Mathematics Atlas

How Proof Is Made
Open Questions

Does the Collatz process really always reach one, from every possible starting number?

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Open Question

Every starting number ever tested by computer, into the astronomically large, reaches one, but no proof rules out either an unbounded starting number whose path never terminates or a hidden cycle other than the trivial one at 1-4-2; Paul Erdos himself is widely quoted as doubting mathematics currently has the tools to settle it.

What would resolve this A general proof covering every positive starting integer, or the discovery of a starting number that provably never reaches one (an unbounded trajectory or a second cycle).
OpenNumber theory / dynamical systemsWolfram MathWorld
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Wolfram MathWorld
Wolfram Research, Inc.View the Source
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