This is not the first time I see posts from this blog on this topic here, and I feel like I'm not qualified to read that, since what I've read in these posts is basically all I know about it anyway, and I don't know why should I even be interested in it — I mean, it's pretty useless, isn't it… But almost every time there's something deeply disconcerting in them.<p>> It’s even been proved that a Collatz counterexample must have certain striking properties, like an enormously long orbit. These proofs are in effect proofs that we will not be able to find a counterexample, even if there is one.<p>I don't know why, but it hits me hard. Maybe it's not the best example, since mathematically applicable numbers can be quite big too, but it still disturbs me similarly to how when I first realized that "there's a countable number of definable numbers". I'm still wondering if it's even fair to say that all that "other" stuff (which is the most of math, and as pointed out in this post — can include all sorts of interesting properties that nothing we can "reach" has) even exists. Math is basically made up by humans anyway, it's both a product and a property of how we think. So what it even means for Collatz conjecture to be wrong, if there's there's just one particular counterexample out there we could never find?