The Simplest Math Problem No One Can Solve - Collatz Conjecture
Вставка
- Опубліковано 29 лип 2021
- The Collatz Conjecture is the simplest math problem no one can solve - it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.
Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
References:
Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. - ve42.co/Lagarias2006
Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963-1999). The ultimate challenge: the 3x, 1, 267-341. - ve42.co/Lagarias2003
Tao, T (2020). The Notorious Collatz Conjecture - ve42.co/Tao2020
A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.
A. Kontorovich and S. Miller Benford's Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.
A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in "The Ultimate Challenge: The 3x+1 Problem," AMS 2010.
Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. - ve42.co/Tao2019
Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. - ve42.co/Conway1987
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1) [Computer software]. www.manim.community/
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Ivy Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang
3d Coral by Vasilis Triantafyllou and Niklas Rosenstein - ve42.co/3DCoral
Coral visualisation by Algoritmarte - ve42.co/Coral
![Самая простая нерешённая задача - гипотеза Коллатца [Veritasium]](/img/n.gif)
Everyone here: "...but just a maaaaybe I'll be the one to solve it."
"I could write a computer program to try and solve it". Because I'm sure nobody has tried that before 😪
You can actually instantly solve for half of all numbers. If all numbers up to an odd N works, (n+1)/2
I too thought i could solve it :D
What is there to solve? There is nothing to solve
@@rabiebabies7812 0 is not positive but it forms a loop. Its also not negative but no number ends up at zero so it is independent loop of itself
Teacher: Why did you not answer the questions on your test.
Me: Because the Math is not ripe enough for me to answer these questions
facts
Imma use this
@@lordsiomai be honest, no you won't
@@anyaburke6636 its 6
@Human Kind its already a 1000 We can make it 2000??
I love how he makes us think that he is the world's greatest mathematician by showing us his picture when saying that, but then shows the other half of the picture.
Well, that isn't even a person who solve the task. It's a computer programme which tries to explain something what isn't actually relevant.
lol
😂 lol
Certainly one of the finest mathematical videos on UA-cam.
Wait ... What?!
3Blue1Brwon be like ? 🫥
“Pick a number”
Me:Fou-
“Seven? Good choice”
Me:but I-
I said 4, I usually say 3 but I said 4 😂
He said seven because seven is more likely to be chosen lmao
I think Im the only one who chose 7
Only reason I'm not liking is bc tbe lile count is at 69
I didn't choose a number at all because no one can make me do math.
This math problem is actually like my trading portfolio, I can start with any number but end at $ 1
you too? :)
I tried to remove the eyelash on the display 🤭
There's that damn eyelash on my screen again!
@@luca6819 .same lol
@@luca6819 You're using youtube in lightmode? ;o
I was once talking to my math teacher and i asked her "why was Bhaskara so annoying" and she told me "he wasn't, he simplified a lot of things into a single calculus", then my friend said "so mathematicians have to simplify math because humans find it too hard when humans themselves created it" and my teacher said "yes, the point of math is simplifying something we made dificult in the first place".
That chat was all i thought about throughout this video.
Love this anecdote. Thank you.
For the video, it only exist because somebody said “no, you need to divide by 2 if it’s an even number” why? “I don’t have a reason why but it makes it complicated so do it”
As someone who is basically math illiterate, this makes almost no sense… makes me ask why we even made math, how it works, how do things even get figured out like the mathematical theorems and stuff… my confusion in difficult math related thingies makes me want to actually understand it more than my school education 😂
@@fletch4231 My thoughts exactly. Invent problems and then try to solve them. As if we didn't have enough problems!
@@fletch4231I'm not very good with math myself, but its origins are very simple. It started as a system of tallies for counting things (typically livestock). That's likely why most counting systems have changes at 5 and/or 10-those are the number of digits on a hand and both hands, the simplest way to tally (cf. Roman V & X, Indo-Arabic 9 to 10, crossing four tally marks, etc.). You probably tally with your fingers subconciously. It evolved into counting more complex things, and you may even have needed to create units of measuring, for parcelling land, weighing grain, and measuring beer. On the note of beer, written language may have developed in the Near East as a medium of accounting, as evidenced by some very early cuneiform tablets mathematically tracking grains and even beer. It slowly got more and more complex as people realized that math is better at describing the universe than it has any right being. Ultimately, it was serendipity that it happened to be our best way of describing the universe, which is absurdly complex.
TL;DR: Math started as a way of tallying and became more complex as its applications were discovered. Math is never purposefully obtuse-it's just our best medium of describing the universe. As the universe is absurdly complex, any system describing it must necessarily also be absurdly complex.
@@jasondelay2931I mean exploring things like that might lead to good discoveries
Here because I have the Collatz Conjecture in a Brilliant coding question.
I have found Brilliant the easiest to jump back into when I have time.
Great loop back Veritasium.
"coding"
im always bewildered when people say that.
coding is just another notation, nothing more.
@@armin3057 dork
@@armin3057 coding is a verb. It's an action. You code something which is to say you program it to behave in a certain way. What you're referring to is code itself, which is another form of notation. Regardless of the programming language, any mathematical function can be represented in code. What you're saying is out of place in response to this comment as it was not referring to the programming language, but the problem-solving aspect of writing code which in itself has nothing to do with notation.
Me: Where should we eat?
Girlfriend: Mathematics is not yet ripe enough for such question
Noo
I love your girlfriend.
Wait, no, it's not what you think it is!!!
LMAO🤣🤣🤣
😝
Lol
I absolutely love how mathematicians always find the most random things to debate over!
ridiculous too
I totally agree. What a waste of time
Not a waste of time. If you can find this solution, probably there is something you can achieve and get.
@@christloen4077 No way
In your mind
When negative numbers have 3 different loops, it makes me wonder if I change not only the seed sign but the operand. And turned out that if I apply 3n-1 for negatives (likewise changing the sign of the objectvie function on the concavity on linear programming), the graphical representation is a mirrored one of the positives. This way the whole set can apply the same rules for positives on 3n+1 including a single loop (-4, -2, -1)
If we try the polynomial 3x + 1 for negatives then we will be stuck in a loop of -7 or -1 everytime for any negative integer. Try this too!
Yes, there are 4 different loops if negatives are used.
The +1 is the key tbh. If you go into non whole numbers any .25 .5 or .75 will loop as an odd number infinitely. Because 1 doesn't make it positive and non of these numbers rise a above 1 ever. they keep a 5 at the end. So it only works on numbers because we have no define of 0 as even OR odd, or both, and dividing it is weird, but also because adding 1 is what DEFINES changing from odd to even.
@@eon2330 That’s what I was thinking if you start the equation from 0 3x0=0 which is still nothing until u add 1 now we’re positive but u can’t get 2 from 1 so now the loop starts u will never get 0 again
@@DaPoloJaywhy did you multiply and add to zero, it's not an odd number. Why do you not divide by 2? 0 divided by 2 is 0. . .and if a previous comment is correct that zero is neither even nor odd, you can't even start at all.
I’m glad I found this channel. Amazing quality content ❤️🙌
Mathematicians: Dont waste your time on this problem
20.7 million people: YES
Just cuz you said that I'm going to code a program that runs through all posible combinations on scratch
3 years year old me : what is maltiplikaton?
Ok
13 Million*
more
Me : "That's interesting puzzle, maybe I can solve it"
Me 22 minutes later : "oh."
Lol
Same I was like I'm gonnna guess a random number and try to do it..but 2⁶⁰ is really a big numbers they tried
@@theultimatetime8029 well, Derek (the narrator in the video) did say that 2 to the 60 is nothing compared to the other numbers tried in Polya's conjecture. The counterexample which disproved Polya's conjecture was 1.845 × 10^361, an immense number. Still, 2 to the 60 is BIG.
@@mjzudba5268 yes ofcourse
@@theultimatetime8029 try 70!,it's bigger or even 2^70!
You can accelerate the conversion by allowing division by 3 beside 2. I noticed that in my own limited search. Fascinating stuff.
I’ve always wondered why mathematicians only look at the patterns of the ’hailstone integers’ with this problem.
Maybe the pattern is found in the numbers that are skipped after doing the equation either with 1 number or after a million numbers
Whoever created all those graph animations is an absolute master in after effects expressions
Amen.
BR?
The thumbnail equals 1 cause 3x_ is 3x nothing so if I did that it would be 0 and if I plus the 1 it = 1
Math
BY "NO ONE" : He meant about Americans cause he himself is a american who dont knows anything about the outside world .
Pretty much every subject in school is really interesting if I’m not forced to learn it
History of the entire world, I guess convinces me.
Pretty much every subject in university is really interesting if I"m not forced to learn it
School in a form of forced education kills interests and produces stupider people. Coersion always makes things worse.
English, grammar
Sorry to hear that you did not have good teachers. I was fortunate to go to a great school that had many good teachers that were able to teach stuff like this in interesting and engaging way. It was the teachers that failed you not the environment where you are 'forced to learn'.
I wanna know who edit his videos.... The hard work ❤ ! We appreciate you bro !!
The change of 3x+1 from branches pattern to 3x+1 on the -y axis where the branch pattern changes to a bar chart is reminiscent of the probability scenario on your video about the stock market and demonstrated with your ballbearing prop, also on -y axis 4,3,1 is viewed eventually as a singular number commencing the bar graph pattern.
Mathway: “Am i a joke to you?”
Photomath: “Answer the question.”
Lol wassup homie
Lmaoo
Ugh those programs are virtual math teachers worst nightmare.
Fun fact: We are not mathematicians but we got interested by this.
People that know math are are mathematicians and also if thay do math they are mathematicians
ikr
I am
Hmmm
@@amirpakravan4389 shut up u ruin the vibe
“Pick a number, any number”
Uhh… 7?
“7? Good choice!”
It always and ultimately comes down to one or shall I say come up to one... the one and only... wherever you'd dig you'll find the one. Just need to open your heart following your eyes opening.
My calculus professor just introduced this conjecture to us last week, and ever since then I've been shamelessly addicted to just bringing up a random number generator for a starting point and wasting away the hours.
nerd
Atleast find better ways of procrastination
@Hence Forgot bricks bit to though to bite on man ill rather have alloyed steel
Ez Answer Is 9 I was Doing my math Homework Bruh
You have a great teacher if they motivated you to spend hours on this!
i wrote this comment to appreciate that those graphs were not just random. There were exact and to the scale.
Ikr
Ikr I wonder how many days or months it took to build all of those. Unless he wrote a program for it then maybe a day or two
@@Sintinium of course he wrote a program for it but I expect the developer probably spent at least 2 weeks on making it.
You dislike the stuff that gets uploaded by my fingers clicking upload? Are you just a h8er boi? I say see you l8er boi. Don't watch the stuff that gets uploaded by my fingers clicking upload anymore. Your dislikes are damaging my good good GOOD reputation. I am a superstar, dear kd
@@Sintinium I think he paid some small company to do that, a single person is unlikely to do that
This reminds me of the Philosophy Wikipedia page, where if you click on the first link in any Wikipedia entry you'll eventually get to Philosophy.
I looked up a train. I ended up at philosophy...
At this point it just looks like mathematicians are creating problems for the heck of it
Mathematicians: *_cries in proofs_*
Scientists: *_laughs in null hypotheses_*
@@Sinaloabricks hypotheses is the plural 🙄
@@Sinaloabricks Who says that we have only the one hypothesis?
Statistician: *does both in bipolarity*
Is not mathematics merely just a part of science anyway?
@@andrewcramer9200 Bipolar Person: "Finally, someone DOES understand me"!
Oh my god, this poor animator. That is a serious amount of dedication. Looks fantastic!
i was just gonna say that! Amazing work by the editor.
It seems like it is made by the same software that 3b1b uses.
Amajing
@@remenyo what is it??
i generated these graphs with python matplotlib, and then save the changing graphs for value of x, in an image sequence, then played them in premiere pro, voila..no animation needed for graphs and bar graphs 😁you can generate graphs with python
Consider the following.
1. there are an infinite number of 2^n numbers.
2. Consider an algorithm that selects a random number and tests it against whether it is a 2^n number. And if so applies the second half of the 3n+1 problem, in which case it will always collapse to the 4 -2-1 sequence.
3. What is the probability that the random number generator will never hit on one of the 2^n numbers.
4. I contend that the probability is zero.
It's not a random process. Consider that 3x-1 has identical statistics but multiple loops.
15:02 why negative numbers have three loops? Well, use positive numbers but change the function from 3x+1 to 3x-1 and you’ll get the same three loops.
-showing his own face
“One of the greatest mathematicians”
Dudes pops out of nowhere
“Mr. Tao”
Lol you had me at the first half not gonna lie
He had me too!
Brilliant!
He had me too
@samridh sood infinity is a number, any number, or all numbers should i say, and no, this is not the problem with this conjecture.
LOL
@samridh sood I think you´re on to something. The Fields Medal is in reach!
"What do you do for a living?"
Mathematician: "I am studying 3x+1."
havent watch the whole video but 3x+1 is impossible to solve bc it has infinite solutions??
Big maffs
no one
not even no one
me: 3x+1 equals 1 because 3x nothing is 0 amd + 1 is 1
When I saw that picture I was like it’s obviously 4x
I disagree
@@fanaticjay3825 bruh what
I've created two simple C++ programs that solve the multiplication of binomials such as (3x + 1), and am looking to do more.
Thank you for this unique & interesting concept. College Calculus major.
Isn't 3x+1 equal to
3x=-1 so
X=-1/3
? Idk what's the problem here btw 😂
@@adamrozek5782Lol this shows the whole video went over your head
What they are trying to solve is , They want to find a number which does not go in 4 2 1 loop
@@adamrozek5782Also it's not a 3x+1=0 😂
For those wondering, Alex K. is the narrator and voice behind the Quanta Magazine’s stunning video on the Riemann Hypothesis. This is like a collab of dreams!
I laughed when he said "one of the greatest mathematicians" and showed his his grinning into the camera
?
@@jAYROCCS1x 12:36
@@John-el5sv i see. thought he meant the guy frm the beginning.
"The world's greatest mathematician: myself"
Humble-bragging or else it's a better way to subvert expectations before revealing truth!
Terry Tao looks like someone who would appreciate the joke. 😅
The animation is everything here.
@DON'T stfu
@DON'T stfu bi-
You both just fell for his trap lmfao
@@WillCrewMusic i didnt even read the pfp the text is too small to see LMAO
@DON'T IM GONNA SAY THE N WORD
I would place my bet on if there IS an exception, it's a new loop not a number that shoots off to infinity (in which case that number in itself would have to be proven to shoot off to infinity and not get into some other insane loop at numbers too high to comprehend)
If we try the polynomial 3x + 1 for negatives then we will be stuck in a loop of -7 or -1 everytime for any negative integer. Try this too!
"This math is weird because of math. We can't do enough math to solve the math - there's just too much math!"
You could start by calling it MATHS
my dumbass brain is quaking
Pretty much lol
Weapons of Math Instruction?
@@holdontoyourwig Unless he's British, why should he?
Your "one of the world's greatest living mathematicians" joke totally killed me.
I was looking for this comment lol
Same here. I thought it was very clever.
* You're , btw I am better than you
@@cortnetisjustbetter not you’re but ok
I immediately knew this would be in the comments as well lol.
When I was pursuing the PhD and exploring research topics, I soon learned the most dangerous question, and the one no professor would sponsor was, "why?"
I feel that the answer lies in a different representation of the natural numbers that kind of represent 'power of 2'-ness, and showing that that can never increase under the operations described.
A big shoutout ot the graphics department for making this 100% more understandable!
a big shout down to yoy that you were'nt able to get such a simple equal...
I really hope this is satire 🤣🤣
@@josiahjray baited :D
@@gniewko123456 Hope so lol
Ah yes, 999 likes
I think a lot of us clicked on this video thinking:
*”oh it can’t be that hard”*
edit: Jesus I didn’t post this comment so ppl could just argue in the replies. It was supposed to be a joke
Its only hard to find if you only work with whole numbers, at least assuming thats how mixed numbers would work
Never mind a simple search says decimals cant be odd or even only integers, so yes it is that hard
@@mlpfanboy1701 i just solved this lol
@@Auromaxis what is it?
It’s easy, 0.
@@Auromaxis ?
Pascal triangle is an example of directed tree
It is used to show how much fluctuation carbon shows in a spectrum in chemistry
Or rather it predicts how many fluctuations carbon can shows in its bonding with hydrogen
The fact that this is the basis to making an organic shaped coral mesmerized me.
wait really? lmao
Wow 4th
Can we not use decimals?
it grows, makes an unpredictable, chaotic but somewhat beautiful image, and then inevitably falls back down to 1. like life and death cycle.
Found the Mathematical Phenomenon A very interesting channel - " Artificial Intelligence plus lottery"
Mad respect to the animators here. That must've been a lot of work.
And how much work on calculator.
Looks like 3blue1brown's framework manim at work
i agree, but there are other people that have animators do even more like haminations (he's a story time animator)
Someone's back is hurtt
we do or best.
Old video but heres recontextulistion thats pretty neat.
Dividing by 2 bit shifts binary numbers to the right.
The 4,2,1 pattern is
100
010
001
Hence, a hamming weight (number of non 0 bits in binary number ) of 1 will lead to the 4,2 ,1 pattern, no matter how large the number is. This is the same as the any number of 2^n observation but bear with me.
Multiplying by 3 in binary is the same as adding the binary value of itself but bit shifted left by 1(and hence you have this beautiful thing where the bit shift left is the odd process, the bit shift right is the even process).
E.g 101 (5) multiplied by 3 is
0101 +
1010
1111
An odd multiple 3 added to by 1 will always either leave the hamming number the same (if the least significant run of ones is size 1 : e.g 010001 + 1 = 010010
Or
Will reduce the hamming weight by n-1 where n is the size of rhe least significsnt run of 1s.
E.g 011(hamming weight of 2) + 1 /
= 100 (hamming weight of 1, hence 2-1 reduction has occured).
New runs of 1's in a 3 multiplication will be isolated with size 1 max.
Dividing an odd number by 2 will move the least significant run of ones to the least significant bit.
This will trigger a termination eventually (with delays only guranteeing a larger reduction in hamming weight)
( not proven) any individual 1s end up in a run of ones before the +1 termination step.
Hence, whilst hamming weight may increase temporarily, the overall pattern caused by the +1 termination and the limitation of of new 1 bits tending towards runs of ones, the overall hamming weight will reduce during iteration of the colletz conjecture processes.
Hence, the hamming weight tends to 1... guranteeing the 4,2,1 loop.
Its not quite a proof. But christ i feel like its close 😅
I like this one. My version was to argue that despite how large the number gets, application of the process results in the number going back to previously checked numbers and everything goes down to 4-2-1, so the conjecture must be true for any natural number
how long did this take
@@kinetik9197 how u mean
Wow …. This is actually really smart
My first thought is, since all numbers which are a power of 2, so 2^n, end up as 1, wouldn't it be easier to rephrase the problem and try to prove (or disprove) that by applying 3n+1 if odd and n/2 if even, all primes eventually give a result that is 2^n?
Looks like a good formula for generating Mountains in a virtual environment.
Ye
that's how they make roller coaster rides
Perlin noise: am I a joke to you?
not really, mountains aren't created by random processes.
If you use a decimal the number will go for ever as eg: 1.23 you would x3+1 =4.69 4.69x3+1 = 15.7 the decimal number will always be multiplied by 3 leavening you with a always odd decimal. If you start with an even decimal the decimal will keep getting divided by 2 until the decimal meets 1 then it’s will continue to rise. Adding a decimal is a way to bypass the number having to turn even every time you times the number by 3 and add 1. You are welcome for me solving it.
him: "pick a number, any number."
me: "eight.."
him: "seven? good choice!"
5... 😭😭
Me: 0.
Him: ok, if it's odd, × 3 + 1, if even, ÷ 2
Me: I think you just broke your calculator.
@@KratonWolf yeah. 0 really isn’t even or odd, so your just stuck
@@savathunthewitchqueen8299 and even if you do plug in zero to 3n+1, you go back to one.
Ikr... I picked 4...
1,2,4,8,16,32,64,128,256
So long as 3x+1 solves for a multiple of doubling, which will also go on to infinity, then so too must the equation
All these numbers are beautiful, but nothing, but this one is weird, but possibily valuable.
"Pick a number"
-"Uh seven?"
"Seven? Good choise!"
-"WHAT THE-"
BRO😂😂
Everyone chooses 7 cause 7 wins everytime lol
SAME
Lol same
I think it’s 3
The amount of graphic work that had to be done for this video is insane.
Exactly what i was thinking, i was like man props to whoever worked on this video
Try a Captain Disillusion video ... And he does those all himself
Really.. wow. Entropy maybe
@@peterh222 *disillusion
Listen ...don't look
Choosing random numbers and applying the rules until you get caught in the loop is a great way to kill time in class, I do it all the time
Schools need more material like this to inspire kids
Shows a picture of himself.
“One of the world’s greatest mathematicians…Terry Tao”
Then includes Terry. Lol
Yeah that was so good
😂, That's was funny , He's also good scientist tooo
12:33
@@dreamer097 thanks
Haha. I came to look for this. Haha.
Math problem no one can solve: Exists
Me: Finally I'm not the only one who is bad at math.
Not able to do a math problem, doesn't make you bad at math.
@@risav202 please explain. i dont agree
@@risav202 Nah.
I literally just saw you on Nas Daily...
@@risav202
I assume that you're not referring to math in general, just a specific math problem.
Those of us with dyscalculia find even basic math challenging, to say the least.
I have noticed that the numbers that have the most difficulty in going down to 1 are those that precede an even number with the characteristic of repeatedly decaying into an even number many times in a row (i.e. those that get to 1 more easily).
Example, the even number below decays several times repeatedly into an even number, easily arriving at the number 1 (as do all the numbers belonging to the group 2x2x2x2x2x2x2):
64 ---> 32, 16, 8, 4, 2, 1
Both the number 63 (the previous one) and 62 (the even number before 64) both have extreme difficulty going down to 1, so the numbers preceding 64 are in the opposite condition to that of 64 (which instead decays very easily to 1, without ever rising upwards).
So, if I choose the number 2048 ( = 2x2x2x2x2x2x2x2x2x2), I assume, based on the above, that 2047 and 2046 decay to 1 very slowly (having many ups and downs).
★ I love this math problem, it's like my life--difficult and unsolvable yet easy to live with if i purposely close my eyes. ❤️
Two things I learned from this video:
1. Mathematicians smile gratuitously in front of cameras.
2. Boring subjects become interesting when they're accompanied by animated graphs.
Two to the 68 power?? lots of time on their hands
@@DGill48 Or maybe lots of mathematicians and machines in the world's hands?
Wait til you find out .9 and 1 are equal
3. wHy DoNt PeOpLe GiVe Me A cHaNcE oN yOuTuBe????!!???!!
are u saying math is boring
I like the amount of people who didn't watch the video for even a moment, and are just here talking about how easy it is to solve 3x+1.
You take my words from my mind :))
I watched it up to 20:57, and had a couple of thoughts along the way.
First off, I hit the loop quickly because my chosen number is 4.
My thoughts were that this could be considered an exercise in looking at every possible angle of a situation, which both has practical applications, and seems likely to sharpen the analytical way of thinking -- or likely to be frustrating because there is no clear answer other than the loop, without finding an alternate path.
A good brain exercise, no question.
Second, while looking at the visual ways to consider this, since I'm an occasional artist, I thought mapping it would be a great way to create some drawings or paintings and either add to them, based on what I saw, or call them finished. Either way, it's great for stimulating the mind.
And if anyone chose to read all this, it's also fun to think about.
12
The video is 20 minutes. LoL. Of course they not going to watch it.
It's 4
You can say that y=2^x is a true solution, since that will always divide down to 1. Take all the whole answers to y=2^x, then try to find any numbers that lead into those using 3x+1. Then continue to extrapolate that out. Figure out if there are any excluded values. Working from the solution back I think would be faster.
I was tought more maths from this video than any of my classes
A couple of days ago he had a poll on what colour would evens and odds would be if they had a colour. The poll decided blue as even and red as odd. In this video, he has the evens as blues and the odds as reds. I love how much he cares about his community and the little details.
Good pickup!
Wow I did the poll a few seconds before scrolling to the video and this comment, I was wondering what the poll was for
Good catch. I like the social experiment that is in itself. That is such an arbitrary question that it should be close to 50/50. But it seems something is tilting us one way. Is it nature or society?
@@NandR I was also thinking the same. Maybe people who prefer the color blue also prefer even numbers, or people who prefer the color red also prefer odds? Just a thought
What about color blind people, there choices may be just a valid, pick any of the two, for maybe they are different shades of the same color??
Imagine being a Math Teacher and you gave an entire class an activity
1. Solve Collatz Conjecture 3x+1 (10 pts.)
The issue isn't solving it but proving it. :)
It's not a problem, it is a pattern. There is no solution. This is literally the formula for how all life grows, 124875 this sequence repeats infinitely, with alternating "branches" of 36363636 also repeating infinitely.
I once had a professor set the proof of the Boltzmann equation on a midterm. That proof exists but for a nonmathematician/nonphysicist (I was studying materials science) it was a beast. The equation is s = k * ln (m). Looks simple doesn't it? That was twenty years ago and I'm still traumatized. Mad props to mathematicians.
Smart in class: *Gets 10pts*
He/She would be barred from further teaching due to academic cruelty beyond comprehension.
Hey all.
If ur seeing this 2024 I have a treat for ya all.
The sum of 4^n with limits k=0 to n, calculated via geometric series.... is equal to (4^(n+1) -1)/3
-1 and then /3 .
So any odd number in form of a sum of the powers of 4 is equal to a power of 4 when 3x+1...
Powers of 4 then immediatly reduce to the 4 2 1 pattern...
The pattern at the end of the conjecture is a side effect of the 2 actual proveable parts of collatz.
Any sum of the powers of 4 multiplied by 3 and adding 1 leads to a power of 4.
A power of 4 divided by 2 will only become odd when it reaches 1.
1 is the sum of the powers of 4... i.e 4^0...
The loop is caused by the coincidence of 1 being the only odd number that is both a power of 4 and a sum of powers of 4 at the same time.
That ending really gave me chills
The transition at 12.33 "World's greatest living mathematician ..." was so hilarious.
Well played sir.. well played.
12:33
Yeah It Got Me Laughing
@@karlmarx828 i love you 😩😩
My favourite capitalist
He said “ONE OF THE world’s greatest living Mathematician".
It seriously doesn't take effort to write 12:33
But seeing your pfp it makes sense since its shikamaru
Me: “tries to do it in negative”
“Gets in a loop anyways”
@UC-cuXojkaoATvG21be0s25w
0 x 3 + 1 = 1
And
1 x 3 + 1 = 4
then divide 4 by 2 it’s 2 then divide it again it’s 1
And yeah we’re stuck no matter how you try it
True
This is really dumb 3x+1=3 because u plus the 0 with the 1 = 3x1
I hate math and dont know anything about it but i still clicked on this vid
@@Mango-rl2yg huh?
@@Mango-rl2yg if you meant 3x+1 where x=0, the result would, indeed be zero. Anything times zero is zero, meaning 3•0=0
From there, you add the one, giving you 1 as a result. My apologies if I misunderstood what you were trying to say!
❤️❤️❤️
Judging from the comments, the Collatz Conjecture could probably have more distinct proofs than the pythagorean theorem! And all of them from engineers, programmers, computer scientists, and amateur physicists with no formal mathematics background! Wonderful!
Not so distinct though. At least 80% of the "proofs" are "Over a given number of steps, the odds of the sequence going down is higher than the odds of it going up". Most of the rest are "It has to hit a power of two eventually".
@@jmodified oh yeah, and let’s not forget the third kind: just look at the last digit, it works for 1,2,3,4, … 8,9. And since every number has those numbers as last digits, it must work for all of them too!
@@AndresFirte Yes, I forgot that one. I think those three cover at least 99%.
The video:
"This seems like a really easy problem which is why a lot of mathematicians are curious about it, since it's actually insanely hard"
Laymen watching this video:
"Pfft, this seems like a really easy problem"
Almost like that was why it was interesting in the first place
If any increasing function can be used to exclude numbers, every positive number can be excluded, meaning all loops must not include positive numbers.
"The simplest math problem no one can solve"
My math professor: oh, looks perfect for the exam!
🤗
congrats on 300 likes
It can be solved.
Edit: So apparently this is an algorithm, so in this case:
f(x)={1;2;3;4} or f(x)=[4;1] (those are random numbers, not a solution). This is the correct way to solve problem like this, which is what you learn in algebra classes
There is always a solution in math, except you need to write it differently than x=7. Also, if there isn't any possible solution (like delta of an angle being less than zero), then you simply write "no answer" and close the case
@@Phantom-el6oe ?
@@Phantom-el6oe He's not doing an exam, are u dumb?
@@Phantom-el6oe but u cant actually do that
Nice work Soviets. You got me.
Hitler be like :
@@HottestBrownMan I was watching this video without signing in, but signed in just to like your comment buddy.
The Cold War won't truly be won until the Collatz Conjecture is resolved.
@@akshatvikramsingh8293 thanks mate.
Ngl i hate your facebook page lol
i have watched this *37* times.
its too good.
*37*
These people have too much time on their hands...
And the power to them !
"Pick a number"
"- Seven?"
"Seven? Good choise!"
"- Looks Back Carefully"
*choice
@@LaniPlayzRoblox *choise
@@keenjoaquin847 *chuse
@@LaniPlayzRoblox choes
@@mrcrunch4635 *cheese
"use Benford's law for tax evasion"
Got it
next they'll invent another law for you to follow
Ffs even when you break the law you gotta follow other laws, huh? ):
@Soul Seeker appropriate name for someone who works at the IRS or on some other auditing team lmao
@@jackrobinson9403 I guess "only break one law at a time" spans between the laws of our society & the laws of mathematics lmao
don't try to divide by 0 while smoking weed kids
Most tax verification algorithms are having the same function in the root file patch 🤞
It’s a nonlinear dynamical system with a point attractor. It perhaps even describes the heat death of the universe. Conway’s game of life is a simple example.
0:26 Seven is the most common number to pick, it's also has an interesting sequence
I have never been someone who liked math during school, but for some reason I find it so completely interesting to learn about on my own time.
cause you don’t have an exam and your future on it while watching this video, but at school,
yes
@@ultraslanmc4619 That's a very good point! No stress to learn it 😂
Actually i liked it at school. But it annoys me at school
Same. Things are so much more interesting when you learn them on your own than when you learn them at school.
The yearn for understanding really seems to increase with age…
".....that not even the world's best mathematicians have been able to solve. "
Me : "Alright, tell what it is, maybe i can solve it. "
I think it's just 10
@@captaincool9636 42. The answer is 42.
@@MP-ut6eb no not at all
@@MP-ut6eb no, you don't know the answer if the best mathematicians don't know it. You're not that guy buddy
@@gbsantana9679 its meme my friend. Its a meme.
I think the reason why this works is if we start with 1 and then apply the inverses of both rules and only leaving the integers, eventually, we can get all positive integers one way or another
I would say that 3n+1 is trying to reach the number to the sequence of 2^n and the division of 2 is used to say "You are coming close to join my family ,but try with someone else".
what do you think about. maybe binary representations could make it easier to understand.
Derek: "Pick a number."
Me: "Four."
Derek: "…He's too dangerous to be left alive."
heheh Good one ;)
Four is my lucky number
Mista: ....
@@justajobro1266 I was waiting for that
He got me at 7 tho :/
"Worlds Greatest living Mathematician"
I see what you did there.
*there
@@chriswebster24 thanks.. Noted!
Ahaha! That sequence took me a second. Nice one! (12:33)
Could I get some clarification?
@Chinmaye Last name Well now it's obvious. Thanks
❤ A matemática é realmente encantadora 😮😮🎉 estou apaixonada!!
15:09 - if you count 3x-1 on the negative side you do get the same 'tree' (mirrored) as the one on the positive side...
Honestly maths should just grow up and solve its own problems
That's what AI is.
I laughed so hard!😂
Thank you
Yeah that was funny as hell
lol
Good one!
Everyone: We can't solve this
Mathematicians: It's the Soviets
Fair enough.
more like
Mathematicians: We can't solve this
The US Government: It's the Soviets
@@_ikako_ the world: Are the US joking?
😂
But it was the Soviets....every single problem is them
When it comes to the 3x+1 conjecture, what are we solving for? Sure we could try and prove it true or false but, what are we solving the conjecture for? What are we looking for in the equation?
So, here's my observations.
2 to the power of any natural number will fit the conjecture. In addition, if we undo the opperation, we take (2^n)-1 and divide by 3, any output that is an odd, whole number will also fit the conjecture.
My idea for solving it would be to see if there was a whole number that *didn't* fit the conjecture but that's just me.
"One of the world's greatest mathematicians... "
*Proceeds to show himself*
I laughed hard that.
Man has some humour
This is the comment I came looking for lol
What's the timestamp for this? I just finished watching but I must not have caught that lol
@@SlimShady-gs8pl 12:36
In theory, all times that the # will go down to the 4,2,1 loop is when the number is 2^x. Using that as a starting point, you could find a trend in how long it takes the number to hit 2^x. Smaller even # have an advantage because the numbers from 2^x are more concentrated there.
Another thing is that the +1 is the only thing that makes sure that you don’t get into a different loop. The blend of addition and multiplication creates an annoying “randomness”.
Without the +1 it will keep being an odd number
I love on how people immediately pointed their fingers to the Soviets for an unsolvable problem
I go to Confucius
@@toolaazy And Confucius says
@@YOUNOTSMART I am confusion, this is kansas, why this arkansoo, america eggsplain
@@anmoldeepsingh9281 😭😂🤣😭😂🤣
@@YOUNOTSMART no more numbers jumping on the graph
I 've been waiting to get struck by a lightening and receive the answers in my singed head. I will let yo u know. Great video!
4:13 Background song that starts here is “Penrose’s Patterns” by Jonny Hyman