The Collatz conjecture is the simplest open problem in mathematics. You can explain it to all your non-mathematical friends, and even to small children who have just learned to divide by 2.

Jan 10, 2026 · Q&A for people studying math at any level and professionals in related fields

Aug 26, 2022 · Therefore the Collatz Conjecture is true. Every number will inevitably transform down to $1$. Sorry for the difficult to read LaTeX, kind of a new user, but feel free to criticize away about …

Mar 31, 2018 · For all those infinite sequences the Collatz-conjecture is immediately proven - the Collatz-transformation (in its Syracuse-formulation) goes in reverse direction of the arrows, for …

Sep 25, 2015 · which extends the collatz function to the complex plane. I think the point to remember is that the way the Collatz function is written definitely influences how it's studied. This allows for new …

Jan 24, 2022 · The Collatz conjecture has moreover a property that most conjectures like Goldbach or Riemann do not have. If there is a diverging trajectory , we might not be able to prove that within …

Nov 14, 2021 · I think it makes sense to consider every case of the generalized version of the Collatz-conjecture to be a Collatz-like problem. Note that this generalized version was proven to be …

Jun 28, 2021 · Collatz conjecture but with 3n − 1 3 n 1 instead of 3n + 1. 3 n + 1. Do any sequences go off to + ∞ + ∞ ?

Dec 27, 2024 · In the case of the Collatz Conjecture, which states that "If a term is even, the next term is one half of it. If a term is odd, the next term is $3$ times the previous term plus $1$. The conj...

6 I've been messing around with the Collatz sequences a bit, and have come across a few patterns - I was wondering if there are any known explanations for these patterns. The first is the plot of stopping …