Anonymous at Mon, 27 May 2024 16:20:50 UTC No. 16196055

>>16195345
>The most fascinating math problem
explain, please.

Anonymous at Mon, 27 May 2024 22:55:45 UTC No. 16196719

>>16196055
They're probably referring to the Collatz Conjecture, which is boring because it's not useful.

Anonymous at Mon, 27 May 2024 23:14:35 UTC No. 16196746

>>16196055
The fact that it seems to be impossibly difficult to solve even for best mathematicians makes it fascinating. There could be a number out there that when plugged into the formula grows towards infinity and never gets down to zero. But most likely nobody will ever know if such a number exists no matter how hard they tried to figure it out.

Anonymous at Mon, 27 May 2024 23:23:52 UTC No. 16196755

>>16196746
I mean one, not zero.

Anonymous at Mon, 27 May 2024 23:42:32 UTC No. 16196769

at this point, trying to solve the collatz conjecture would be functionally useless. the amount of computational power needed to make progress on this problem just wouldn't be worth it. but oh well, anything for the citation count to go up, right?

Anonymous at Mon, 27 May 2024 23:52:19 UTC No. 16196783

>>16195345
To solve this problem you need to perform the algorithm on all numbers at the same time, which is impossible. Because completing an infinite process is impossible, and even talking about completing an infinite process is gibberish. This problem humbles mathniggers because you can’t use any niggerlicious tricks to “solve” it. Like claiming 1 + 2 + 3… = -1/12.

Anonymous at Tue, 28 May 2024 00:08:56 UTC No. 16196815

>>16196783
>>16195345

define "niggerlicious tricks"

are you referring to zeta function regularization? if so, i would argue that 1 + 2 + 3 + 4 + ⋯ = −1/12 is perfectly valid, as it uses previous math research to prove this series true


however, this problem is stupid as a whole. it's computational brute-force brainrot at the end of it. many computeniggers have tried and tried again to find a solution to this conjecture as our technological capabilities increased, and time and time again, they have failed.

the only use for this problem in this day and age is to be objectified as the "impossible problem" for the nigger-loving edutainment creators to cover, so that the 11yo retards watching said shitload of content can consume this "information" and act like they are experts in the field.

really, it is a problem that should be put to rest

Anonymous at Tue, 28 May 2024 00:25:01 UTC No. 16196836

>>16195345
A few months ago I tried representing numbers as sums of powers of 2, but I didn’t really get anywhere. The problem still becomes increasingly complex and you can’t get a hold of it, but I only looked at it for a day or two

Anonymous at Tue, 28 May 2024 07:22:19 UTC No. 16197292

>>16196836
But every integer can trivially be expressed as a sum of powers of 2. Or were you being sarcastic?

Anonymous at Tue, 28 May 2024 13:27:12 UTC No. 16197686

>>16195345
>>16196746
if it got solved, whats the application for it?

This problem is just useless mental masturbation

Anonymous at Tue, 28 May 2024 21:24:23 UTC No. 16198224

>>16197686
If this was solved, the technique employed in its solution might be useful, just not the thing itself.

Anonymous at Tue, 28 May 2024 21:36:18 UTC No. 16198241

The Collatz conjecture is false. There exists a number sufficiently large for which it is false, it's just too large for us to ever find it. Same as the Riemann hypothesis and the Goldbach conjecture.
There's a counterexample for each of these, just too big for us to ever find.

Anonymous at Tue, 28 May 2024 22:44:20 UTC No. 16198330

>>16196836
> Anon fails to reinvent base 2
LMAO, let me guess: you got all the COVID boosters.

Anonymous at Tue, 28 May 2024 22:47:23 UTC No. 16198335

>>16195345
> fascinating math problem
Meh, most probably is just some kind of halting problem.

Anonymous at Tue, 28 May 2024 23:04:39 UTC No. 16198356

>>16197686
>t. woke leftist pseud who doesn't understand how hard sciences like math and physics work

Pretty much every abstract, seemingly irrelevant result in mathematics has had significant applications across physics, computer science, mathematical biology, economics, complex systems, etc. Even if a mathematical result is seemingly disconnected from physical applications, it will pretty much always have implications for other mathematical theories, and then for working science as a result. Even very abstract resulting in measure theory and set theory ultimately have applications, since a lot of progress has been made, e.g. in probability theory and quantum mechanics, by using the methods of measure theory.

Regarding number theory, and the Collatz conjecture, in particular, if it were solved it would likely revolutionize modern number theory, which would have immediate consequence for fields like cryptography. The same could be said for a problem like the Riemann Hypothesis. Any of these major problems, if solved, would revolutionize their respective subfields of math in ways that we cant really predict.

I know normies are obsessed with muh applications and muh "scientific progress", and the whole Trust the Science™ worldview that goes along with it, but there's actually a lot more to science than improving economic efficiency or developing new products for conooomeristic bugmen. Science is about about understanding the nature of reality and our place in it. I realize it difficult for normie bugmen to appreciate those sorts of concerns, but most elite scientists are motivated by a deep seated curiosity about the universe, rather than a desire to discover new preservatives to improve the shelf-life of goyslop or new algorithms to help improve the computational complexity of the algorithms on your TurboTax software. That might be all that normies and urbanite bugmen care about, but science actually has much deeper philosophical and metaphysical significance.

Anonymous at Tue, 28 May 2024 23:29:07 UTC No. 16198385

>>16195345
The Collatz conjecture seems difficult because it exhibits what's called scale invariance.

A function X(t) is scale invariant if

[math]X(\lambda t) = M_{\lambda}X(t)[/math]

Where the M is a random variable which is independent of your choice of t.

Anonymous at Wed, 29 May 2024 04:22:21 UTC No. 16198649

>>16195345
its missing an equal sign

Anonymous at Wed, 29 May 2024 07:46:34 UTC No. 16198824

>>16195345
How is your first Number Theory course?

Anonymous at Wed, 29 May 2024 08:34:40 UTC No. 16198876

proof by induction of collatz conjecture

1. step: trivial for millons of numbers

2. induction
proven to be true to 1...n-1
if n is even, then next step is n/2 <= n-1 and is proven
if n is odd, then
n is 2k+1
next step is 3(2k+1)+1=6k+4
next step is (6k+4)/2=3k+2
if k is even, k=2p
next step is 3p+1
but p=(n-1)/4
thus 3p+1 is less than n-1


and is proven
therefore only remaining check
is
k is odd, k=2s+1
3(2s+1)+2+1=6s+6
next step is 3s+3
but s=((n-1)/2-1)/2
thus s=(n/2-3/2)/2
thus s=n/4-3/4

thus 3s+3 is less than n-1

all cases leads to number less than n-1. but by induction, they were already proven
qed

Anonymous at Wed, 29 May 2024 20:12:37 UTC No. 16199551

>>16196783
Wildberger is proud of you. Keep sharing the truth!

Anonymous at Wed, 29 May 2024 20:17:20 UTC No. 16199564

>>16198241
How do you know this? Can you give an arguemnt of the existence of such numbers?

Anonymous at Wed, 29 May 2024 21:14:54 UTC No. 16199681

>>16198876
>k is odd, k=2s+1
>3(2s+1)+2+1=6s+6
No.
n=2k+1=2(2s+1)+1=4s+3
The next step therefore is 3(4s+3)+1=12s+10
next step is 6s+5

6s+5=6(n/4-3/4)+5=3n/2+1/2 > n

27=2(2*6+1)+1,
82=12*6+10,
41=6*6+5=3*27/2+1/2 > 27,
124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, ...

Anonymous at Wed, 29 May 2024 21:25:52 UTC No. 16199705

>>16196746
>solve
Solve what? That's not a propostion to falsify, there is nothing to solve.
it just says "3 of something plus 1", da fuck is that?

Anonymous at Wed, 29 May 2024 22:01:09 UTC No. 16199774

>>16195345
>>16196746
>any odd number multiplied by an odd number yields an odd number
>any odd number + 1 yields an even number
>thus, the game works in cycles
>200% increase on an odd
>average of 75% decrease on an even
Probability tells me that if the expected outcome after each cycle is less than 1 then all infinite games should converge to 1.
I don't know. I'm still in Calc1, but I don't see how it could ever increase infinitely.

I did come up with this graph estimating the number of cycles (odd then even-chain is counted as 1 cycle) to return to 1.
Interestingly enough for every order of magnitude increase it takes about 8 additional cycles to return to 1.
So that's neat. I guess.

Anonymous at Wed, 29 May 2024 23:28:53 UTC No. 16199901

>>16199774
>Probability tells me that if the expected outcome after each cycle is less than 1 then all infinite games should converge to 1.
Probabilistic arguments do suggest that the conjecture is true, but they don't constitute a proof. There could be one chain that just happens to keep climbing.

If the Collatz conjecture is false (and personally I don't think it is) it will probably be because some other loop besides 4-2-1 exists. The number of steps in this loop would be an enormous number though (at least 12 digits long).

Anonymous at Thu, 30 May 2024 01:48:08 UTC No. 16200093

3x + 1 = 4x

Anonymous at Thu, 30 May 2024 16:52:16 UTC No. 16201033

>>16200093
did i actually kill the thread with this?