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.

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 …

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

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 …

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 …

Nov 3, 2024 · Here is a curiosity about negative Collatz sequences that it would be interesting to investigate: Do the -5 loop numbers ever become more frequent than the -1 loop and -17 loop …

Oct 20, 2024 · As per Wikipedia, it's been stated that Wielandt was able to prove Perron-Frobenius Theorem using Collatz-Wielandt Formula: A common thread in many proofs is the Brouwer fixed …

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 …

Aug 5, 2019 · On November 3, 2023, my project verified the validity of the Collatz conjecture for all numbers less than $1.5 \times 2^ {70}$ ($= 1536 \times 2^ {60}$). This is the moment when the …