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Number Theory
Open
Collatz Conjecture
Starting from any positive integer, repeatedly apply n → n/2 if even and n → 3n + 1 if odd. Does every trajectory eventually reach 1?
- Impact
- 72 /100
- Funded
- $6,100
- Donors
- 245
- Of goal
- 51%
Why this matters
Collatz is famously easy to state and stubbornly hard to prove. It is a proving ground for new ideas about iterative maps, reverse trees, and probabilistic heuristics on the integers.
What a solution unlocks
- New machinery for simple-looking arithmetic dynamics
- Transferable tools for other 3x+1-type maps
- Clearer limits of current proof techniques
Downstream impact
Even partial structural theorems have historically seeded ideas in ergodic theory and computer-assisted proof — a full resolution would be a landmark of elementary-looking mathematics.
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