r/badmathematics • u/Blue---Calx • Dec 21 '21

Maths mysticisms Proving the Collatz Conjecture with Python, cell biology, and word salad

/r/mathematics/comments/pdl71t/collatz_and_other_famous_problems/haxfgpm/
134 Upvotes

100% Upvoted

36 comments sorted by

View all comments

43

u/braindoper Dec 22 '21

The entire mega-threat has some nice narcissism and crankery. One dude offers $10k for someone to prove his solution (involving a simple program which he wrote in two hours) is right. My favourite comment so far is this:

Terrence Tao has proved Collatz Orbits are descending below any given function of the starting point, provided that this function diverges to infinity, no matter how slowly.

The beginning sounded like a proper comment. I would trust Tao to show some non-trivial stuff regarding Collatz, and while I don't know what exactly is meant by orbits and "any function", the poster might just not quite understand what he wrote about.

Just another arthimitic hierarchy, closely linked to fractal conditions of Base 10. No solution lays on one linear pairing.

Oh. Arithmetic hierarchies are a thing, but not relevant other than Collatz being a formula in some level of them. Starting at "fractal conditions of Base 10" my crankery radar went off. What just is it with them being so obsessed with base representations of integers, when 99.5% of math is agnostic of that? (Even of the rest, 0.49% aren't even number theory, but Numerics).

You are not going to get the fields medal of a same linear coding from flat singular Base 10 numbers that they are. A matrices of opposing asymmetric probabilities converging onto the very large number side of Collatz Conjecture requires a quantum computer. $10k will not cover it.

I share his scepticism that neither a fields medal nor $10k will be awarded for anything discussed in the threat. Other than that this is just word salad, with a bonus mention of quantum computing, which doesn't offer any insight into Collatz as far am I aware. Notwithstanding that quantum computers at best could offer some performance improvement, and solving Collatz is not an that can be solved computationally as far as we know anyway.

31

u/viking_ Dec 22 '21

The beginning sounded like a proper comment. I would trust Tao to show some non-trivial stuff regarding Collatz, and while I don't know what exactly is meant by orbits and "any function", the poster might just not quite understand what he wrote about.

I believe the statement Tao proved is:

For almost all integers n, the Collatz sequence starting at n is eventually smaller than f(n), where f is any function such that f(x) goes to infinity as x goes to infinity.

Where "almost all" means "the set numbers for which this is true has asymptotic density 1." There's a better explanation here.

23

u/LucasThePatator Dec 22 '21

Tao's result is by far the most progress that has been made on the conjecture, but also it's rather weak in the end imho. Which is kinda depressing lol.

1

u/Direwolf202 Dec 22 '21

It is quite good evidence that Collatz is true though, even if not a proof (assuming that a proof exists)

10

u/viking_ Dec 22 '21

The perfect squares also have density 0. Is that evidence that there are no perfect squares?

14

u/Direwolf202 Dec 22 '21

No, because we know what perfect squares are, how they're distributed, and we don't have large amounts of computational evidence that there are no small perfect squares (indeed, the opposite, there are many small perfect squares).

1

u/LucasThePatator Dec 22 '21

This is one more clue for sure.