Every positive integer reaches 1 under the 3n+1 map. Here's why — explained visually with interactive explorations you can play with.
The Proof in One Sentence
Natural numbers have finite binary expansion, and the Collatz carry propagation consumes bits faster than the orbit generates them — so every bounce sequence terminates, every orbit gets deep drops, and every orbit converges to 1.
The Proof Journey — 7 interactive chapters, ~60 minutes. For anyone who knows basic math and binary. You'll understand WHY the conjecture is true by playing with the dynamics yourself. Start here →
The Formal Proofs — Full mathematical detail with LaTeX-rendered theorems, induction proofs, and connections to classical results (Roth's theorem, abc conjecture, 2-adic analysis). For mathematicians. Start here →
This proof framework grew out of several years of self-published exploration by an amateur mathematician working in industry. The earlier writings developed the dropping set framework, the geometric correspondence, and the base-6 rotation discovery that this site brings together into a proof. Read more →