The Simplest Math Problem No One Can Solve - Collatz Conjecture

What people said

Cites Mr Tsjolder from codidact · 2021-08 · Mathematics Stack Exchange · on “Why does this “proof” for the Collatz conjecture not work?”

After seeing a video [this video] on the Collatz conjecture [LINK] , I kind of played around with it a bit and found the following result (which can be shown by induction): $$\underbrace{f \circ \ldots \circ f}_{N \text{ times}}(2^N x - 1) = 6^{\left\lceil\frac{N}{2}\right\rceil} x - 2 + (N + 1) \mathbin{\mathrm{mod}} 2.$$ If the Collatz conjecture were true, then $\forall x \in \mathbb{N} : \lim_\limits{N \to \infty} \underbrace{f \circ \ldots \circ f}_{N \text{ times}}(x) = 1$ . However, the result above would imply that for any number of function applications, $N$ , there is an (infinite set of) input(s) that will be larger than the inputs and therefore can not be one. So, even if $N \to \inft

Cites Fuzzy_Bunnys · 2021-10 · Mathematics Stack Exchange · on “Veritasium on Collatz — Clarification about loops”

I have watched Veritasium [LINK] 's recent video [this video] on the Collatz conjecture. At 11m17s [this video] , he mentions that if you can show that for every seed value, there is at some point a number less than the seed value in the sequence generated by the Collatz function, then you've proven the conjecture. Doesn't this condition preclude a loop? If I have some loop, won't it at some point include a reduction in value? For example, if I have a loop that goes $12 \to 15 \to 64 \to 72 \to 12$ can't I just say, well $72$ is my seed value, since $12 < 72$ , then $72$ must reduce, and all the other values in the loop reduce as well? I understand its a popular video, and it's not a precise definitio

Cites Iffat Iqbal · 2025-02 · Mathematics Stack Exchange · on “Pattern in perfect squares? Has this been found before?”

I have a snow day here in Toronto and I wanted to kill some time by rewatching the very well-known Veritasium video on the Collatz conjecture [this video] . I found this strange pattern at around 15:45 where the perfect squares kind of form a ripple pattern while you increase the bounds and highlight where the perfect squares are. Upon further inspection, I also saw that these weren't just random pixels either, they were the actual squares. Why might this happen? Here is what it looks like, these sideways parabola-like structures expand and are followed by others similar structures from the right. [LINK] [LINK] My knowledge of math is capped off at the Linear Algebra I am learning right now in Gr