The 3x+1 Problem [video]

> Why does this need to be solved?

Obviously it "doesn't". Equally obviously this is mathematics, and it's worth doing if it's interesting.

But a somewhat more serious answer is this: the fact that we don't know the answer to this relatively simple question implies strongly that we don't know how numbers work. And if there are obvious gaps in our understanding of number theory that show themselves in trivial ways like this, there are probably more serious questions that we could answer if we had a better framework.

And that's sort of how hard problems in mathematics work. They aren't solved by amazing insight within their own realm, they turn out to be evidence that a new branch of theory needs to be developed first.

I don't get why this is being downvoted. For me math is pretty much a mystery, in a sense that it seems so arbitrary once you move from simple concepts that were initially grounded in a real world (like counting pebbles or splitting a circle). And it's not because I'm particularly badly educated, after all I believe we all can agree that Eugene Wigner [1] knew a bit of math and he still was wondering the same thing [2].

So soheil's question doesn't seem ignorant of meaningless to me. One could probably reframe it to become something similar to philosophy of Gödel's theorems, in lines of "there may (or may not) exist an infinite number of problems in number theories that are very simply formulated but are impossible/hard to prove or disprove". Consequence of that being that our abilities to have a definitive proof of statements are negligible and we're thus fundamentally trapped in an infinitely small space of outer mathematical universe.

I'm sorry if I'm saying something stupid here (or on the contrary, some well-known fact), like I said, I know nothing about mathematics so the two are equally possible to me.

[1] https://en.wikipedia.org/wiki/Eugene_Wigner [2] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...

About a week ago, I spent several hours after midnight in this ultimate nerd trap.

I started with powers of 2 that obviously reduce to the cycle and tried to apply these transitions inferring larger and larger sets of numbers whose binary representation satisfies specific regular expressions on 0 and 1s, but got lost pretty quickly.

My intuition is that, given that several generalizations of Collatz Conjecture are undecidable (equivalent to a halting problem), this process is in the territory of being not yet Turing-complete but already undecidable. But I am pretty sure many people way smarter than me tried this approach as well.

It's so someone can use it as a coding challenge in a technical interview, of course.

I think you misunderstood the answer with the problem. Coming with the answer to this problem is clearly difficult. But what makes 3x+1 as a problem so hard to come up with?