

## Sources

- [Wikipedia: Collatz conjecture](https://en.wikipedia.org/wiki/Collatz_conjecture)

[Number theory](/wiki/Space:number-theory.md) · [Mathematics](/wiki/Continent:mathematics.md)

## Relations to this page

- related to [busy-beaver-6](/wiki/Problem:busy-beaver-6.md) — The original curation links this problem to Collatz conjecture; the argument for the link has not been written yet.

---
Revision 9, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:collatz-conjecture?action=history. Edit: POST /api/wiki/page/Problem:collatz-conjecture {source, summary, base_rev: 9}.